Question

An alternating current is given by \( i=14.14 \sin 377 t \) find 

1. RMS value of current. 

2. Frequency. 

3 . Instantaneous value of current when \( t-3 mS \). 

4. Time taken by current to reach 10 Amp for third time after passing through zero and increasing positively.

Answer 1

Given i = 14.14 sin 377t

(i) RMS  value of current

i_rms = \(\frac{I_m}{\sqrt2}\)

i_rms = \(\frac{14.14}{\sqrt2}\)

i_rms = 10 ampere

(ii)  Frequency

\(\omega\) = 377

2πf = 377

f = 377/2π

f = 377/6.28

f = 60.03 Hz

(iii) Instantaneous current

I = 14.14 sin 377 t

I = 14.14 sin (377x 3 x 10^-3)

I = 14.14 x sin (1.131)

I = 12.78 amp