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10/10/2009 JNTUK Examination Section – I B.Tech [RR,R05 and R07] Supplementary Examination Time Table

10/10/2009 JNTUK Examination Section – II B.Tech [R07] ,III B.Tech [R07] and IV B.Tech [R05] I Semester Regular and Supplementary Examination Time Table

think why this image is posted thr is something in this actually our blog is found some caste feelings in some areas so we ewnt asked some people about this we will post their reviews in their areas

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Endrum superstar Rajinikanth
(great stylish actor by his own never found)


the first 3d picture in india and made by indians(soundary rajinikanth)

Rajinikanth was the fourth child to his parents. His original name was Sivaji Rao Gaekwad. He lost his mother at the age of five. Rajinikanth was born on December 12 1949 in Karnataka. Rajinikanth's schooling was at the Acharya Patasala in Bangalore and then at the Vivekananda Balak Sangh which is a unit of the Ramakrishna Mission. His mother tongue is Marathi . Rajinikanth got married to Lata, an English literature
for more download his profile download

chiranjeevi

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Balakrishna


Nandamuri Balakrishna fondly called by his fans as NBK,Balayya needs no introduction. He entered the film Industry at the age of 14 through his home production Tatammakala, in which he had the opportuinty to work with the two legends of Tollywood, Late Sri NTR and Dr. Bhanumati Ramakrishna. For 10 successive years he acted off and on in movies mostly produced under his home production. 1984 is the year when his first movie as a solo hero was released and interestingly he acted in very less number of movies made under his home productions after that.
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(victory) Venkatesh:

Daggupati Venkatesh, Venky for his fans and Victory Venkatesh for the box office, needs no prologue. Venkatesh, brainy and brawny, graduated with MBA degree from Montery University, USA. Though lucky in terms of resources, Venkatesh made it to the top with his own style of acting.
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03/10/2009 JNTUK Examination Section – II and III B.Tech II Semester Supplementary Examination Time Table

03/10/2009 JNTUK Examination Section – II,III & IV B.Tech I Semester II Mid(Quiz) Examination Time Table

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MICRO PROCESSORS

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E-CAD LAB MANUAL

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LAB MANUAL
this is for our jntu juniors(1st B.tech)

check edc lab manual by jntu with all the circuit diagrams and procedure by jntu dont follow the old records they may right or wrong do u give guantee for that
with all the viva questions

to download manual pls click here download

Download Kaspersky
Internet Security 2010
Anti-Virus 2010

for keys and regular updates visit
click here to visit

Virender Sehwag

Virender Sehwag (Hindi: वीरेंद्र सेहवाग) (born 20 October 1978, in Delhi, India), affectionately known as Viru, is one of the leading batsmen in the Indian cricket team. Sehwag is an aggressive right-handed opening batsman and an occasional right-arm off-spin bowler. He played his first One Day International in 1999 and joined the Indian Test cricket team in 2001. In April 2009, Sehwag became the only Indian to be honored as the Wisden Leading Cricketer in the World for his performance in 2008.for more download
Yuvraj singh

Yuvraj Singh is an Indian Cricket player and has served the Indian One Day International (ODI) Cricket team as its Vice-Captain since the year 2007 to the year 2008. Yuvraj is famous for having hit 6 sixes in a over bowled by Stuart Broad during a Twenty-20 match against England in the 2007 World Twenty-20 Cricket tournament.
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valentino rossi

Valentino Rossi, (born February 16, 1979 in Urbino),[1] is an Italian professional motorcycle racer and multiple MotoGP World Champion. He is one of the most successful motorcycle racers of all time, with 8 Grand Prix World Championships to his name. According to Sports Illustrated, Rossi is one of the highest earning sports personalities in the world, having earned an estimated $34 million in 2007.[2]
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SANIA MIRZA


In a cricket obsessed country like India, tennis player Sania Mirza's hysterical fan following speaks volumes about her achievements. Mirza's meteoric rise to stardom has made her an inspiration for the young sports enthusiasts across the country. By becoming the first Indian woman to reach the third round of a Grand Slam tournament at the 2005 Australian Open, Mirza proved that tennis in India is not merely dominated by the male counterparts. She improved her Grand Slam performance by reaching the fourth round of the US Open in the same year. Read on to know more about the profile of tennis star Sania Mirza.
FOR MORE WATCH HER SMALL PROFILE

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Sourav Ganguly(bengal tiger):

Sourav Chandidas Ganguly (Bengali: সৌরভ গাঙ্গুলী) ( pronunciation (help•info)) (born 8 July 1972) is a former Indian test cricketer, and captain of the Indian national team. As of October 2008, he was India's most successful Test captain to date, winning 21 tests out of 49 tests he captained[1] and leading India into the 2003 World Cup finals.[2] An aggressive captain, Ganguly is credited with having nurtured the careers of many young players who played under him.
for more details download this document


Roger Federer


"Federer" redirects here. For other uses, see Federer (disambiguation).
Roger Federer (born 8 August 1981) is a Swiss professional tennis player. As of September 2009, he is ranked world No. 1 by the Association of Tennis Professionals (ATP), having previously held the number one position for a record 237 consecutive weeks.[6] Many sports analysts, tennis critics, and former and current players consider Federer to be the greatest tennis player of all time.
to know more about his profile check this document download






Nicknamed "Rafa", Rafael Nadal has took the tennis world by storm over the past 5 years as he has made his way on the professional tennis circuit to number 2 in the world with a staggering clay-court winning streak of 60 consecutive matches.
He was born June 3rd 1986 in Manacor, Mallorca to Sebastián and Ana María. He has great sporting heritage as his Uncle is former F.C. Barcelona footballer Miguel Ángel Nadal. Between 1986 and 2001 (the year in which he turned pro at only age 15) he developed a brilliant all round game playing left-handed despite being naturally right-handed.

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Early days
Born in Mumbai (then Bombay) into a middle-class family, Sachin Tendulkar was named after his family’s favourite music director Sachin Dev Burman. He went to Sharadashram Vidyamandir School where he started his cricketing career under coach Ramakant Achrekar. While at school, he was involved in a mammoth 664 run partnership in a Harris Shield game with friend and team mate Vinod Kambli. In 1988/1989, he scored 100 not-out in his first first-class match, for Bombay against Gujarat. At 15 years and 232 days he was the youngest to score a century on debut.
Sachin Ramesh Tendulkar, generally known as Sachin Tendulkar is an Indian Cricket player who is considered to be one of the all time greatest batsmen to have ever played the game of Cricket. The renowned Cricket magazine Wisden ranked Sachin Tendulkar the 2nd all time greatest Test Cricket batsman, only after Sir Donald Bradman at the 1st place in the year 2002. Also, the magazine ranked him the 2nd all time greatest ODI batsman after Viv Richards at the first spot.

for more details on whole career download

to download songs pls click here download
MOVIE REVIEWS

Kurradu (2009)
Cast : Varun Sandesh, Neha Sharma
Producer : Kiran
Director : Sandeep Gunnam
Music : Achu
Lyrics : Ananth Sri Ram

to download click here

Shankam (2009)
Cast : Goipchand and Trisha
Producer : Pulla Rao and Bhagwan
Director : Shiva
Music : Thaman S

Click below to Download all the songs (320 VBR - 47 MB)

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to download the songs pls click here download

THIS IS THE LETTER BY JNTU K

In view of the declaration of holidays by the University on 3rd, 4th and 5th August,
2009, the following is the reschedule of on-line examinations and M.Tech./ M.Pharmacy
– II Semester examinations


TO GET FULL TIME TABLE AND MORE INFO PLS DOWNLOAD THE DOCUMENT DOWNLOAD

LETTER BY JNTUK

I am by the direction of the Hon’ble Vice-Chancellor, in view of the tragic demise of the Hon’ble Chief Minister Dr. Y. S. Rajasekhar Reddy garu, the online examinations and End examinations scheduled on 04-09-2009 and 05-09-2009 are postponed.


