# Superposition Thereom

Discussion in 'Homework Help' started by Evilsanta31, Dec 29, 2014.

1. ### Evilsanta31 Thread Starter New Member

Dec 29, 2014
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0
New to the site so be easy with me. Started doing my HNC in electrical and electronic engineering and one of my questions is to solve current through the load resistor using different methods. One of those methods is the superposition theorem and tbh I just cant understand how it works. Ive seen the superposition theorem link and tried following but I just dont get how it works, can anyone give me a real simplified way of doing it or a few pointers in the right direction.

Thanks Alan

2. ### Evilsanta31 Thread Starter New Member

Dec 29, 2014
23
0
Here is my attempt at it from what I understand hopefully its right.

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3. ### WBahn Moderator

Mar 31, 2012
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Basically it boils down to the following: For a linear circuit with, say, two independent voltage sources and two independent current sources, the voltage at any point in the circuit will be of the form:

$
V_n \; = \; a_1V_1 \. + \. a_2V_2 \. + \. b_1I_1 \. + \. b_2I_2
$

where the 'a' and 'b' values are constants ('a' is dimensionless and 'b' has units of V/A, or ohms). You get a comparable equation for the current at any point in the circuit, except now the 'a' coefficients have units of A/V while the 'b' coefficients are dimensionless.

No matter what we adjust the voltage sources or current sources to, this equation will still apply and we just need to use the new values for the voltage and current source outputs.

But this means that we can set one of the sources to its actual value and set all of the other sources to zero and what we will get is the portion of the above equation corresponding to just the term for the source that is on. If we repeat this procedure for each source in turn, then we will end up with four values that, when added together, give us the same value as if we had evaluated the expression with all four turned on at the same time. This is what superposition is all about.

So we turn off all but one source by setting the voltage across all voltage sources (that are off) to zero, but that means that the voltage source is acting like a short circuit so we can just replace all 'off' voltage sources with a short. Similarly, we turn set the current through all current sources (that are off) to zero, but that means that the current source is acting like an open circuit so we can just replace all 'off' current sources with an open.

We repeat this process for each independent source keeping track of all of the voltages and currents that are of interest to us and then adding them all up at the end.

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