Can I Calculate a Power Triangle with Given Voltage and Current?

[AngusBurger]

This is an enquiry into whether something is possible, so the numbers might be rubbish to work with.

If I apply a voltage of v=25sin(wt+0.2rads) to a circuit, with a resultant current of i=15sin(wt-0.5rads), can I work out all three sides of a power triangle? I've been working on it for about an hour but with no such luck.

This is what I have done so far:

V_RMS*I_RMS = 25*15 = 375 Volt-Amps

So long as that is correct, my guess would be that I have to find the True Power, perhaps using the formula P=VIcosϕ, and then I can use Pythagorus theorem to find the volt-amps reactive (var), which would be with the formula var²=VA²-W². If that's not right, I assume I would have to work backwards in order to calculate an impedance?

Any help with this would be much appreciated. I think that it is possible using only a source voltage and resultant current, but am obviously to new to the subject to properly hack it out.

 

[tiny-tim]

Welcome to PF!

Hi AngusBurger! Welcome to PF!

(have an omega: ω )

The instantaneous power is P(t) = V(t)I(t).

If you multiply it out, and use a bit of trig, you find that P(t) = V_rmsI_rms(cosφ + cos2ωt).

(So the average power is P_av = V_rmsI_rmscosφ.)

You don't need to find the impedance for this.