Question

A series LCR circuit has L = 1mH, C = 0.1 $\mu$F and R = 10 $\Omega$ . It is connected across a source of alternating emf of 5V but of variable frequency. Find (i) the frequency at which the impedance is minimum (ii) the current at resonance.

• A. $\frac{{10}^5}{2\pi }Hz,\frac{1}{2}A$
• B. $\frac{{10}^4}{2\pi }Hz,\frac{1}{2}A$
• C. $\frac{{10}^2}{2\pi }Hz,\frac{1}{2}A$
• D. $\frac{{10}^3}{2\pi }Hz,\frac{1}{2}A$

Answer 1

The correct option is A $\frac{{10}^5}{2\pi }Hz,\frac{1}{2}A$

$L\omega =\frac{1}{\omega C};{\omega }^2=\frac{1}{LC}=\frac{1}{{10}^{-3}\times {10}^{-7}}$
$\omega ={10}^5;f=\frac{{10}^5}{2\pi }Hz$
$I=\frac{V}{R}=\frac{5}{10}=\frac{1}{2}A$