FOR MORE INFO DOWNLOAD THIS DOCUMENT HERE DOWNLOAD

The JNTU was divided in to different units as JNTUH, JNTUK, JNTUA and
JNFA&A Universities on 20-08-2009. JNTUH has conducted the November 2008
examination also. The students who are admitted in 2004 or before who have passed out
in 2008 May/November or earlier examinations were issued Provisional Certificates or
Consolidated Marks Memos by JNTU Hyderabad. All such students have to approach
JNTU Hyderabad for any other certificates.

FOR MORE INFO PLS DOWNLOD THIS DOCUMENT BY CLICKING HERE DOWNLOAD

In view of several representations received from students and Principals of the
Colleges under JNTUK, regarding the revaluation by challenge, it is decided in the
Directors meeting to introduce Revaluation by Challenge. A Challenging fee of
Rs. 10,000/- for subject is to be paid by the candidate for revaluation by challenge. The
revaluation will be carried out by a committee consisting of three members out of which
one member may be nominated by Principal of the College from where the candidate
has studied and two members will be nominated by the University. The candidate will
forfeit the challenging fee if the difference in the marks given by the committee is not
more than 15% of the maximum marks compared to the marks already shown in the
marks list. If the marks are more than 15%, the challenge fee will be returned to the
candidate. After the challenge valuation, if the marks are more than 15% or there is a
change in the status i.e., fail to pass, the new marks will be awarded, otherwise, the
previous marks will remain.

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Dr. Yeduguri Sandinti Rajasekhara Reddy, popularly known as YSR, is an astute politician and a charismatic mass leader who has carved for himself a niche in State politics by his exemplary devotion and dedication to the uplift of the downtrodden and neglected segments of society. Born on July 8, 1949, in Pulivendula in the backward Rayalaseema region, YSR has always struggled to secure the rights of the poor and the underprivileged.
Son of late Sri Y.S.Raja Reddy, a dynamic leader in his heyday, Rajasekhara Reddy evinced interest in politics right from his student days. While studying in M R Medical College, Gulbarga, Karnataka, he served as President of the Students union. He was elected leader of the House Surgeon's Association in S V Medical College, Tirupati.
After completing MBBS, he served as Medical Officer at the Jammalamadugu Mission Hospital for a brief period. In 1973, he established a 70-bed charitable hospital, named after his father late Y.S.Raja Reddy at Pulivendula. His family established one polytechnic and one degree college in Pulivendula, which were later handed over to the well-known Loyola group of institutions.
Rajasekhara Reddy's sound business acumen, entrepreneurial skills, and, above all, his transparency brought him laurels in the business arena. On the flip side, his success also brought him many adversaries, political and otherwise, who were desperately looking for a shred of evidence to prove umpteen charges against him. In the end, their mud-slinging did not yield a single point that could paint the mass leader in bad light. In fact, his detractors became red-faced, as they had to swallow their words.
Groomed by a family deeply involved in public service, YSR entered active politics in 1978 and contested elections, four times to enter the State Legislative Assembly and an equal number of times to enter the Lower House of Parliament. A winner in all that he does, YSR won all the elections he contested. Even today his admirers exclaim: "He (YSR) defeats defeat."
During his 25-year-long political career, YSR has served the people in multiple capacities, both in Government as well as in Party. He was President of the Andhra Pradesh Congress Committee (APCC) twice - 1983-1985 and 1998-2000. During 1980-1983, he was a minister holding important portfolios related to Rural Development, Medical & Health and Education etc. From 1999 to 2004 he was the Leader of Opposition in the eleventh state assembly.
As a champion of the masses, his stentorian voice in the assembly, raised particularly during debates that sought to lend voice to the voiceless millions, forced the Government to retrace several anti-people steps it contemplated. YSR has been instrumental in orchestrating several mass struggles, while highlighting issues facing peasants, weavers, Dalits, youth and women. His relentless fight for clearance of pending irrigation projects, particularly in the backward Rayalaseema region, has earned for him a special place in the hearts of millions of farmers. His unremitting struggle against certain anti-people economic measures that were sought to be introduced in the name of "reforms", including the frequent increases in power tariff and indiscriminate privatization of public sector units, exalted him far above the street smart politicians.
Even as a novice in the legislature, YSR rallied all the Congress MLAs from the Rayalaseema region and led an indefinite hunger strike demanding solution to the water crisis. He also led a Paadayaatra from Lepakshi to Pothireddipadu in Kurnool district. The 14-day hunger strike of legislators under his leadership in August 2000 to register protest against the hike in power charges is still fresh in the memory of people. By systematically exposing the misdeeds of the then Government, both inside and outside the Assembly, YSR was playing his political role to the hilt.
During mid-summer in 2003, he led an unprecedented 1400 Km long Paadayaatra covering all backward areas in the state to understand the ground realities of living conditions of the people there.
Now, as Chief Minister, the crowning glory of this studded political career, he can proudly claim to be the quintessence of a politician who, with vision focused on the coming generations as well, has earned the title of a statesman. Amidst a bewildering number of turncoats among politicians, who thrive in "shifting loyalties", YSR stands out as a sterling example of the old guard in pristine Indian politics.
This explains why he has never turned his back on the Congress party, which nurtured his political moorings. The lure of power and pelf could not divert him, when the party was briefly out of power, from his mission to hold the reins of power as a trusted lieutenant of the Congress and, more importantly, as a darling of the masses. Sworn in as Chief Minister of Andhra Pradesh on 14.05.2004.
YSR's Personality
A modest Personality:
Dr.Reddy,unlike most politicians, reflects the spirit of a true Indian who walks his talk.While his thought is dressed with all that is modern and ennobling, Dr.Reddy's person is invariably clothed in traditional costumes that include dhoti and a shirt made of handloom cloth.In all of his public and private conversations, he speaks from the core of his heart. Naturally, he hates hypocrisy.

As a demanding Chief Minister, YSR expects bureaucrats to do their job meticulously, and present before him only facts that are shorn of all publicity-oriented and manipulative figures. He does not tolerate hype and extravaganza in communicating official messages. He wants incontrovertible facts stated in a simple language that is intelligible even to the unlettered, because taking administration to the people is an article of faith for him.
His Philosophy of Life:
Dr. Rajasekhara Reddy strongly believes that the human life is a boon provided by the Almighty to share one's blessings with others, while serving less privileged human beings.

