In a series (L-C ) - (R ) circuit, the inductive reactance is twice the resistance and the capacitive reactance is (1 / 3 ) rd of the inductive reactance. The power factor of the circuit is

Step-by-step solution

In (L-C-R ) circuit, (X_L=2 R and X_C= X_L 3 ) Impedance of (L-C-R ) circuit is given as ( aligned Z & = R^2+ (X_L-X_C )^2 & = R^2+ (X_L- X_L 3 )^2 & = R^2+ ( 2 X_L 3 )^2 = R^2+ 4 X_L^2 9 aligned ) ( aligned & = R^2+ 4 9 (2 R)^2 = R^2+ 16 9 R^2 & = 25 R^2 9 Z= 5 3 R & Power factor = & = R Z = R 5 R / 3 = 3 5 =0.6 & aligned )