# In Diar Need of HELP! PLEASE!!!!!(Current phase)

#### lsecrease

Joined Sep 4, 2008
6
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!!!

#### Ratch

Joined Mar 20, 2007
1,068
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

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#### Papabravo

Joined Feb 24, 2006
12,301
Can you do it without using calculus? I know it, but maybe the OP doesn't.

#### Ratch

Joined Mar 20, 2007
1,068
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