"Don't count the years you want to live. Ask yourself how much you have done for society at large with whatever opportunities the Almighty has provided you", is Dr. Reddy's word of advice for those who have excuses for not doing even what is within their means.

It is this humane principle that prompted him to take pioneering steps to ensure delivery of social security pensions to the needy in the first week of every month.
His stature:
Though measuring 5'7", Reddy looks majestically simple in his appearance with an ever-smiling genial countenance. This in fact overshadows his unfailing willpower to achieve his targets with the resilience and tenacity of a spider.

When YSR undertook his unprecedented 1500-KM-long Padayaatra (march on foot) in scorching sun during summer in 2003,covering backward areas of the state in particular, few people could discern the underlying motive: knowing first-hand the real problems of the people in their own language and their doorstep.
His Mission:
As around 75% of the population in India depend upon agriculture for livelihood, most administrative efforts should be focused on the rural economy, he believes.

Citing renowned economists, Dr. Reddy regrets that neglect of the agriculture and irrigation sectors in recent years have become the bane rural economy. As a proactive Chief Minister, he embarked upon a massive programme of executing 26 major irrigation projects to create 65 lakh acres of new ayacut.
His Motto:
Dr. Reddy's motto is that the ultimate objective of any program executed under a democratic set-up should be prompt and dependable delivery of sevices to the common man.

With this as the guiding principle, YSR has advised bureaucrats at all levels to help revive the functioning of the administrative system at all levels without habitually looking for autocratic 'diktats'. 'Decentralization of administrative power within the guidelines of the policy framed by the government reflects the true spirit of democratic governance", Dr. Reddy argues.
His strength:
Dr Reddy's strength lies in his stature as a mass leader since his advent in politics. Whether in or out of power, he has always championed the cause of the common man. This has endeared him to all segments of the Congress party as well.

Even after becoming the Chief Minister in May 2004, Dr Reddy makes it a point to address all the problems that are brought before him directly by people, cutting through bureaucratic hurdles, every day.

If any scheme or programme under formulation is placed before him for approval, its outcome is a foregone conclusion that is dependent on Dr. Reddy's invariable query: "How best will it benefit the people at large or ensure good governance?"
His 'pastime':
A curious 'pastime' of Dr Reddy is to feel the pulse of people in rural areas on Sundays through the Rajiv Palle Batta.

The Rajiv Palle Baata is a novel mass contact programme under which the Chief Minister reaches out to even unmotorable areas in the rural areas for personally collecting feedback on the implementation of various programmes. This programme has become extremely popular, because it highlights not what the Chief Minister does in the glare of official publicity, but what his officials may not have done in the people's own words.

In view of the rational changes brought about in administrative matters following the success of Rajiv Palle Baata, the Chief Minister now extended the programme to urban areas through Rajiv Nagara Baata.
His Approach:
The Chief Minister's emphasis on development of the rural economy does not presuppose a blinkered approach towards new and emerging technologies.

Dr.Reddy is committed to a balanced approach towards giving thrust to information technology, bio-technology and all sectors that enhance industrial and agricultural production. His watchword is total transparency in all transactions and deals that envisage public-private partnerships or involve private investments. Because, YSR believes he is simply a custodian of people's trust that is invaluable.

It is not a coincidence that he loves the company of children and often "gets lost" in their World that is founded on trust of the highest order.









Dr. Y.S. Rajasekhara Reddy, popularly known as YSR, is an astute politician and a charismatic mass leader who has carved for himself a niche in state politics by his exemplary devotion and dedication to the uplift of the downtrodden and neglected segments of the society. Born on July 8, 1949, in Pulivendula in the backward Rayalaseema region, YSR has always struggled to secure the rights of the poor and the underprivileged.
Serving the Society:
YSR evinced keen interest in politics from his student days. After completing his MBBS, he served as Medical Officer at Jammalamadugu Mission Hospital for a brief period. In 1973, he established a 70-bed hospital named after his father at Pulivendula. His family established one polytechnic college and one-degree college, which were handed over to the well known educational Institution later. YSR’s business acumen, entrepreneurial skills, and above all his transparency brought him laurels in the arena.
Entering Political Arena:
Groomed by a family deeply involved in public service, YSR entered active politics in 1978 and contested elections, four times to enter the State Legislative Assembly and an equal number of times to enter the Lower House of Parliament.
On the side of the People:
During his 25-year long political career, YSR has served the people in various capacities, both in government as well as in the party. He was President of Andhra Pradesh Congress Committee (APCC) twice. During 1980-83 he was a minister holding the portfolios of Rural Development, Medical & Health and Education etc. From 1900 to 2004 he was the Leader of Opposition in the eleventh assembly of the state. During this period he forced the government to retrace several anti-people steps. YSR has been instrumental in orchestrating several mass struggles, while highlighting many issues facing peasants, weavers, dalits and women. His relentless fight for clearance of pending irrigation projects, particularly in the backward region of Rayalaseema, has earned him a special place in the hearts of millions of farmers. His unremitting struggle against certain anti-people measures that were sought-t-be introduced in the name of ‘reforms’, including frequent increases in power tariff and indiscriminate privatization of public sector units, exalted him far above the street-smart politicians.
Paadayaatra:
During mid summer of 2003, he led an unprecedented 1400Km Paadayaatra (walk) covering all backward areas in the state to understand the ground realities of living conditions of the common man.
Now, as Chief Minister, the crowning glory in his studded political career, he can proudly claim to the quintessence of a politician who, with vision focused on the coming generations as well, has earned the title of statesman. The lure of power and pelf could not divert him, when the party was briefly out of power, from his mission to hold the reins of power as a trusted lieutenant of the party and, more importantly, as a darling of the masses.
He was sworn in as Chief Minister of Andhra Pradesh on 14.05.2004.
Vision:
To see all regions of the state equally develop in all the sectors that ensure better living standards of the present and coming generations by creating infrastructure, providing employment opportunities, empowering marginalized sections and making the state IT Hub of the world and the Rice bowl of India.
Shaping up AP as IT Hotspot:
• The state government is developing Tier-2 cities as IT Clusters besides the capital Hyderabad, and creating infrastructure for the industry to spread IT industry across the state.
• It is providing connectivity through air with nine new airports, by road with thousands of Km of new roads, by sea with three new ports and urban infrastructure like MRTS and Outer Ring Road.
• The state is embarked on developing Human Resources through Institutions of Excellence like BITS, ITT, New Universities, Jawahar Knowledge Centers, National Institute of Pharmaceutical Education and Research to meet the requirement of the industry.
• Government of AP is setting up Public Schools with public-private partnership to meet the growing needs of the industry by bridging the urban-rural divide.
• •Steps are taken by the government to double the power production capacity to ensure incessant supply for both industrial and domestic needs.
Water to Every Field:
• AP is concentration on providing irrigation facilities as more than 65% people of the state is dependent on agriculture.
• Only 40% of the available land is under assured irrigation now.
• State aimed to double it by spending over $20 billion on various irrigation projects on priority basis.
Health Care:
• The state government initiated multi pronged strategy for HIV/AIDS Control.
• •Arogya Sree- A health insurance scheme to facilitate major surgeries in heart diseases, cancer and kidney etc. for the poor through public-private partnership is already under way.
Accelerated Growth of Industry:
• IT exports registered a growth of 51% as against the national average of 36%.
• Steel production is doubled.
• Cement production is doubled.
• Paper production is doubled.
• Textiles and Garments is doubled.
• Footwear, Gems and Jewelry industries are coming up.


