How do I get v0 using superposition in this circuit?

Question

I'm trying to get the value of \$V_o\$ in this circuit. Here's the circuit:

Using Superposition theorem:

So first, we remove the voltage source and replace it with a short circuit. Then we calculate \$V_o\$.

Second, we remove the 1A current source replace it with an open circuit, then we calculate \$V_o\$.

Third, we remove 2A current source and replace it with an open circuit, then we calculate \$V_o\$.

Finally, we should add the three values of \$V_o\$ that we got in each case and thus we get the final answer of the total \$V_o\$.

My problem is that I'm unable to calculate the value of \$V_o\$ in each case, what exactly should I do after removing the source to get \$V_o\$. Any help is much appreciated!

Answer 1

No, you pick a single source to use in your 1st analysis and, for ALL the other sources, you make them short (voltages) or open (current). That's how superposition works for each source. Then you add the individual voltages derived for each \$V_O\$ to produce the final value of \$V_O\$.

In other words:

Use one source with the others disabled then step and repeat for each source: -

Answer 2

The superposition principle states that the voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across (or currents through) that element due to each independent source acting alone.

So you have to turn off all the sources (shorting voltage sources and opening current sources) except the source you would like to know its response on \$V_o\$.

In your problem you have 3 sources, so you will have 3 values that their sum will produce \$V_o\$.

Here is our original circuit.

First step:

Remove l1 and l2 current sources and calculate the voltage across R4. Assume it is \$v_1\$.

Second step:

Remove B1 and l1 sources, and calculate the voltage across R4 again. Assume it is \$v_2\$.

Third step:

Remove B1 and l2 sources, and calculate the voltage across R4 again. Assume it is \$v_3\$.

Final step:

Calculate the algebraic sum.

\$V_o\$= \$v_1 + v_2 + v_3 \$.