How Do You Calculate Energy Supplied in Different Time Intervals of a Circuit?

[smith5753]

Homework Statement

For the element shown below, v(t) = ½ t Volts and i(t) = 12t-4t2 Amps.

a)Find the instantaneous power p(t) as a function of time.

b)Find the energy supplied (this value can be negative or positive for each range) to the element for the following three time ranges:

0 < t < 3, 3 < t < 4, 0 < t < 4, those are less than or equal to.

Homework Equations

There is a picture of the circuit that show that it satisfies the Passive Sign Convention.

P(t) = V(t) i(t)

w= the integral of P(t)

The Attempt at a Solution

for part a. I multiplied the given V times the i and found p(t) to = 6t^2 - 2t^3 watts.

for part b. I attempted to take the integral of P(t) from the first point listed; 0 < t < 3

I don't understand the integration. Do i integrate from infinitie to 0, then from 0 to 3, and then from 3 to infinitie?? I am so lost at this point.

 

[rock.freak667]

Just integrate form 0 to 3

EDIT: also if you have infinity in the limits, the polynomial will tend to infinity as t→ inf.