Question
The equation of alternating current is :
$$I = 50\sqrt 2 \sin 400\pi t\,amp.$$ Then the frequency and root mean square of current are respectively
A.
$$200\,Hz,50\,amp$$
B.
$$400\pi \,Hz,50\sqrt 2 \,amp$$
C.
$$200\,Hz,50\sqrt 2 \,amp$$
D.
$$50\,Hz,200\,amp$$
Answer :
$$200\,Hz,50\,amp$$
Solution :
$$\eqalign{
& 2\pi nt = 400\pi t \cr
& \therefore n = 200 \cr
& {I_0} = 50\sqrt 2 \,amp. \cr
& r.m.s.{\text{ current}} = \frac{{{I_0}}}{{\sqrt 2 }} = 50\,amp. \cr} $$