conservation of avg power - help me set up the equation

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Joined Mar 21, 2009
I'm working through the Clayton Paul text "Analysis of Linear Circuits" (1989!) and I'm stuck on a simple conservation of power exercise. Drill problem 6.18 on page 292.

The exercise is just "Verify the conservation of average power". The circuit was previously solved in the text for the current through the resistor, i(t). That formula is indicated on the diagram.

I'm having trouble setting up the equation for power.

At this point in the text, the concepts of AC power, phasor circuits, and the power equations have been derived.

Given that inductors and capacitors don't consume real power, I was trying to develop my equation with just the resistor (Power absorbed = 1/2 I^2*R) and the two independent sources (= V1*i(t) + (V1 - Vr)*I1). But, I couldn't get it to work out.

This should be straightforward, but I'm struggling. Anyone see the equation?

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