Problem about superposition theorem

Question

For the circuit given below the voltage across the resistor is definitely 5V. If we add more than two sources the voltage will remain same as before. circuit

If we try to analyze the circuit with superposition then first we have to make one of the source inactive. If we make one voltage source inactive then we can find the voltage 0V. enter image description here After that we have to make inactive the another source. At that time the voltage remains 0V.

So if we add the two voltages according to superposition theorem the voltage across the load is 0V. How???

Because you need to know when to short supplies, and when to leave them open. BTW in the last example to the supply there is no load just a short — Voltage Spike, Aug 01 '17 at 01:01

score 2 · Accepted Answer · answered Sep 08 '14 at 19:33

You are misapplying the superposition theorem. When you calculate the response to a source, other sources must be passivated. In the case of a voltage source, the same is replaced by a short circuit.
If in this particular case, try to apply the theorem, both sources will be connected in short, implying that the voltage on the resistance would be zero, while each voltage source should deliver an infinity current.
Clearly, there is a singularity for which circuit theory of lumped parameters does not apply.

If the voltage sources they were replaced by real models, considering its internal resistance

schematic

^{simulate this circuit – Schematic created using CircuitLab}

you can apply the Superposition Theorem smoothly.

Yeah.. I've just edited it. – Raihan Khalil Sep 09 '14 at 01:19 — Raihan Khalil, Sep 09 '14 at 01:19

Amit Hasan · Answer 2 · 2014-09-09T07:41:04.833

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Two condition you must consider to apply superposition theorem-

The number of sources of the network must be two or more.
Sources are not in series (current sources) or parallel (voltage sources).

The second condition says that you cannot apply super position theorem in a circuit where two voltage sources are connected in parallel. Therefore, the circuit you are showing doesn’t give you a valid result when you use superposition theorem.

We can change the circuit to something else so that superposition theorem is applicable but that wouldn’t be the given problem.

edited Sep 09 '14 at 07:41

answered Sep 09 '14 at 01:50

Amit Hasan

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second condition is sources are not in series or parallel. If we connect two voltage source in series then we can definitely apply superposition theorem.. so?? – Raihan Khalil Sep 09 '14 at 03:39
@RaihanKhalil - It means voltage sources should not be in parallel and current sources should not be in series. – Amit Hasan Sep 09 '14 at 07:39

score 1 · Answer 3 · answered Sep 09 '14 at 07:58

There is a singularity in your circuit. You connected two voltage sources in parallel. When you connect voltage sources with different values, \$\frac{\text{value}} {\text{zero}}\$ singularity occurs when calculating the current. And \$\frac{\text{zero}}{\text{zero}}\$ singularity with same ones. And you can't use the superposition theorem in a circuit with a singularity like this.

But don't worry. In practice, you can connect two identical voltage sources in parallel, and it will work in theory if you assume that there is a single source instead of them. Just assume that there is only one 5V voltage source in cases like this.

Problem about superposition theorem

3 Answers3