Superposition Problem with Four Voltage and Current Sources

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

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    Comments

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

    1. Sophie Kovalevsky Avatar
      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.

      1. Dr. Yaz Z. Li Avatar

        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

    2. Sophie Kovalevsky Avatar
      Sophie Kovalevsky

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

    3. abrar Avatar
      abrar

      i want super position problems with 3 sources

    4. sham Avatar
      sham

      i will appreciate u please include the more problems

    5. sham Avatar
      sham

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

      1. sham Avatar
        sham

        k thank u

      2. Lalit shete Avatar
        Lalit shete

        Use superposition theorom to determine the voltage across the current source in circuit

    6. Phung Cao-Minh Avatar

      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!

      1. Dr. Yaz Z. Li Avatar

        The voltage across the resistor is 2V. Therefore, I_{10\Omega}=\frac{2V}{10 \Omega}=0.2 A.

    7. rehan Avatar
      rehan

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

      1. Dr. Yaz Z. Li Avatar

        For superposition solved problems, see these.
        For nodal analysis prolems, check out the ebook and these.

    8. alveena Avatar
      alveena

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

    9. anubhab91 Avatar
      anubhab91

      Your works are very helpful.

    10. anubhab91 Avatar
      anubhab91

      I can’t download your eBook, please help.

    11. Awesome Avatar
      Awesome

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

    12. anil Avatar
      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

    13. ansari anas Avatar
      ansari anas

      nice

    14. adarsh minz Avatar
      adarsh minz

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

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