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)