Understanding AC Power: Maximum and Minimum Currents on Resistor and Inductance

[0fibonacci1]

Homework Statement

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

Homework Equations

Um = U / V2
Im = I / V2

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 * I am plmin=- 1/2 Um *Im

 

[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:

[tex]P = VI =\ V_{max}I_{max}\cos(\omega t + \phi/2)\cos(\omega t - \phi/2)[/tex]
[tex]=\ V_{max}I_{max}(\cos\phi + \cos2\omega t)/2[/tex]​

(because [itex]2cosAcosB = cos(A-B) + cos(A+B))[/itex])

[tex]=\ V_{rms}I_{rms}(\cos\phi + \cos2\omega t)[/tex]
[tex]=\ \left(V_{rms}^2\left/|Z|\right.\right)(\cos\phi + \cos2\omega t)[/tex]​

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

 

[NascentOxygen]

The Attempt at a Solution

prmax = U*I=(Um/V2)*(Im/V2)=(Um*Im)/2.

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