Q. 95.0( 1 Vote )

An alternating current is given by

i = i1 cos ωt + i2 sin ωt.

The rms current is given by





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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