An alternating current is given by i = i₁ t - i₂ t . The rms current is given by

Step-by-step solution

The given alternating current is i = i₁ t - i₂ t The mean square value of the current over a complete cycle is: = = i₁^2 + i₂^2 - 2i₁ i₂ Using the standard average values over a full cycle: = 1 2 , = 1 2 , and = 0 = i₁^2 ( 1 2 ) + i₂^2 ( 1 2 ) - 0 = i₁^2 + i₂^2 2 The rms current is the square root of the mean square current: i_ rms = = i₁^2 + i₂^2 2 Answer: i₁^2 + i₂^2 2