- #1

hogrampage

- 108

- 1

## Homework Statement

Calculate the power absorbed by each element at t = 0

^{-}, t = 0

^{+}, and t = 200ms.

## Homework Equations

P[itex]_{L}(t)[/itex] = [itex]\frac{V_{0}^{2}}{R}e^{-Rt/L}(1-e^{-Rt/L})[/itex]

P[itex]_{R}(t)[/itex] = [itex]\frac{V_{0}^{2}}{R}(1-e^{-Rt/L})[/itex]

P[itex]_{V}(t)[/itex] = -(P[itex]_{L}(t)[/itex] + P[itex]_{R}(t)[/itex])

## The Attempt at a Solution

-10u(-t)V = -10V for t <= 0; 0V for t > 0

__: V = -10V, i = -10A__

**t = 0**^{-}P

_{R}(0

^{-}) = (-10)

^{2}(1) = 100W

P

_{L}(0

^{-}) = 0W

P

_{V}(0

^{-}) = -100W

**: V = -10V, i = -10A**

__t = 0__^{+}P

_{R}(0

^{+}) = (-10)

^{2}(1) = 100W

P

_{L}(0

^{+}) = 0W

P

_{V}(0

^{+}) = -100W

**:**

__t = 200ms__P[itex]_{L}(0.2)[/itex] = [itex]\frac{(-10)^{2}}{R}e^{-4(0.2)}(1-e^{-4(0.2)})[/itex] = 25W

P[itex]_{R}(0.2)[/itex] = [itex]\frac{(-10)^{2}}{R}(1-e^{-4(0.2)})[/itex] = 30W

P[itex]_{V}(0.2)[/itex] = -(25 + 30) = -55W

I'm not completely sure I did this problem correctly (particularly worried about the powers for 0

^{-}and 0

^{+}). If I did not, I would greatly appreciate any feedback (mistakes you see, hints, etc.). I don't want to go further in my homework until I understand this basic problem first.

Thanks!