Integration/electricity

thepikminman

My question is:

A circuit element has a voltage v(t) =12 V and is also drawing a current of i(t) = 2e^−t Amps .
Find an expression for the power consumed in this element, and compute the energy from 0 to
infinity.

So I think p(t) would be just 24e^-t. I dont know how to get the integral, and i dont know if that is the right function either, because I used p=vi which gives the instantaneous power, but the question says find an expression for the power CONSUMED. Can anyone help?

FoxT

thepikminman wrote: »

My question is:

A circuit element has a voltage v(t) =12 V and is also drawing a current of i(t) = 2e^−t Amps .
Find an expression for the power consumed in this element, and compute the energy from 0 to
infinity.

So I think p(t) would be just 24e^-t. I dont know how to get the integral, and i dont know if that is the right function either, because I used p=vi which gives the instantaneous power, but the question says find an expression for the power CONSUMED. Can anyone help?

You are right, The instantaneous power consumed by the element at time t is P(t) = v(t)*i(t).

Note that Energy is Joules, Power is joules per second. What you are being asked to do here is find the integral sum of P(t), in order to find the total amount of energy consumed.

The total energy consumed then is the integral from zero to infinity of (24e^-t ) dt

-FoxT

thepikminman

Thanks, this helped alot!