Question

The frequencies at which the current amplitude in an LCR series circuit becomes $\frac{1}{2}$ times its maximum value, are 212 rad s–1 and 232 rad s–1. The resistance value in the Question: the circuit is R = 5 Ω. The self-inductance in the circuit is _____ mH.

Answer 1

$\frac{i}{i_{max}}$=$\frac{1}{\sqrt2}$
=$\frac{\frac{V_0}{Z}}{\frac{V_0}{R}}$
⇒$\frac{R}{Z}=\frac{1}{\sqrt2}$ and $\frac{1}{212C}$−212L=232L−$\frac{1}{232C}$
⇒212L=$\frac{1}{232C}$
so 400L2=R2
⇒L=$\frac{5}{20}$
⇒L=250 mH