In a series LCR circuit alternating e.m.f. and current are given by the equations V = V₀ ( t) and I = I₀ ( t + 3 ) respectively. The average power dissipated in the circuit over one cycle of a.c. is ( 60^ = 0.5)

Step-by-step solution

The given equations for alternating e.m.f. and current are: V = V₀ ( t) I = I₀ ( t + 3 ) The phase difference between the voltage and current is = 3 = 60^ . The average power dissipated in an a.c. circuit over one cycle is given by: P_ avg = V_ rms I_ rms Substituting V_ rms = V₀ 2 and I_ rms = I₀ 2 : P_ avg = ( V₀ 2 ) ( I₀ 2 ) 60^ Since 60^ = 1 2 : P_ avg = V₀ I₀ 2 1 2 = V₀ I₀ 4 Answer: V₀ I₀ 4