in a driven series RLC circuit the current leads the voltage

in a driven, series RLC circuit, the current leads the voltage of the function generator by 60degrees at w=40rad/s. If R=5ohms, what should be added (in series) to the circuit to maximize the power supplied by the function generator. The answer is 217mH inductor. I need to know how to solve it though.

Solution

given

w = 40 rad/s

R = 5 ohms

phi = 60 degrees

In inductive ckt only current leads volatge.

so, the ckt must have an inductor.

we know, tan(phi) = (XL/R)

tan(phi) = XL/R

XL = R*tan(phi)

w*L = R*tan(phi)

L = R*tan(phi)/w

= 5*tan(60)/40

= 0.217 H

= 217 mH