Thévenin’s Theorem – Circuit with An Independent Source

Written by

Yaz

Electrical Circuits, Electrical Circuits Problems, Resistive Circuits

Use Thévenin’s theorem to determine $V_O$ .

Fig. (1-26-1) – The Circuit

Solution
To find the Thévenin equivalent, we break the circuit at the $4\Omega$ load as shown below.

Fig. (1-26-2) – Breaking the circuit at the load

So, our goal is to find an equivalent circuit that contains only an independent voltage source in series with a resistor, as shown in Fig. (1-26-3), in such a way that the current-voltage relationship at the load is not changed.

Fig. (1-26-3) – Replacing the Thevenin equivalent circuit

Now, we need to find $V_{Th}$ and $R_{Th}$ . $V_{Th}$ is equal to the open circuit voltage $V_{OC}$ shown in Fig. (1-26-2). The current of $2\Omega$ resistor is zero because one of its terminals is not connected to any element; therefore, current cannot pass through it. Since the current of $2\Omega$ resistor is zero, the $9V$ voltage source, $3\Omega$ and $6\Omega$ resistors form a voltage divider circuit and the voltage across the $6\Omega$ resistor can be determined by the voltage devision rule. Please not that we are able to use the voltage devision rule here just because the current of the $2\Omega$ resistor is zero. You may ask that there is no reason to prove that the current of the $2\Omega$ resistor is zero in the original circuit shown in Fig. (1-26-1). That is correct. However, we are calculating $V_{OC}$ for the circuit shown in Fig. (1-26-1) and this is a different circuit. The Thévenin theorem guarantees that $V_{Th}=V_{OC}$ , it is not saying that $V_{OC}$ is the voltage across the load in the original circuit.

$V_{6\Omega}=\frac{6\Omega}{3\Omega+6\Omega}\times 9 V= 6V$
Since the current of the $2\Omega$ resistor is zero:
$V_{OC}=V_{6\Omega}=6V$
$V_{Th}=V_{OC}=6V$
Now, we need to find $R_{Th}$ . An easy way to find $R_{Th}$ for circuits without dependent sources is to turn off independent sources and find the equivalent resistance seen from the port. Recall that voltage sources should be replace with short circuits and current sources with open circuits. Here, there is only a voltage source that should be replaced by short circuit as shown in Fig. (1-26-4).

Fig. (1-26-4) – Turning off the voltage source to find Rth

It is trivial to see that the $3 \Omega$ and $6 \Omega$ resistors are connected in parallel and then wired in series to the $2\Omega$ resistor. Therefore,
$R_{Th}=(3\Omega || 6\Omega)+2\Omega=\frac{3\Omega \times 6\Omega}{3\Omega + 6\Omega}+2\Omega=4\Omega$ .
Now that $V_{Th}$ and $R_{Th}$ are found, we can use the Thévenin equivalent circuit depicted in Fig. (1-26-3) to calculate $V_O$ in the original circuit shown in Fig. (1-26-1). The voltage devision rule can be used here to find $V_O$ . We have,
$V_{O}=\frac{4\Omega}{R_{Th}+4 \Omega}\times V_{Th}=\frac{4\Omega}{4\Omega+4 \Omega}\times 6V=3V$ .

Thévenin thevenin equivalent circuit Thevenin_Norton Thévenin’s Equivalent Thévenin’s Theorem

Comments

38 responses to “Thévenin’s Theorem – Circuit with An Independent Source”

January 23, 2011

madhuri

It is good.But,it could be more better to give some more information.

Reply
January 23, 2011

madhuri

It is good.But,it could be more better to give some more information and examples.

Reply
1. January 25, 2011
  
  Dr. Yaz Z. Li
  
  Sure
  
  Reply
January 25, 2011

manasa

How to find the current through given(particular) resistor when a source voltage is given?

Reply
1. January 29, 2011
  
  Dr. Yaz Z. Li
  
  Dear Mansa,
  
  Your question is very general. All methods explained here can be used and the best method is totally depended on the circuit topology. Please explain or give a link to image of the circuit that you are talking about.
  
  Reply
January 25, 2011

manasa

What are the steps to be followed to find the current through given (particular) resistor when a source voltage is given using norton’s theorem?

Reply
January 31, 2011

syed humayoon shah

sir i am the student of electronic engineering but i am not satisfied from my university teachers,as they are not so much attentive and hardworking……….so plzzzzzzz tell me how can i learn my basics of electronic circuits course concept wise…..i need your kind supports,becoz i wanna to become a great engineer of the furture.
regsrds

Reply
1. January 31, 2011
  
  Dr. Yaz Z. Li
  
  Dear syed humayoon shah,
  
  If you are a hardworking student, you do not need university teachers. There are a handful of resources such as books, notes, websites,… that you can read and learn.
  
