Question

A series $LCR$ circuit containing a resistance of $120\Omega$ has angular resonance frequency $4\times {10}^{5}rad{s}^{-1}$. At resonance the voltages across resistance and inductance are $60V$ and $40V$, respectively. The value of inductance $L$ is

• A. $0.1mH$
• B. $0.2mH$
• C. $0.35mH$
• D. $0.4mH$

Answer 1

The correct option is B $0.2mH$

At resonance the reactance of inductor and the capaciotr cancel each other,
$L\omega =\frac{1}{C\omega }$ and total $Z=R\Omega$
resonance frequency = ${\omega }_r=4\times {10}^{5}rad/s$
let the current at resonance be $I$.
$V_R=I\times R=60V\Rightarrow I=\frac{60}{120}A$
$V_L=I\times L{\omega }_r=40V\Rightarrow L=0.2mH$