# Questions on Ac power.

1. May 9, 2013

### 0fibonacci1

1. The problem statement, all variables and given/known data

I have some questions about powers in AC circuit. What is the maximum and minimum current power on resistor and inductance.

2. Relevant equations

Um = U / V2
Im = I / V2

3. The attempt at a solution
prmax = U*I=(Um/V2)*(Im/V2)=(Um*Im)/2. But answer seems to actually be that prmax = Um*Im, how can that be? And for plmax = 1/2 Um * Im plmin=- 1/2 Um *Im

2. May 9, 2013

### tiny-tim

hi 0fibonacci1!

your notation is difficult to understand

here's an extract from the pf library on impedance
Power:

Power = work per time = voltage times charge per time = voltage times current:

$$P = VI =\ V_{max}I_{max}\cos(\omega t + \phi/2)\cos(\omega t - \phi/2)$$
$$=\ V_{max}I_{max}(\cos\phi + \cos2\omega t)/2$$​
(because $2cosAcosB = cos(A-B) + cos(A+B))$)
$$=\ V_{rms}I_{rms}(\cos\phi + \cos2\omega t)$$
$$=\ \left(V_{rms}^2\left/|Z|\right.\right)(\cos\phi + \cos2\omega t)$$​

So (instantaneous) power is the constant part, $P_{av} = V_{rms}I_{rms}\cos\phi$ (the average power), plus a component varying with double the circuit frequency, $V_{rms}I_{rms}\cos2\omega t$ (so a graph of the whole power is a sine wave shifted by a ratio $\cos\phi$ above the x-axis).​

3. May 10, 2013

### Staff: Mentor

It almost seems that you might be using V2 as denoting 2 ?