How do I use superposition to solve a circuit?

Yes, this is a pedagogical question. While answering another recent question, I wanted to refer the OP to concise instructions for using superposition to solve circuits. I found that all the easily found resources online were somewhat deficient. Typically they were unclear about what kinds of circuits superposition applies to, or about the actual method to apply the superposition theorem to a circuit problem. So,

What kinds of circuits can be solved by superposition?

How are different kinds of sources treated when solving by superposition?

What are the steps to solve a circuit using the superposition theorem?

Answer

Superposition theorem
"The superposition theorem for electrical circuits states that for a linear system the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internal impedances."

What kinds of circuits can be solved by superposition?

Circuits made of any of the following components can be solved using superposition theorem

• Independent sources


• Linear passive elements - Resistor, Capacitor and Inductor


• Transformer


• Linear dependent sources

What are the steps to solve a circuit using the superposition theorem?

Follow the algorithm:

1. Answer = 0;


2. Select the first independent source.


3. Replace all independent sources in original circuit except the selected source with its internal impedance.


4. Calculate the quantity (voltage or current) of interest and add to Answer.


5. Exit if this was the final independent source. Else Goto step 3 with selecting next source.

The internal impedance of a voltage source is zero and that of a current source is infinity. So replace voltage source with a short circuit and current source with open circuit while executing step 3 in the above algorithm.

How are different kinds of sources treated when solving by superposition?

The independent sources are to be treated as explained above.

In case of dependant sources, do not touch them.