Ok, I realize this to be true but how do you prove that a circuit whose current is 90 degrees out of phase with the driving voltage consumes no power, averaged over an entire cycle???

Thanks a MILLION!!!

 

lsecrease,

Ok, I realize this to be true but how do you prove that a circuit whose current is 90 degrees out of phase with the driving voltage consumes no power, averaged over an entire cycle???

Why, it is childishly simple. Assuming sinusoidal waveforms, we get the average power by taking the average of the instantaneous power over a complete period. The instantaneous power of a "90 degrees out of phase" voltage*current is proportional to sin(x)*cos(x). The integral of sin(x)*cos(x) is (sin^2(x))/2. Pluging in the limits of the period 0 to 2*pi gives 0. Dividing by the period to get the average is still 0. Doing the same with and in-phase voltage*current means using either sin^2(x) or cos^2(x), which gives an answer of 1/2.

Ratch

 

Can you do it without using calculus? I know it, but maybe the OP doesn't.

 

Papabravo,

Can you do it without using calculus? I know it, but maybe the OP doesn't.

Until the OP says otherwise, I will assume he does.

Ratch