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check here click here

http://books.google.com/books?id=M9_2dtPsvbsC&lpg=PA1&dq=electromagnetic%20field%20by%20u.a.%20bakshi&pg=PA24&output=embed" width=500 height=500>

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I B.Tech Regular/Supplementary R07 & R05 Examination Results June-2009[Last date for Recounting 03/09/2009]

DOWNLOAD JOSH AUDIO SONGS HERE CLICK HERE

guys can you run is the site that helps you to check YOURS system is compatible to run your required game or not

SO TO CHECK CLICK HERE

click here

download:http://www.ziddu.com/download/5036691/cnds.doc.html

http://www.ziddu.com/download/4909187/I-BTECH-R07.pdf.html

previous year questionpapers for 1st b.tech

aug/sep-2007 papers


aug-2008 papers


april/may 2007 papers


R07
april/may 2007 papers





RR

hai guys sorry for late

eng
http://www.ziddu.com/download/4268043/english_3RDMID.pdf.html
m1
this is doc file to edit
http://www.ziddu.com/download/4705006/maths1httpvyceteee.co.cc.doc.html

this is pdf file for direct print out

http://www.ziddu.com/download/4705007/maths1httpvyceteee.co.cc.pdf.html

a.p

http://www.ziddu.com/download/4360785/ap3new.pdf.html



cds


this is pdf file for direct print out

http://www.ziddu.com/download/4705811/cds.pdf.html

this is doc file to edit

http://www.ziddu.com/download/4705812/cds.doc.html

due to mid exams rest other subjects will be updated on sunday by admin

Ohm's Law
When an applied voltage E causes a current I to flow through an impedance Z, the value of the impedance Z is equal to the voltage E divided by the current I.
Impedance = Voltage / Current Z = E / I
Similarly, when a voltage E is applied across an impedance Z, the resulting current I through the impedance is equal to the voltage E divided by the impedance Z.
Current = Voltage / Impedance I = E / Z
Similarly, when a current I is passed through an impedance Z, the resulting voltage drop V across the impedance is equal to the current I multiplied by the impedance Z.
Voltage = Current * Impedance V = IZ
Alternatively, using admittance Y which is the reciprocal of impedance Z:
Voltage = Current / Admittance V = I / Y
________________________________________
Kirchhoff's Laws
Kirchhoff's Current Law
At any instant the sum of all the currents flowing into any circuit node is equal to the sum of all the currents flowing out of that node:
Iin = Iout
Similarly, at any instant the algebraic sum of all the currents at any circuit node is zero:
I = 0
Kirchhoff's Voltage Law
At any instant the sum of all the voltage sources in any closed circuit is equal to the sum of all the voltage drops in that circuit:
E = IZ
Similarly, at any instant the algebraic sum of all the voltages around any closed circuit is zero:
E - IZ = 0
________________________________________
Thévenin's Theorem
Any linear voltage network which may be viewed from two terminals can be replaced by a voltage-source equivalent circuit comprising a single voltage source E and a single series impedance Z. The voltage E is the open-circuit voltage between the two terminals and the impedance Z is the impedance of the network viewed from the terminals with all voltage sources replaced by their internal impedances.
________________________________________
Norton's Theorem
Any linear current network which may be viewed from two terminals can be replaced by a current-source equivalent circuit comprising a single current source I and a single shunt admittance Y. The current I is the short-circuit current between the two terminals and the admittance Y is the admittance of the network viewed from the terminals with all current sources replaced by their internal admittances.
________________________________________
Thévenin and Norton Equivalence
The open circuit, short circuit and load conditions of the Thévenin model are:
Voc = E
Isc = E / Z
Vload = E - IloadZ
Iload = E / (Z + Zload)
The open circuit, short circuit and load conditions of the Norton model are:
Voc = I / Y
Isc = I
Vload = I / (Y + Yload)
Iload = I - VloadY
Thévenin model from Norton model
Voltage = Current / Admittance
Impedance = 1 / Admittance E = I / Y
Z = Y -1
Norton model from Thévenin model
Current = Voltage / Impedance
Admittance = 1 / Impedance I = E / Z
Y = Z -1
When performing network reduction for a Thévenin or Norton model, note that:
- nodes with zero voltage difference may be short-circuited with no effect on the network current distribution,
- branches carrying zero current may be open-circuited with no effect on the network voltage distribution.
________________________________________
Superposition Theorem
In a linear network with multiple voltage sources, the current in any branch is the sum of the currents which would flow in that branch due to each voltage source acting alone with all other voltage sources replaced by their internal impedances.
________________________________________
Reciprocity Theorem
If a voltage source E acting in one branch of a network causes a current I to flow in another branch of the network, then the same voltage source E acting in the second branch would cause an identical current I to flow in the first branch.
________________________________________
Compensation Theorem
If the impedance Z of a branch in a network in which a current I flows is changed by a finite amount Z, then the change in the currents in all other branches of the network may be calculated by inserting a voltage source of -IZ into that branch with all other voltage sources replaced by their internal impedances.
________________________________________
Millman's Theorem (Parallel Generator Theorem)
If any number of admittances Y1, Y2, Y3, ... meet at a common point P, and the voltages from another point N to the free ends of these admittances are E1, E2, E3, ... then the voltage between points P and N is:
VPN = (E1Y1 + E2Y2 + E3Y3 + ...) / (Y1 + Y2 + Y3 + ...)
VPN = EY / Y
The short-circuit currents available between points P and N due to each of the voltages E1, E2, E3, ... acting through the respective admitances Y1, Y2, Y3, ... are E1Y1, E2Y2, E3Y3, ... so the voltage between points P and N may be expressed as:
VPN = Isc / Y
________________________________________
Joule's Law
When a current I is passed through a resistance R, the resulting power P dissipated in the resistance is equal to the square of the current I multiplied by the resistance R:
P = I2R
By substitution using Ohm's Law for the corresponding voltage drop V (= IR) across the resistance:
P = V2 / R = VI = I2R
________________________________________
Maximum Power Transfer Theorem
When the impedance of a load connected to a power source is varied from open-circuit to short-circuit, the power absorbed by the load has a maximum value at a load impedance which is dependent on the impedance of the power source.
Note that power is zero for an open-circuit (zero current) and for a short-circuit (zero voltage).
Voltage Source
When a load resistance RT is connected to a voltage source ES with series resistance RS, maximum power transfer to the load occurs when RT is equal to RS.
Under maximum power transfer conditions, the load resistance RT, load voltage VT, load current IT and load power PT are:
RT = RS
VT = ES / 2
IT = VT / RT = ES / 2RS
PT = VT2 / RT = ES2 / 4RS
Current Source
When a load conductance GT is connected to a current source IS with shunt conductance GS, maximum power transfer to the load occurs when GT is equal to GS.
Under maximum power transfer conditions, the load conductance GT, load current IT, load voltage VT and load power PT are:
GT = GS
IT = IS / 2
VT = IT / GT = IS / 2GS
PT = IT2 / GT = IS2 / 4GS
Complex Impedances
When a load impedance ZT (comprising variable resistance RT and variable reactance XT) is connected to an alternating voltage source ES with series impedance ZS (comprising resistance RS and reactance XS), maximum power transfer to the load occurs when ZT is equal to ZS* (the complex conjugate of ZS) such that RT and RS are equal and XT and XS are equal in magnitude but of opposite sign (one inductive and the other capacitive).
When a load impedance ZT (comprising variable resistance RT and constant reactance XT) is connected to an alternating voltage source ES with series impedance ZS (comprising resistance RS and reactance XS), maximum power transfer to the load occurs when RT is equal to the magnitude of the impedance comprising ZS in series with XT:
RT = |ZS + XT| = (RS2 + (XS + XT)2)½
Note that if XT is zero, maximum power transfer occurs when RT is equal to the magnitude of ZS:
RT = |ZS| = (RS2 + XS2)½
When a load impedance ZT with variable magnitude and constant phase angle (constant power factor) is connected to an alternating voltage source ES with series impedance ZS, maximum power transfer to the load occurs when the magnitude of ZT is equal to the magnitude of ZS:
(RT2 + XT2)½ = |ZT| = |ZS| = (RS2 + XS2)½
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Kennelly's Star-Delta Transformation
A star network of three impedances ZAN, ZBN and ZCN connected together at common node N can be transformed into a delta network of three impedances ZAB, ZBC and ZCA by the following equations:
ZAB = ZAN + ZBN + (ZANZBN / ZCN) = (ZANZBN + ZBNZCN + ZCNZAN) / ZCN
ZBC = ZBN + ZCN + (ZBNZCN / ZAN) = (ZANZBN + ZBNZCN + ZCNZAN) / ZAN
ZCA = ZCN + ZAN + (ZCNZAN / ZBN) = (ZANZBN + ZBNZCN + ZCNZAN) / ZBN
Similarly, using admittances:
YAB = YANYBN / (YAN + YBN + YCN)
YBC = YBNYCN / (YAN + YBN + YCN)
YCA = YCNYAN / (YAN + YBN + YCN)
In general terms:
Zdelta = (sum of Zstar pair products) / (opposite Zstar)
Ydelta = (adjacent Ystar pair product) / (sum of Ystar)
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Kennelly's Delta-Star Transformation
A delta network of three impedances ZAB, ZBC and ZCA can be transformed into a star network of three impedances ZAN, ZBN and ZCN connected together at common node N by the following equations:
ZAN = ZCAZAB / (ZAB + ZBC + ZCA)
ZBN = ZABZBC / (ZAB + ZBC + ZCA)
ZCN = ZBCZCA / (ZAB + ZBC + ZCA)
Similarly, using admittances:
YAN = YCA + YAB + (YCAYAB / YBC) = (YABYBC + YBCYCA + YCAYAB) / YBC
YBN = YAB + YBC + (YABYBC / YCA) = (YABYBC + YBCYCA + YCAYAB) / YCA
YCN = YBC + YCA + (YBCYCA / YAB) = (YABYBC + YBCYCA + YCAYAB) / YAB
In general terms:
Zstar = (adjacent Zdelta pair product) / (sum of Zdelta)
Ystar = (sum of Ydelta pair products) / (opposite Ydelta)


