Superposition Problem with Four Voltage and Current Sources

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Electrical Circuits, Electrical Circuits Problems, Resistive Circuits

Determine $V_x$ and $I_x$ using the superposition method.
A circuit with four voltage and current sources to be solved by the superposition method
Solution
I. Contribution of the $-5V$ voltage source:

To find the contribution of the $-5V$ voltage source, other three sources should be turned off. The $3V$ voltage source should be replaced by short circuit. The current source should be replaced with open circuits, as shown below.

Superposition - Finding the contribution of the -5V voltage source

It is trivial that $I_{x1}= \frac{-5 V}{2 \Omega}=-2.5 A$ . The current of the $3\Omega$ resistor is zero. Using KVL, $-(-5V)+V_{3\Omega}-V_{x1}=0 \to V_{x1}=-(-5V)=5V$ .

II. Contribution of the $3V$ voltage source:
Similarly, the $-5V$ voltage source becomes a short circuit and the current source should be replaced with open circuits:
Superposition - Contribution of the 3V voltage source

The current of the $2\Omega$ resistor is zero because of being short circuited. It is trivial that $I_{x2}= 0 A$ (current of an open circuit). The current of the $3\Omega$ resistor is also zero. Using KVL, $-(3V)+V_{2\Omega}+V_{x2}+V_{3\Omega}=0 \to V_{x2}=3V$ .

III. Contribution of the $-1A$ current source:
The voltage sources should be replaced by short circuits and the $2A$ current source becomes with open circuit:

Superposition - Contribution of the -1A current source
Again, the $2\Omega$ resistor is short circuited and its current is zero. it is clear that $I_{x3}= 1 A$ . The current of the $3\Omega$ resistor is equal to $-1A$ . Using KVL, $V_{x3}+V_{3\Omega}=0 \to V_{x3}+(-1A)\times (3\Omega)=0 \to V_{x3}=3V$ .

IV. Contribution of the $2A$ current source:
Likewise, the voltage sources should be replaced by short circuits and the $-1A$ current source becomes with open circuit:
Superposition - Contribution of the 2 A current source

Again, the $2\Omega$ resistor is short circuited and its current is zero. it is also trivial that $I_{x4}= 0A$ . The current of the $3\Omega$ resistor is $2A$ . Using KVL, $V_{x4}+V_{3\Omega}=0 \to V_{x4}+(2A)\times (3\Omega)=0 \to V_{x4}=-6V$ .

V. Adding up the individual contributions algebraically:

$V_x=V_{x1}+V_{x2}+V_{x3}+V_{x4}=5V+3V+3V-6V\to V_x=5V$
$I_x=I_{x1}+I_{x2}+I_{x3}+I_{x4}=-2.5A+1A+0A-0A\to I_x=-1.5A$

Superposition Superposition Method Superposition_Method Turning sources off

Comments

19 responses to “Superposition Problem with Four Voltage and Current Sources”

January 28, 2011

Sophie Kovalevsky

Dr, where can I contact u?
Do you have a email where i could contact u? I have some problem to public in the web.

Reply
1. January 29, 2011
  
  Dr. Yaz Z. Li
  
  Hi Sophie,
  My email is yaz at solved-problems dot com. I promoted you account and you should be able to submit problems from here
  
  Thanks,
  Yaz
  
  Reply
January 29, 2011

Sophie Kovalevsky

I’m so really excited teacher.
Thank you so much to active my account to submit problem.

Reply
March 1, 2011

abrar

i want super position problems with 3 sources

Reply
September 14, 2011

sham

i will appreciate u please include the more problems

Reply
September 14, 2011

sham

i will appreciate u please include the more problems 4 Responses to Superposition Problem with Four Voltage and Current Sources

Reply
1. September 14, 2011
  
  sham
  
  k thank u
  
  Reply
2. December 6, 2020
  
  Lalit shete
  
  Use superposition theorom to determine the voltage across the current source in circuit
  
  Reply
October 17, 2011

Phung Cao-Minh

Dear Dr. Yaz Z. Li,
In Problem 1-13: Voltage of A Current Source, question b (http://circuits.solved-problems.com/413/ideal-independent-sources).

I want to find out the current across resistor 10 Ohm, = ?.

Thank you so much!

Reply
1. October 17, 2011
  
  Dr. Yaz Z. Li
  
  The voltage across the resistor is 2V. Therefore, $I_{10\Omega}=\frac{2V}{10 \Omega}=0.2 A$ .
  
  Reply
October 30, 2011

rehan

sir can u tell me some more example of nodal and superposition analyses

Reply
1. October 30, 2011
  
  Dr. Yaz Z. Li
  
  For superposition solved problems, see these.
  For nodal analysis prolems, check out the ebook and these.
  
  Reply
November 20, 2011

alveena

sir can you plz guide about some source transformation problems as well….

Reply
March 17, 2012

anubhab91

Your works are very helpful.

Reply
March 17, 2012

anubhab91

I can’t download your eBook, please help.

Reply
October 27, 2013

Awesome

Thank you so much. I love your notes. Short but precise !

Reply
January 25, 2015

anil

Sir this all numericals are very helpful but I have some small questions arrise in my mind which I want to know xo sir plz tell me how can I contact u plz

Reply
September 13, 2015

ansari anas

nice

Reply
August 20, 2018

adarsh minz

one requested problem from my side is a circuit containing two independent current sources using superposition theorem

Reply