Question

For the series $L C R$ circuit shown in figure, what is the resonance frequency and the amplitude of the current at the resonating frequency?

• A. $2500\, rad\, s ^{-1}$ and $5 \sqrt{2} A$
• B. $2500\, rad\, s ^{-1}$ and $5 A$
• C. $2500\, rad\, s ^{-1}$ and $\frac{5}{\sqrt{2}} A$
• D. $250\, rad\, s ^{-1}$ and $5 \sqrt{2} A$

Answer 1

Answer: (A)

Here, $R=44 \,\Omega,\, L=8\, mH =8 \times 10^{-3}\, H$
$C=20\, \mu F =20 \times 10^{-6}\, F$
$\omega_{r}=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{8 \times 10^{-3} \times 20 \times 10^{-6}}}$
$\omega_{r}=\frac{1}{4 \times 10^{-4}}=\frac{10^{4}}{4}=2500\, rad\, s ^{-1}$
$I_{0}=\frac{V_{0}}{R}=\frac{\sqrt{2} V_{ rms }}{R}$
$=\frac{\sqrt{2} \times 220}{44}$
$=5 \sqrt{2}\, A$