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

Step-by-step solution

Equation of alternating current, aligned & i=i₁ t+i₂ t & Let i₁=I & and i=I & i=I t+I t & =I( t + t ) & i=I ( t+ ) & rms value of i₁ , & i_ rms = I 2 & aligned From Eqs. (i) and (ii), we get gathered i₁^2+i₂^2=I^2 ^2 +I^2 =I^2 i₁^2+i₂^2 =I gathered i₁^2+i₂^2=I^2 ^2 +I^2 ^2 =I^2 ( ^2 + ^2 ) From Eqs. (iii) and (iv), we get i_ rms = i₁^2+i₂^2 2