# Homework Help: Superposition Principle to Solve Circuit

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1. Feb 13, 2015

### Gwozdzilla

1. The problem statement, all variables and given/known data

2. Relevant equations

KVL: ΣV = 0
KCL: ΣI = 0

v = iR

3. The attempt at a solution
I started by removing the independent current source to leave an open circuit. Then I attempted nodal analysis at nodes v1, v2, and v3:

KCL @ v1:
(v1 - v2)/10 = v1/40

KCL @ v2:
(v2 - v1)/10 - 4io + (v2 - (-30))/20 = 0

KCL @ v3:
v3 = -30 V

io = (v1 - v2)/10

Plugging equation 4 into euation 2 and simplifying gives...

.1v2 - .1v1 -.4v1 + .4v2 + (v2 - (-30))/20 = 0

.55v2 - .5v1 + 1.5 = 0

Simplifying equation 1:

.1v1 - .1v2 = .025v1

v2 = .75v1

Plugging this in...

.55(.75v1) - .5v1 + 1.5 = 0

...

v1 = 17.1V

v2 = 12.9V

This makes io = .42A which is wrong.

Where did I mess up?

2. Feb 13, 2015

### Staff: Mentor

In your first node equation you've fallen into the trap of giving a wrong sign to one of the terms. This happens most often when one tries to write the equation on both sides of the equal sign rather than as a sum of terms all on one side. It's natural to think that the two current terms are equal and so write them both as positive values on either side, but consider what happens if you move a term from one side to the other.