The instantaneous current in a a.c circuit is I = 0.5 sin 314t. find frequency and I_rms .

We know the sinusoidal AC equation

I = I_o sin(wt)

compare it with

I = 0.5 sin(314t)

I_o = 0.5 A

w = 314 s^-1

w is angular frequency which is equal to 2pi*f

2*pi*f = 314

2*3.14*f = 314

f = 314 / 3.14 x 2 = 100/2 = 50 Hz

Hence the frequency of sinusoidal AC is 50 Hz.

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Now recall the relation of rms current and peak current.

I_rms = I_o / √2 = 0.5 / √2 = 0.35 A