Question 212: AC fundamentals

Question

An LCR series circuit of capacitance 62.5 nF and resistance of 50 $\Omega$, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is __________ mH.
(Take $\pi^2=10$)

Accepted Answer

$\because$ For maximum amplitude of current, circuit should be at resonance.
$
\begin{aligned}
& 	herefore X_{L}=X_{C} \\
& \omega L=\frac{1}{\omega C} \\
& L=\frac{1}{\omega^{2} C} \\
& =\frac{1}{\left(2 \pi 	imes 2 	imes 10^{3}ight)^{2} 	imes 62.5 	imes 10^{-9}} \\
& =100 ~\mathrm{mH}
\end{aligned}
$

AC fundamentals

An LCR series circuit of capacitance 62.5 nF and resistance of 50 \Omega, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is __________ mH. (Take \pi^2=10)

Integer / Numeric Answer Type