Introduction
Provided below are notes and various common formula used in designing electrical circuits.


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Direction of currents
The terminology when representing the direction of the positive current flow is as follows

Electron drift which is the flow of electrons in an electrical circuit flows from negative to positive .

Electric batteries by convention are identified as shown in the figure below..

A simple dc circuit illustrates the various relationships and directions is shown below..


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Ohms law
V = Voltage (Volts)
I = Current (Amperes)
R = Resistance (Ohms)
W = Power (Watts) V = I.R = Sqrt (W . R) = W / I
I = V / R = Sqrt( W / R) = W / V
R = V / I = W / I2 = V2 / W
W = VI = V2 / R = I2 . R General Form of Ohms law
R = ρ . L / A
L = Length (metres),
A = Area (metre2 ),
ρ = resistivity (Ω /metre)



________________________________________
Additive Resistances
Resistors in Series
R_total = R 1 + R 2 + R 3...
Voltage across Resistors in Series
V total = V R1 + V R2 + V R3.. Resistors in Parallel
R total = 1/ (1/R 1 + 1/R 2 +1/R 3...)
The Voltage across Resistors in Parallel is the Same = V



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Alternating Current Supplies
Alternating Voltage
v = V max. sin ω. t = V max .sin(2.π.f.t)
v = instantaneous voltage
V_max = maximum voltage,
t = time (seconds) from from point of zero rising voltage in sinusoidal variation.,
ω = angular velocity rads/sec,
f = frequency (cycles /sec)

The average value of a sinusoidal alternating quantity is calculated at 0.637x maximum value
The Root Mean Square(RMS) value of a sinusoidal alternating quantity is calculated at 0.707 x maximum value.
The form factor of a wave is the RMS value / average Value = (for a sinusoidal wave) 1.1
The peak (crest) factor is the peak value / RMS value = 1.414

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Kirchoff's Laws
Kirchoffs First law.
The total current flowing towards a junction is equal to the total current flowing away from that junction. i.e the algebraic sum of the currents flowing towards a junction is zero

Kirchoff's Second Law
In a closed circuit the algebraic sum of the products of the current and the resistance of each part of the circuit is equal to the resultant e.m.f in the circuit.

As an example of Kirchoff's second law it is required to find the currents in each branch in the circuit shown below

First it can be seen that I 3 = I 1 + I 2.......a)
In AFEB 2V - 3V = (I 1. 1 Ω) - I 2.2Ω) Therefore .... -1 A = I 1 - 2.I 2.......(b)
IN BEDC 3V = (I 2.2 Ω) + (I 3.3 Ω ) Therefore.... 3A = 2.I 2 + 3 .I 3 ...... (c)
Substituting for I 3 in c) .. 2.I 2 + 3.I 1 + 3.I 2 = 3A Therefore 3.I 1 + 5.I 2 = 3A .....d)
- 3 times b).... -3.I 1 + 6.I 2 = 3A..
and adding the last two equations 11.I 2 = 6A. and therefore
I 2 = (6/11) A.... (I 1 = 2.I 2 - 1) ... so I 1 =(1/11) A and I 3 = I 1 +I 1 so I 3 = (7/11) A

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Superposition Theorem
Superposition Theorem.
This theorem states that in any network containing more than one source , the current in, or the p.d across, any branch can be found by considering each source separately and adding their effects: The omitted sources (of e.m.f) being replaced by resistances equivalent to their internal resistances.



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Reciprocity Theorem
Reciprocity Theorem.
This theorem states that if a current is produced at point a in a network by a source acting at point b then the the same current would be produced at b by the same value source acting at point a

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Thevenin's Theorem
Thevenin's Theorem.
This theorem is used to determine the voltage / current flow across / through two points say A and B in a complicated circuit which includes and number of sources and loads. The theorem states

The current through a resistance R connected across any two points A and B of an active network ( a network containing one or more sources of e.m.f. ) is obtained by dividing the p.d. between A and B with R disconnected , by ( R + r ) where r is the resistance of the network measure between A and B with R disconnected and the sources of e.m.f replaced by their internal resistance.

