CBSE Class 12 · 2007 · Alternating CurrentShort Answer

Distinguish between the terms 'effective value' and 'peak value' of an alternating current. An alternating current from a source is represented by

I = 10 sin (314 t)

. Write the corresponding values of
(i) its effective value,
(ii) the frequency of the source.

Answer: (i) $I_{e f f} = \frac{I _{0}}{2} = 7.07$ A;
(ii) $f = 50$ Hz.

Solution

The peak value is the maximum value the current attains in a cycle; the effective (rms) value is the steady current giving the same heating,

I_{e f f} = \frac{I _{0}}{2}

.
Comparing

I = 10 sin (314 t)

with

I = I_{0} sin 2 π f t

I_{0} = 10

A and

2 π f = 314

.
(i)

I_{e f f} = \frac{10}{2} = 7.07 A

(ii)

f = \frac{314}{2 π} = 50 Hz

CBSE Class 12 Board · 2007 · Subjective