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Verification of Thevenin Theorem

Objective: To Verify Thevenin Theorem.

Its provides a mathematical technique for replacing a given network, as viewed from two terminals, by a single voltage source with a series resistance. It makes the solution of complicated networks quite quick and easy. The application of this extremly useful theorem will be explained with the help of following simple example.




Circuit diagram:







 Suppose, it is required to find current flowing through load resistance RL, as shown in above figure.


This expression proceed as under:


1) Remove RL from the circuit terminals A and B and redraw the circuit as shown in figure. Obviously, the terminal have become open circuited.



Circuit diagram:






2) Calculate the open circuit Voltages VO.C. which appears across terminals A and B when they are open .ie. when RL is removed.


As seen, V.O.C.= drop across R2= IR2 where I is the circuit current when A and B is open.


                                                                                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»I«/mi»«mo»=«/mo»«mfrac»«mi»E«/mi»«mrow»«mi»r«/mi»«mo»+«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»+«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«msub»«mi»V«/mi»«mrow»«mi»o«/mi»«mo».«/mo»«mi»c«/mi»«mo».«/mo»«/mrow»«/msub»«mo»=«/mo»«mi»I«/mi»«mo»*«/mo»«msub»«mi»R«/mi»«mrow»«mn»2«/mn»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mrow»«/msub»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mrow»«mi»E«/mi»«mo»*«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«mrow»«mi»r«/mi»«mo»+«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»+«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»

 It is also called Thevenin voltage(Vth).


3) Now, imagine the battery to be removed from the circuit, leaving its internal resistance r behind and redraw the circuit as shown in figure below.


Circuit diagram:







When viewed inwards from the terminals A and B, the circuit consists of two parallel paths: one containing R2 and another containing


(R1+r). The equivalent resistance of the network as viewed from these terminals is given as,


                                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«msub»«mi»R«/mi»«mrow»«mi»t«/mi»«mi»h«/mi»«/mrow»«/msub»«mo»=«/mo»«mfrac»«mrow»«mo»(«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»+«/mo»«mi»r«/mi»«mo»)«/mo»«mo»*«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«mrow»«mo»(«/mo»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»+«/mo»«mi»r«/mi»«mo»+«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»)«/mo»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»
The resistance "Rth" is also called Thevenin equivalent resistance.
Consequently , as viewed from terminals A and B, the whole network (excluding R1) can be reduced to single source ( called thevenin's
source) whose e.m.f equal to VO.C. and whose internal reistance equal to Rth.  

4) RL is now connected back across terminals A and B from where it was temporaily removed earlier. Current flowing through RL is given by, 
                                                       «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd/»«/mtr»«mtr»«mtd»«msub»«mi»I«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mfrac»«msub»«mi»V«/mi»«mrow»«mi»t«/mi»«mi»h«/mi»«/mrow»«/msub»«mrow»«mo»(«/mo»«msub»«mi»R«/mi»«mrow»«mi»t«/mi»«mi»h«/mi»«/mrow»«/msub»«mo»+«/mo»«mi»R«/mi»«msub»«mo»)«/mo»«mi»L«/mi»«/msub»«/mrow»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»

 Circuit Diagram:


Cite this Simulator:

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