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## Homework Statement

For the above circuit, find the coefficients of the linear relationship v

_{out}= a

_{1}v

_{s1}+ a

_{2}i

_{s2}+ a

_{3}i

_{s3}by superposition. Then find the power delivered to R

_{3}when v

_{s1}= 100 V, i

_{s2}= 2 A, and i

_{s3}= 4 A. Given: R

_{1}= 20 Ω, R

_{2}= 60 Ω, and R

_{3}= 20 Ω.

## Homework Equations

Ohm's Law: V = IR

KVL: V

_{1}+ V

_{2}+ ... V

_{n}= 0 for closed loops

KCL: I

_{1}+ I

_{2}+ ... I

_{n}= 0 going in an out of a node

Voltage Division: V

_{1}= V

_{source}* (R

_{1}/(R

_{1}+R

_{2}))

## The Attempt at a Solution

I think I got the first two coefficients (though I could be incorrect). I found v

_{out}

^{1}= v

_{s1}*(R

_{3}/(R

_{1}+R

_{2}+R

_{3})) = 0.2V

_{s1}through voltage division. I'm pretty certain that's correct.

I also found that v

_{out}

^{2}= I

_{s2}*R

_{3}= 20I

_{s2}, though I'm not quite as certain about that.

But I absolutely cannot wrap my head around finding v

_{out}

^{3}(when all independent sources are eliminated except I

_{s3}). I understand that in that situation, the I

_{s2}branch essentially disappears and we are left with I

_{s3}in parallel with a branch with R

_{2}and a branch with R

_{1}and R

_{3}, but we can't combine those since v

_{out}

^{3}must stay isolated. I'm not sure what to do.