1. ## differentiation

RMS Value of Current

i = 4sin $/pi$t is 2.828A
(hint given) $sin^2 /theta = 1/2 (1-cos 2 /theta)$
see attached for my efforts so far.

2. Originally Posted by batman121
RMS Value of Current

i = 4sin $/pi$t is 2.828A
(hint given) $sin^2 /theta = 1/2 (1-cos 2 /theta)$
see attached for my efforts so far.
The mean square current:

$p=\frac{1}{2} \int_0^2 [i(t)]^2~dt\ \ {\rm{Amps}}^2$

(the $1/2$ and the limits of integration because the current is periodic with period $2$), so putting in the expression for $i(t)$ :

$p=\frac{1}{2} \int_0^2 [4 \sin(\pi t)]^2~dt= 4 \int_0^2 [1- \cos(2 \pi t)]~dt=8$

hence the root mean square is $\sqrt{p}=2 \sqrt{2}\approx 2.828\ \ {\rm{Amps}}$.

RonL