Consider a general network containing voltage and current sources. The network can be replaced by a single source of e.m.f (E) with and internal resistance r. E being the e.m.f. across A- B with the load disconnected and r being the total resistance of the circuit measured across A-B with the load disconnected and the e.m.f. sources replaced by their internal resistances.

As an example of this theorem it is necessary to find the p.d across A-B in the figure below.

First remove the resistance R and calculate V. As there is no current flow there is no p.d. across R 2
The current through R 3 is E 1 / (R 1 + R 3).. The p.d. across R 3 = ....V = is E 1. R 3 / ( R 1 + R 3)
The resistance of the network = r = R 2 + (R 1 .R 3) / (R 1 + R 3)

Thevenin's theorem states that the circuit above can be replaced by the simple circuit as shown below

The current flow I = V / (r +R)..The pd. across R = V.R/ (r+R)

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Start Delta Conversions
The star delta conversion formula are useful if loads are connected in a star or delta arrangement and it is more convenient to convert to the other arrangement which may be more simpler to resolve for a particular problem....

The relationships are properties of the load impedances and are independent of the voltages and does not imply three phase working....

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Capacitors
Q = V . C therefore I = C dV/dt
Q = Charge (Coulomb)
V = Potential Difference (Volts)
C = Capacitance (Farad) V = V / X c
X c = Capacitive Reactance (Ω )
X c = 1 / (2 π f C )
f = frequency (Herz)

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Addition of Capacitors
Capacitors in Parallel
C total. V = Q total = Q 1+Q 2+Q 3...
C total. V = V.C 1+V.C 2+V.C 3...
C total = C 1+C 2+C 3... Capacitors in Series
1/C total = 1/C 1 + 1/C 2 + 1/C 3...

C total = 1/ (1/C 1 + 1/C 2 + 1/C 3...)

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Inductances
V = L.dI/dt
L = Inductance (Henry) I = V/ X L
X L = Inductive Reactance (Ω )
X L =2 π f L
f = frequency (Herz)

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Additive Inductances
Inductances in Series
L total = L 1 + L 2 + L 3... Inductances in Parallel
1 / L total = 1 / L 1 + 1 / L 2 + 1 / L 3 ...

L total = 1/ ( 1 / L 1 + 1 / L 2 + 1 / L 3 ) ...

DIVIDER CIRCUITS AND KIRCHHOFF'S LAWS

* Voltage divider circuits
* Kirchhoff's Voltage Law (KVL)
* Current divider circuits
* Kirchhoff's Current Law (KCL)
* Contributors

Voltage divider circuits

Let's analyze a simple series circuit, determining the voltage drops across individual resistors:



From the given values of individual resistances, we can determine a total circuit resistance, knowing that resistances add in series:

From here, we can use Ohm's Law (I=E/R) to determine the total current, which we know will be the same as each resistor current, currents being equal in all parts of a series circuit:

Now, knowing that the circuit current is 2 mA, we can use Ohm's Law (E=IR) to calculate voltage across each resistor:

It should be apparent that the voltage drop across each resistor is proportional to its resistance, given that the current is the same through all resistors. Notice how the voltage across R2 is double that of the voltage across R1, just as the resistance of R2 is double that of R1.

If we were to change the total voltage, we would find this proportionality of voltage drops remains constant:

The voltage across R2 is still exactly twice that of R1's drop, despite the fact that the source voltage has changed. The proportionality of voltage drops (ratio of one to another) is strictly a function of resistance values.

With a little more observation, it becomes apparent that the voltage drop across each resistor is also a fixed proportion of the supply voltage. The voltage across R1, for example, was 10 volts when the battery supply was 45 volts. When the battery voltage was increased to 180 volts (4 times as much), the voltage drop across R1 also increased by a factor of 4 (from 10 to 40 volts). The ratio between R1's voltage drop and total voltage, however, did not change:

Likewise, none of the other voltage drop ratios changed with the increased supply voltage either:

For this reason a series circuit is often called a voltage divider for its ability to proportion -- or divide -- the total voltage into fractional portions of constant ratio. With a little bit of algebra, we can derive a formula for determining series resistor voltage drop given nothing more than total voltage, individual resistance, and total resistance:

The ratio of individual resistance to total resistance is the same as the ratio of individual voltage drop to total supply voltage in a voltage divider circuit. This is known as the voltage divider formula, and it is a short-cut method for determining voltage drop in a series circuit without going through the current calculation(s) of Ohm's Law.

Using this formula, we can re-analyze the example circuit's voltage drops in fewer steps:



Voltage dividers find wide application in electric meter circuits, where specific combinations of series resistors are used to "divide" a voltage into precise proportions as part of a voltage measurement device.

One device frequently used as a voltage-dividing component is the potentiometer, which is a resistor with a movable element positioned by a manual knob or lever. The movable element, typically called a wiper, makes contact with a resistive strip of material (commonly called the slidewire if made of resistive metal wire) at any point selected by the manual control:

The wiper contact is the left-facing arrow symbol drawn in the middle of the vertical resistor element. As it is moved up, it contacts the resistive strip closer to terminal 1 and further away from terminal 2, lowering resistance to terminal 1 and raising resistance to terminal 2. As it is moved down, the opposite effect results. The resistance as measured between terminals 1 and 2 is constant for any wiper position.

Shown here are internal illustrations of two potentiometer types, rotary and linear:



Some linear potentiometers are actuated by straight-line motion of a lever or slide button. Others, like the one depicted in the previous illustration, are actuated by a turn-screw for fine adjustment ability. The latter units are sometimes referred to as trimpots, because they work well for applications requiring a variable resistance to be "trimmed" to some precise value. It should be noted that not all linear potentiometers have the same terminal assignments as shown in this illustration. With some, the wiper terminal is in the middle, between the two end terminals.

The following photograph shows a real, rotary potentiometer with exposed wiper and slidewire for easy viewing. The shaft which moves the wiper has been turned almost fully clockwise so that the wiper is nearly touching the left terminal end of the slidewire:

Here is the same potentiometer with the wiper shaft moved almost to the full-counterclockwise position, so that the wiper is near the other extreme end of travel:

If a constant voltage is applied between the outer terminals (across the length of the slidewire), the wiper position will tap off a fraction of the applied voltage, measurable between the wiper contact and either of the other two terminals. The fractional value depends entirely on the physical position of the wiper:

Just like the fixed voltage divider, the potentiometer's voltage division ratio is strictly a function of resistance and not of the magnitude of applied voltage. In other words, if the potentiometer knob or lever is moved to the 50 percent (exact center) position, the voltage dropped between wiper and either outside terminal would be exactly 1/2 of the applied voltage, no matter what that voltage happens to be, or what the end-to-end resistance of the potentiometer is. In other words, a potentiometer functions as a variable voltage divider where the voltage division ratio is set by wiper position.

