Question

1. An alternating current is given by I = 50 sin 100 n t.
Find the frequency of current, mean current during a
positive half-cycle, virtual current and the current at
t=(1/300) s.
Ans. 50 Hz, 31.8 A, 35.4 A, 43.3 A.​

Answer 1

Given,

An alternating current is given by I = 50 sin 100π t.

To find: the frequency of current, mean current during a positive half-cycle, virtual current and the current at t=(1/300) s.

Solution:

The equation of a.c is given as:

I = I₀ sinωt

here, I₀ = 50 , ω = 100π

then, Frequency =  ω/ 2π = 100π / 2π =  50 Hz

Mean value of ac during postive half-cycle can be given as:

Im = I₀ / (π/2) = 50 * 2 / 3.14 = 31.8 A

Virtual current can be given as:

Iv = I₀ / √2 = 50 / 1.414 = 35.4 A

And, Current at time T can be given as:

I = 50 sin 100πt

at t = 1/300 sec,

I = 50 sin(100*π *1/300)

or, I = 50 sin(π/3)

or, I = 50 *√3 / 2

or, I = 50*1.732 / 2

or, I = 43.3 A