  Reply
February 4, 2011

smita

its very gud…..

Reply
February 22, 2011

bakhtawer

sir i have a prolum in which at last there is no paralaell circuit with the load so how can i ind the voltage

Reply
1. March 1, 2011
  
  Dr. Yaz Z. Li
  
  Would you show me an example?
  
  Reply
March 5, 2011

Prachiti

Sir pls tell me how to solve problems on equivalent resistances based on star-delta transformation effectively….

Reply
April 28, 2011

kishore

sir, nodal analysis using kcl can lead us quick ans

Reply
1. May 27, 2011
  
  Dr. Yaz Z. Li
  
  Yes, but it is asked to solve this problem by Thévenin’s Theorem.
  
  Reply
June 12, 2011

Mahesh

sir, why capacitor acts as open circuit at steady state current ?

Reply
1. June 12, 2011
  
  Dr. Yaz Z. Li
  
  This is unrelated to this post.
  Anyway, $i_c(t)=C\frac{V_c(t)}{dt}$ . $V_c(t)$ is constant in steady state, therefore $\frac{V_c(t)}{dt}=0$ and $i_c(t)=0$ . This shows that no current passes through a capacitor so it acts like an open circuit.
  
  Reply
August 3, 2011

kartheeka.k

sir i dont understand how to solve thevinens thearom with dependent sources

Reply
August 7, 2011

mufu tee

very very nice blog. More grease to your elbow

Reply
August 29, 2011

likitha

how can we find vth and rth if another resistor of 5 ohms is conected parallel to 4 ohm resistor?

Reply
October 5, 2011

Shrabanee

Sir,if v hv d load resistance parallel wth source voltge nd current n some resistances with it how cn v find d thevenin’s equivqlent voltage across that load resistance?

Reply
November 15, 2011

george

great work,l think more examples willn’t be less appreciated

Reply
December 18, 2011

Amit

How to solve a problem when load is connected with a current or voltage source?
Will the voltage across the load(Vth) will be equal to the voltage of the battery itself?

Thank you

Reply
January 12, 2012

ambi

how can we solve the superposition theorem problems using thevenin theorem… also when two voltage sources on opposite sides have opposite polarity…..

Reply
January 24, 2012

C M Kashif Abrar

this web realy help me in my study.
Thanks for this Great work.

Reply
February 16, 2012

Anusha

I think i have a silly doubt. But i dont understand how 3 ohm and 6 ohm resistors are connected in parallel in that problem 🙁 .. can u pls explain?? I’m new to these concepts.

Reply
1. February 16, 2012
  
  Dr. Yaz Z. Li
  
  Two elements are connected in parallel if they are connected at both sets of terminals.
  3 ohm and 6 ohm are in parallel only when we make the 9V voltage zero to find Rth, as shown in Fig. (1-26-4).
  
  Reply
March 31, 2012

d rishab

sir i truly appreciate ur problem solving and i would love to see more examples i want to get registered in ur website but i am encountering problems please it would be good if u fix it

Reply
April 2, 2012

Christina

dear sir,
please include complicated circuit’s solutions also.

Reply
April 3, 2012

Susmita

hi,plz give some examples of thevenin’s and norton’s theorem with dependent source.

thanks in advance.

Reply
April 15, 2012

allan

sir, may i get Io by dividing V0 by 4 Ohms? thanks.

Reply
April 15, 2012

Osama

I am student of Material Science and Engineering but i am studying basic circuits as a subject in 4rth semester. You explained the theorem very well . I forward this link to my classmates hope they’ll find it helpful .Thanks

Reply
April 20, 2012

Aselano King

Do you always enter the electric current from the cathode or the anode

Reply
May 8, 2012

sourav mukherjee

this examples are to simple give some complicated ones.

Reply
June 2, 2012

adrian

Hi, I don’t understand why you directly eliminated the 4ohm resistance in order to calculate the thevenin equivalent voltage, if for instance you also have another 6ohm resistance between the 4ohm and the 6ohm resistance, would you take both of them out to also calculate the thevenin equivalent voltage?
Thanks.

Reply
May 3, 2013

Shubhamoy Maity

Please,solve my problem….three resistance of 8 ohm,8 ohm and 4 ohm conected in paraller with two series resistance 5 & 3 ohm which are conected with a voltage source of 10 volt.then,calculate current through 4 ohm.by thevinin theorem.

Reply
1. March 17, 2015
  
  Mokoena M.M
  
  sir I was asking if we are given two resistors that are parallel&series with A on the bottom left then B top right how do we find equivalent resistance
  
  Reply
June 9, 2018

Prasant Nair

But the solution vo is 3v?

Reply
November 20, 2018

dhanushka

dear sir ,
what if the batteries are having internal resistance.must it be considered when calculating open cct voltage(Vth).?????????

Reply