Q. 95.0( 1 Vote )

An alternating current is given by

i = i1 cos ωt + i2 sin ωt.

The rms current is given by

A.

B.

C.

D.

Answer :

The rms value of current is given by


… (i), where


i = current = i1 cos ωt + i2 sin ωt …. (ii)(given), t = time, ω = angular frequency, T = time period.


Now, squaring on both sides of (ii), we get


i2 = i12cos2ωt + 2i1i2sinωtcosωt + i22sin2ωt … (iii)


=


ow, … (v), where ω = angular frequency, T = time period = 2π/ω


Therefore, (iv) becomes:


=> [since sin nπ = 0, cos 0 = cos 2nπ = 1]


Hence, rms value of current i is (Ans)

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