Given voltage and current equations, find instantaneous Power

[dphysics]

Homework Statement

The voltage across and current through a certain device are given by:
v(t) = 5cos(4*pi*t)
i(t) = .1cos(4*pi*t)

Determine:
(a) the instantaneous power p(t) at t= 0 and t = .25 seconds
(b) the average power pav, defined as the average value of p(t) over a full time period of the cosine function (0 to .5 seconds)

Homework Equations

Power = Voltage * Current

The Attempt at a Solution

(a) I plugged 0 and .25 in for t into both of the equations, and multiplied the answers together. For both t = 0 and t = .25, I got .5 Watts for my answer. In the back of the book, it says for t = 0 it should be 0 watts, and for t=.25 s .5 watts. I got the answer correctly for t=.25s, but what am I missing for the beginning part? I have been going over this problem for a while now and I cannot figure it out for the life of me.

(b) 1/(b-a) *integral (i(t)*v(t)) evaluated from a to b, a being 0 and b being .25 seconds. I'm pretty sure this is the right direction for this part.

Thanks in advance for your time / help!

 

[Redbelly98]

(a) I agree with your answer, the power is 0.5 W at t = 0 s. You might double-check that the expressions for v and i you used are correct, but it sounds like you've looked things over pretty carefully already.

(b) Yes, that's exactly the way to do it. Integrate p over 1 period.