## Fundamentals of Electrical Engineering

$P = 37.5W$
Start by setting up the integral to solve for rms. We want rms current because it will give us the same average power. $i_{rms} = \sqrt {100/ \pi * \int^{\pi}_0 sin^4 (t) *dt }$ Use a trig identity to simplify the sin term into terms of cosine with different frequencies. Then integrate to get: $i_{rms} = \sqrt {100/ \pi *(3*t/8 - \frac{1}{4}*sin(2x) + \frac{1}{32}*sin(4x)|^{\pi}_0 }$ $i_{rms}= \sqrt {\frac{3*100}{8}}$ Now calculate power using $P = i^2 *R$ $P = (6.1237)^2 *1$ $P = 37.5W$