# Circuit Elements - Power Dissipated

Given the circuit shown in the attachment find: values and power dissipated.

(Please see attachment for complete question and diagram. Thanks)

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#### Solution Preview

I call 200 V V in my work to follow, 40 ohms is R1 , 300 ohms is Ra, and 75 ohms is Rb. ia + ib goes through V and R1. ia goes through Ra and ib goes through Rb. Vo is an unknown potential and ia and ib are unknown currents.

I know charge and currents are conserved.

Potential is conserved/

The power delivered by the potential elements is lost in the resistors of this circuit as the current moves through them.

So I have some circuit equations 1) V-(ia + ib)R1 -iaRa = 0

2) V-(ia + ib)R1 = Vo

3) V(ia + ib) + Voib = P P is the power

4) (ia + ib)^2 R1 + ia^2Ra + ib^2Rb = P

and then I worried as I see a quadratic that I am going to have to solve in ia or ib and I spent about two hours wrestling with this to find that the quadratic collapses as the constant term goes to zero ...

#### Solution Summary

This solution is provided in 797 words. It uses circuit equations to solve for all of the problems.