This application of the potentiometer is a very useful means of obtaining a variable voltage from a fixed-voltage source such as a battery. If a circuit you're building requires a certain amount of voltage that is less than the value of an available battery's voltage, you may connect the outer terminals of a potentiometer across that battery and "dial up" whatever voltage you need between the potentiometer wiper and one of the outer terminals for use in your circuit:

When used in this manner, the name potentiometer makes perfect sense: they meter (control) the potential (voltage) applied across them by creating a variable voltage-divider ratio. This use of the three-terminal potentiometer as a variable voltage divider is very popular in circuit design.

Shown here are several small potentiometers of the kind commonly used in consumer electronic equipment and by hobbyists and students in constructing circuits:

The smaller units on the very left and very right are designed to plug into a solderless breadboard or be soldered into a printed circuit board. The middle units are designed to be mounted on a flat panel with wires soldered to each of the three terminals.

Here are three more potentiometers, more specialized than the set just shown:

The large "Helipot" unit is a laboratory potentiometer designed for quick and easy connection to a circuit. The unit in the lower-left corner of the photograph is the same type of potentiometer, just without a case or 10-turn counting dial. Both of these potentiometers are precision units, using multi-turn helical-track resistance strips and wiper mechanisms for making small adjustments. The unit on the lower-right is a panel-mount potentiometer, designed for rough service in industrial applications.

* REVIEW:
* Series circuits proportion, or divide, the total supply voltage among individual voltage drops, the proportions being strictly dependent upon resistances: ERn = ETotal (Rn / RTotal)
* A potentiometer is a variable-resistance component with three connection points, frequently used as an adjustable voltage divider.

Kirchhoff's Voltage Law (KVL)

Let's take another look at our example series circuit, this time numbering the points in the circuit for voltage reference:

If we were to connect a voltmeter between points 2 and 1, red test lead to point 2 and black test lead to point 1, the meter would register +45 volts. Typically the "+" sign is not shown, but rather implied, for positive readings in digital meter displays. However, for this lesson the polarity of the voltage reading is very important and so I will show positive numbers explicitly:

When a voltage is specified with a double subscript (the characters "2-1" in the notation "E2-1"), it means the voltage at the first point (2) as measured in reference to the second point (1). A voltage specified as "Ecg" would mean the voltage as indicated by a digital meter with the red test lead on point "c" and the black test lead on point "g": the voltage at "c" in reference to "g".

If we were to take that same voltmeter and measure the voltage drop across each resistor, stepping around the circuit in a clockwise direction with the red test lead of our meter on the point ahead and the black test lead on the point behind, we would obtain the following readings:



We should already be familiar with the general principle for series circuits stating that individual voltage drops add up to the total applied voltage, but measuring voltage drops in this manner and paying attention to the polarity (mathematical sign) of the readings reveals another facet of this principle: that the voltages measured as such all add up to zero:

This principle is known as Kirchhoff's Voltage Law (discovered in 1847 by Gustav R. Kirchhoff, a German physicist), and it can be stated as such:

"The algebraic sum of all voltages in a loop must equal zero"

By algebraic, I mean accounting for signs (polarities) as well as magnitudes. By loop, I mean any path traced from one point in a circuit around to other points in that circuit, and finally back to the initial point. In the above example the loop was formed by following points in this order: 1-2-3-4-1. It doesn't matter which point we start at or which direction we proceed in tracing the loop; the voltage sum will still equal zero. To demonstrate, we can tally up the voltages in loop 3-2-1-4-3 of the same circuit:

This may make more sense if we re-draw our example series circuit so that all components are represented in a straight line:

It's still the same series circuit, just with the components arranged in a different form. Notice the polarities of the resistor voltage drops with respect to the battery: the battery's voltage is negative on the left and positive on the right, whereas all the resistor voltage drops are oriented the other way: positive on the left and negative on the right. This is because the resistors are resisting the flow of electrons being pushed by the battery. In other words, the "push" exerted by the resistors against the flow of electrons must be in a direction opposite the source of electromotive force.

Here we see what a digital voltmeter would indicate across each component in this circuit, black lead on the left and red lead on the right, as laid out in horizontal fashion:

If we were to take that same voltmeter and read voltage across combinations of components, starting with only R1 on the left and progressing across the whole string of components, we will see how the voltages add algebraically (to zero):

The fact that series voltages add up should be no mystery, but we notice that the polarity of these voltages makes a lot of difference in how the figures add. While reading voltage across R1, R1--R2, and R1--R2--R3 (I'm using a "double-dash" symbol "--" to represent the series connection between resistors R1, R2, and R3), we see how the voltages measure successively larger (albeit negative) magnitudes, because the polarities of the individual voltage drops are in the same orientation (positive left, negative right). The sum of the voltage drops across R1, R2, and R3 equals 45 volts, which is the same as the battery's output, except that the battery's polarity is opposite that of the resistor voltage drops (negative left, positive right), so we end up with 0 volts measured across the whole string of components.

That we should end up with exactly 0 volts across the whole string should be no mystery, either. Looking at the circuit, we can see that the far left of the string (left side of R1: point number 2) is directly connected to the far right of the string (right side of battery: point number 2), as necessary to complete the circuit. Since these two points are directly connected, they are electrically common to each other. And, as such, the voltage between those two electrically common points must be zero.

Kirchhoff's Voltage Law (sometimes denoted as KVL for short) will work for any circuit configuration at all, not just simple series. Note how it works for this parallel circuit:

Being a parallel circuit, the voltage across every resistor is the same as the supply voltage: 6 volts. Tallying up voltages around loop 2-3-4-5-6-7-2, we get:

Note how I label the final (sum) voltage as E2-2. Since we began our loop-stepping sequence at point 2 and ended at point 2, the algebraic sum of those voltages will be the same as the voltage measured between the same point (E2-2), which of course must be zero.

The fact that this circuit is parallel instead of series has nothing to do with the validity of Kirchhoff's Voltage Law. For that matter, the circuit could be a "black box" -- its component configuration completely hidden from our view, with only a set of exposed terminals for us to measure voltage between -- and KVL would still hold true:

Try any order of steps from any terminal in the above diagram, stepping around back to the original terminal, and you'll find that the algebraic sum of the voltages always equals zero.

Furthermore, the "loop" we trace for KVL doesn't even have to be a real current path in the closed-circuit sense of the word. All we have to do to comply with KVL is to begin and end at the same point in the circuit, tallying voltage drops and polarities as we go between the next and the last point. Consider this absurd example, tracing "loop" 2-3-6-3-2 in the same parallel resistor circuit:



KVL can be used to determine an unknown voltage in a complex circuit, where all other voltages around a particular "loop" are known. Take the following complex circuit (actually two series circuits joined by a single wire at the bottom) as an example:

To make the problem simpler, I've omitted resistance values and simply given voltage drops across each resistor. The two series circuits share a common wire between them (wire 7-8-9-10), making voltage measurements between the two circuits possible. If we wanted to determine the voltage between points 4 and 3, we could set up a KVL equation with the voltage between those points as the unknown:









Stepping around the loop 3-4-9-8-3, we write the voltage drop figures as a digital voltmeter would register them, measuring with the red test lead on the point ahead and black test lead on the point behind as we progress around the loop. Therefore, the voltage from point 9 to point 4 is a positive (+) 12 volts because the "red lead" is on point 9 and the "black lead" is on point 4. The voltage from point 3 to point 8 is a positive (+) 20 volts because the "red lead" is on point 3 and the "black lead" is on point 8. The voltage from point 8 to point 9 is zero, of course, because those two points are electrically common.

