Three series A.C. circuits (i) RC (ii) RL and (iii) LC (where values of L and C are such that `X_L = X_C`) are connected turn by turn with a given A.C. source with angular frequency `omega`. If power consumed in these circuits are respectively `P_1, P_2` and `P_3` then .......

Options

A. `P_1 gt P_2 gt P_3`
B. `P_1 = P_2 lt P_3`
C. `P_1 = P_2 gt P_3`
D. `P_1=P_2 =P_3`

Answer

C

Explanation

`P_1=V^2/sqrt(R^2+X_C^2)cos phi_1`
(where `phi_1` is such that `tan phi_1=(|-X_C|)/R`) ….(1)
`P_2=V^2/sqrt(R^2+X_L^2)cosphi_2`
(Where `phi_2` is such that `tan phi_2 =X_L/2` ) …..(2)
`rArr P_1=P_2` (`because X_L = X_C` and cos`phi_1=cosphi_2` because `X_L=X_C`) ....(3)
`P_3=V^2/(|X_L-X_C|)cos (pi/2)=0`....(4)
From (3) and (4) , `P_1=P_2 gt P_3`