Question

(a) An alternating voltage v = v_msinωt applied to a series LCR circuit drives a current given by i =i_msin(ωt + ϕ). Deduce an expression for the average power dissipated over a cycle. 

(b) For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Explain. 

(c) Determine the current quality factor at resonance for a series LCR circuit with L = 1.00mH, 1.00nF and R =100Ω connected to an a.c. source having peak voltage of 100V.

Answer 1

(b) The power is P = V_rms I_rmscosϕ. If cosϕ is small, then current considerably increases when voltage is constant. Power loss, we know is I²R. Hence, power loss increases.