The electric current in the circuit is given as i = i0 (t/T)
Q. The electric current in the circuit is given as i = i0 (t/T). The r.m.s current for the period t = 0 to t = T is _____.

(A) i0 / √2

(B) i0 / √3

(C) i0

(D) i0 / √6

Correct Answer: i0 / √3

Explanation

The r.m.s value of a time varying current is defined as:

irms = √( 1/T ∫0T i² dt )

Given current:

i = i0 (t/T)

Substituting:

irms = √( 1/T ∫0T i02 (t²/T²) dt )

= √( i02 / T³ ∫0T t² dt )

∫0T t² dt = T³ / 3

irms = √( i02 / 3 )

irms = i0 / √3

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