A problem of finding output voltage using Superposition Theorem

Question

I have approached the problem by trying to find out the current through the 2 ohm internal resistor.

Considering only the 6 A current source,the current I1 in the 2 ohm resistor is calculated to be 1 A in the downward direction.

Considering only the 4 A current source,the current I2 in the 2 ohm resistor becomes 2 A in the downward direction.

Considering only the 6 V source,the current I3 in the 2 ohm resistor comes out to be 1 A in the upward direction.

. . . The net current I in the 2 ohm resistor becomes 2 A in the downward direction.

Now,since the current is flowing from the positive to the negative terminal inside the voltage source,we can assume it being charged.

So,output voltage V0 becomes V0=E+Ir which gives the result of 10V.

Now,some of my engineering batchmates are insisting that positive and negative terminals be assigned to the ideal voltage(in the sense opposite to the polarities of the output source)source and current I3 be flown in the downward direction.

Hence,I have resorted to questioning on this platform to resolve the above stated conflict.

Thanks a lot for reading.

Answer 1

If I understand your question, your batchmates are correct. You can't solve the problem without a defined polarity for the ideal voltage source. The answer could be 10 V as you calculated, or it could be -2 V depending on the polarity of the 6 V. So, to remove the ambiguity you should assign a polarity to the source on the diagram.

If your batchmates are suggesting that the polarity of the source must be opposite of the polarity you defined as "Vout" I don't see that as a requirement anywhere in the problem statement, so you should ask them for their reasoning.

Answer 2

The polarity of the 6V source needs to be indicated or assumed

Answer 3

The polarity of 6V voltage source is not indicated. Assuming it is up or down, then you can use one source at a time. You may want to do the exercise both ways.

Hint:

The general rule of superposition theorem with energy sources are:

If the energy source is a voltage source, it is short circuited when not used. If the energy source is a current source, it is open circuited when not in use.

These energy sources such as a current or voltage source are called stimuli. Use one source at a time and use mesh or nodal analysis to calculate the current in the branch on right. Assume names for current sources and voltage source as \$I_{i1}, I_{i2}, V_{1} \$. Final current in the branch on right should be \$I = I_{i1} + I_{i2} + I_{V1} \$. Output voltage should be (I*2) -/+ 6v depending on polarity of 6V voltage source.