Question

The oscillating current in an electrical circuit is as follows, where I is measured in amperes and t is measured in seconds. I = 7 sin(60πt) + cos(120πt). Find the average current for each time interval. (Round your answers to three decimal places.) (a) 0 ≤ t ≤ 1 60 amps

Answer 1

Answer:

Explanation:

Given

$I=7\sin (60\pi t)+\cos (120\pi t)$

$=\frac{1}{\frac{1}{60}}\times \int_{0}^{\frac{1}{60}}7\sin (60\pi t)dt+\int_{0}^{\frac{1}{60}}\cos (120\pi t)dt$

$=60\left [ \frac{-7}{60\pi }\cos (60\pi t)+\frac{1}{120\pi }\sin (120\pi t)\right ]_{0}^{\frac{1}{60}}$

$=60\left [ \frac{-7}{60\pi }\left ( \cos \pi-\cos 0\right )+\frac{1}{120\pi }\left ( \sin (2\pi )-\sin (0)\right )\right ]$

$=\frac{-7}{\pi }\left ( -1-1\right )+\frac{1}{2\pi }\left ( 0-0\right )$

$=\frac{14}{\pi }$