Our final answer for the voltage from point 4 to point 3 is a negative (-) 32 volts, telling us that point 3 is actually positive with respect to point 4, precisely what a digital voltmeter would indicate with the red lead on point 4 and the black lead on point 3:

In other words, the initial placement of our "meter leads" in this KVL problem was "backwards." Had we generated our KVL equation starting with E3-4 instead of E4-3, stepping around the same loop with the opposite meter lead orientation, the final answer would have been E3-4 = +32 volts:

It is important to realize that neither approach is "wrong." In both cases, we arrive at the correct assessment of voltage between the two points, 3 and 4: point 3 is positive with respect to point 4, and the voltage between them is 32 volts.

* REVIEW:
* Kirchhoff's Voltage Law (KVL): "The algebraic sum of all voltages in a loop must equal zero"

Current divider circuits

Let's analyze a simple parallel circuit, determining the branch currents through individual resistors:

Knowing that voltages across all components in a parallel circuit are the same, we can fill in our voltage/current/resistance table with 6 volts across the top row:

Using Ohm's Law (I=E/R) we can calculate each branch current:

Knowing that branch currents add up in parallel circuits to equal the total current, we can arrive at total current by summing 6 mA, 2 mA, and 3 mA:

The final step, of course, is to figure total resistance. This can be done with Ohm's Law (R=E/I) in the "total" column, or with the parallel resistance formula from individual resistances. Either way, we'll get the same answer:

Once again, it should be apparent that the current through each resistor is related to its resistance, given that the voltage across all resistors is the same. Rather than being directly proportional, the relationship here is one of inverse proportion. For example, the current through R1 is twice as much as the current through R3, which has twice the resistance of R1.

If we were to change the supply voltage of this circuit, we find that (surprise!) these proportional ratios do not change:

The current through R1 is still exactly twice that of R3, despite the fact that the source voltage has changed. The proportionality between different branch currents is strictly a function of resistance.

Also reminiscent of voltage dividers is the fact that branch currents are fixed proportions of the total current. Despite the fourfold increase in supply voltage, the ratio between any branch current and the total current remains unchanged:

For this reason a parallel circuit is often called a current divider for its ability to proportion -- or divide -- the total current into fractional parts. With a little bit of algebra, we can derive a formula for determining parallel resistor current given nothing more than total current, individual resistance, and total resistance:

The ratio of total resistance to individual resistance is the same ratio as individual (branch) current to total current. This is known as the current divider formula, and it is a short-cut method for determining branch currents in a parallel circuit when the total current is known.

Using the original parallel circuit as an example, we can re-calculate the branch currents using this formula, if we start by knowing the total current and total resistance:

If you take the time to compare the two divider formulae, you'll see that they are remarkably similar. Notice, however, that the ratio in the voltage divider formula is Rn (individual resistance) divided by RTotal, and how the ratio in the current divider formula is RTotal divided by Rn:

It is quite easy to confuse these two equations, getting the resistance ratios backwards. One way to help remember the proper form is to keep in mind that both ratios in the voltage and current divider equations must equal less than one. After all these are divider equations, not multiplier equations! If the fraction is upside-down, it will provide a ratio greater than one, which is incorrect. Knowing that total resistance in a series (voltage divider) circuit is always greater than any of the individual resistances, we know that the fraction for that formula must be Rn over RTotal. Conversely, knowing that total resistance in a parallel (current divider) circuit is always less then any of the individual resistances, we know that the fraction for that formula must be RTotal over Rn.

Current divider circuits also find application in electric meter circuits, where a fraction of a measured current is desired to be routed through a sensitive detection device. Using the current divider formula, the proper shunt resistor can be sized to proportion just the right amount of current for the device in any given instance:

* REVIEW:
* Parallel circuits proportion, or "divide," the total circuit current among individual branch currents, the proportions being strictly dependent upon resistances: In = ITotal (RTotal / Rn)

Kirchhoff's Current Law (KCL)

Let's take a closer look at that last parallel example circuit:

Solving for all values of voltage and current in this circuit:

At this point, we know the value of each branch current and of the total current in the circuit. We know that the total current in a parallel circuit must equal the sum of the branch currents, but there's more going on in this circuit than just that. Taking a look at the currents at each wire junction point (node) in the circuit, we should be able to see something else:

At each node on the negative "rail" (wire 8-7-6-5) we have current splitting off the main flow to each successive branch resistor. At each node on the positive "rail" (wire 1-2-3-4) we have current merging together to form the main flow from each successive branch resistor. This fact should be fairly obvious if you think of the water pipe circuit analogy with every branch node acting as a "tee" fitting, the water flow splitting or merging with the main piping as it travels from the output of the water pump toward the return reservoir or sump.

If we were to take a closer look at one particular "tee" node, such as node 3, we see that the current entering the node is equal in magnitude to the current exiting the node:

From the right and from the bottom, we have two currents entering the wire connection labeled as node 3. To the left, we have a single current exiting the node equal in magnitude to the sum of the two currents entering. To refer to the plumbing analogy: so long as there are no leaks in the piping, what flow enters the fitting must also exit the fitting. This holds true for any node ("fitting"), no matter how many flows are entering or exiting. Mathematically, we can express this general relationship as such:

Mr. Kirchhoff decided to express it in a slightly different form (though mathematically equivalent), calling it Kirchhoff's Current Law (KCL):

Summarized in a phrase, Kirchhoff's Current Law reads as such:

"The algebraic sum of all currents entering and exiting a node must equal zero"

That is, if we assign a mathematical sign (polarity) to each current, denoting whether they enter (+) or exit (-) a node, we can add them together to arrive at a total of zero, guaranteed.

Taking our example node (number 3), we can determine the magnitude of the current exiting from the left by setting up a KCL equation with that current as the unknown value:

The negative (-) sign on the value of 5 milliamps tells us that the current is exiting the node, as opposed to the 2 milliamp and 3 milliamp currents, which must were both positive (and therefore entering the node). Whether negative or positive denotes current entering or exiting is entirely arbitrary, so long as they are opposite signs for opposite directions and we stay consistent in our notation, KCL will work.

Together, Kirchhoff's Voltage and Current Laws are a formidable pair of tools useful in analyzing electric circuits. Their usefulness will become all the more apparent in a later chapter ("Network Analysis"), but suffice it to say that these Laws deserve to be memorized by the electronics student every bit as much as Ohm's Law.

* REVIEW:
* Kirchhoff's Current Law (KCL): "The algebraic sum of all currents entering and exiting a node must equal zero"

Contributors

Contributors to this chapter are listed in chronological order of their contributions, from most recent to first. See Appendix 2 (Contributor List) for dates and contact information.

Jason Starck (June 2000): HTML document formatting, which led to a much better-looking second edition.

Ron LaPlante (October 1998): helped create "table" method of series and parallel circuit analysis.

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