An alternating current is expressed as i = i₁ t + i₂ t . The rms value of this current is

Step-by-step solution

The given alternating current is i = i₁ t + i₂ t . The rms value of the current is given by i_ rms = i^2 , where i^2 is the mean square value of the current over a complete cycle. Squaring the current expression: i^2 = (i₁ t + i₂ t)^2 i^2 = i₁^2 ^2 t + i₂^2 ^2 t + 2 i₁ i₂ t t Taking the average over one complete cycle: i^2 = i₁^2 ^2 t + i₂^2 ^2 t + i₁ i₂ 2 t Since the average values over a full cycle are ^2 t = 1 2 , ^2 t = 1 2 , and 2 t = 0 , we get: i^2 = i₁^2 ( 1 2 ) + i₂^2 ( 1 2 ) + 0 = i₁^2 + i₂^2 2 Therefore,