RCL Circuits?

Question

A series RCL circuit operating at 60.0 Hz contains a 35-Ωresistor and an 8.2-μF capacitor. If the power factor of the circuit is +1.00, what is the inductance of the inductor in this circuit?

Answer 1

If the power factor = 1, then the circuit is acting as if it is purely resistive in nature. Since the circuit has L and C reactive components in it, this suggest that the circuit is at series resonance. Thus, L and C must be resonance at 60 Hz.

Using: Fr = 1 / (6.28 x sq-rt (L x C)) and solving for L

L = 1 / (6.28^2 x 60 Hz^2 x 8.2^-6) = 0.86 Henry's