Power Dissipation in a Resistor: Calculate Average

[dortec]

A resistor draws a current i=8sinwt at a voltage of v=200sinwt. Calculate the average power dissipated in the resistor.

What i did is p=ui = 1600sin^2 (wt) and i got stuck:P i don't think it's the right equation.. the answer should be 800W .. and that's nothing like it.
Could someone help me ?

 

[tiny-tim]

Hi dortec!

(have an omega: ω and try using the X² tag just above the Reply box )

Hint: for a resistor, the power factor, cosφ, is 1, and so P_average = V_rmsI_rms

 

[dortec]

Can you rephrase what you just said please. i actually didnt understand. wat's rms? and what do u mean by have an omega.. can u re-explain please:S

 

[tiny-tim]

Hi dortec!

rms means "root-mean-square" … do you know what that is?

(if you don't, you can get the same result by finding the average value of sin²ωt, which you get by integrating it from 0 to 2π)

(and where you typed w, I assumed you would have preferred ω. )

 

[dortec]

nope i don't know what root-mean-square:S and my bad for the omega thing:P.. can u please show me how to solve it?

 

[tiny-tim]

ok, never mind if you haven't done root-mean-square …

just find the average value of your original P(t) = 1600sin²ωt, which you get by integrating it from 0 to 2π/ω, and dividing by … ?

(alternatively, just write 1600sin²ωt in terms of cos2ωt and/or sin2ωt, and then the average is obvious )