Doubt in Superposition Theorem

I think the problem comes down to looking at how to use the principle of superposition without understanding what it is all about.

For a linear circuit (and superposition only applies to linear circuits), the solution for every voltage or current in the circuit will be of the form:



for a circuit with two independent voltage supplies and two independent current supplies.

If x is a voltage, the A and B will be dimensionless and C and D will have units of resistance. If x is a current, then A and B will have dimensions of conductance while C and D will be dimensionless. The important this is that the quantity of interest, x, will be a linear sum of terms with each term involving exactly one of the independent supplies.

Now, this can be written in terms of four partial results



where



If we can find the four simpler quantities, then we can just add them together to get the final result.

But what does mean, physically? Well, what did the original expression for x mean, physically? Simple. It told us how to find the value of x as a function of different values for the outputs of the four independent sources. So what if we just choose to set all but one of these to zero? Again, simple. All we are left with is the single term that we did not set to zero.

From a circuit standpoint, this is the same as setting the voltage on a voltage source to zero, meaning that any amount of current can flow through the supply but no voltage can appear across it. Well, that is the description of a piece of wire, so we can effectively set the voltage on a voltage source to zero by replacing it with a short circuit. Similarly, setting the current on a current source to zero means it can have any voltage across it, but can have no current through it, which is the description of an open circuit. So we turn off current supplies by replacing them with an open circuit.

Thus, in its simplest form, we can turn off all the independent supplies and then turn one of them on and analyze all the quanties in the circuit we are interested in. Then turn that one back off and turn on another one and do the same thing. We keep doing this until each supply has been turned on exactly once and then add all the results together.

 

A constant voltage source maintains a constant voltage between two nodes but lets any amount of current (source or sink) to flow through the source in order to achieve that.

A constant current source maintains a concetant current between two nodes but lets any amount of voltage (source or sink) to appear across the source in order to achieve that.