An RLC series circuit has a resistance R of 20 Ω and a

An RLC series circuit has a resistance R of 20 Ω and a current which lags behind the applied voltage by 45º. If the voltage across the inductor is twice the voltage across the capacitor, what is the value of inductive reactance?

Given R = 20Ω Current lags behind the applied voltage by 45º
and V_L = 2 V_C
IX_L = 2IX_C
or X_L = 2X_C.......(i)

tan 45° =	V_L − V_C	=	I(X_L − X_C)	=	X_L − X_C
	V_R		I_R		R

1 =	X_L − X_C
	R

or X_L – X_C = R = 20 ....(ii)
From equations (i) and (ii)

X_L −	X_L	= 20
	2

or X_L = 40 Ω
This is the required value of inductive reactance.