How Does Power Calculation Translate to Energy Absorption in a Circuit?

[XodoX]

1. A circuit element is shown below, with the voltage v(t) and the current i(t) defined. The
voltage and current are given as
v (t ) = 5sin (t ) [V]
i (t ) = −10cos (t ) [A] .
Calculate the power that the element is delivering.

b) For the same circuit in the previous problem, calculate the amount of energy that the circuit
element absorbs between t = 0 and t = 1 .

I don't get the b0 part. The solution for the first part is 50 sin(t) cos(t) [W]. How do I get the amount of energy for that time frame?

 

[berkeman]

1. A circuit element is shown below, with the voltage v(t) and the current i(t) defined. The
voltage and current are given as
v (t ) = 5sin (t ) [V]
i (t ) = −10cos (t ) [A] .
Calculate the power that the element is delivering.

b) For the same circuit in the previous problem, calculate the amount of energy that the circuit
element absorbs between t = 0 and t = 1 .

I don't get the b0 part. The solution for the first part is 50 sin(t) cos(t) [W]. How do I get the amount of energy for that time frame?

What kind of a circuit element is it? Why are they asking about delivering power in one part, and absorbing power in the other part?

To get energy over a time period, you just integrate the power multiplied by dt over the time interval.

 

[XodoX]

I forgot how to take the integral of cos/sin

u= sin(t) du=cos(t) dt

Maybe you can explain the next step to me:) I think that once I got the result of it I am done.

 

[berkeman]

I forgot how to take the integral of cos/sin

u= sin(t) du=cos(t) dt

Maybe you can explain the next step to me:) I think that once I got the result of it I am done.

The wikipedia.org article on integration by parts is pretty reasonable:

http://en.wikipedia.org/wiki/Integration_by_parts

.