Question

An LCR series circuit of capacitance $625\ nF$ and resistance of $50 \ \Omega$ is connected to an AC source of frequency $20\ kHz$ For maximum value of amplitude of current in circuit, the value of inductance is ___ $mH$. (Take $\pi^2 =10$)

Answer 1

$f=\frac {1}{2π\sqrt {LC​​}}$

$2000\ Hz=\frac {1}{2\pi \sqrt {L×62.5×10^{−9​}​}}$

$L=\frac {1}{4\pi^2×2000^2×62.5×10^{−9}}$
$L=0.1\ H$
$L=100\ mH$

So, the answer is $100$.