#### Answer

a) Power is given by: $P(t) = 20sin(100 \pi t)$
b) $.127 J$
c) 0 J

#### Work Step by Step

a) Power is equal to the voltage times the current. Thus, we find:
$P(t) = 2 \times 10sin(100 \pi t) = 20sin(100 \pi t)dt$
b) The energy is given by the integral of the power over time. Thus, we find:
$w = \int_{t_0}^{t} P(t)dt = \int_{0}^{.01}20sin(100 \pi t)dt $
Using a calculator to evaluate the integral, we find:
$\fbox{w = .127 J}$
c) The energy is given by the integral of the power over time. Thus, we find:
$w = \int_{t_0}^{t} P(t)dt = \int_{0}^{.02}20sin(100 \pi t)dt $
Using a calculator to evaluate the integral, we find:
$\fbox{w = 0J}$