Question

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

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

Answer 1

Answer: (A)

Here, $R=44\Omega ,L=8mH=8\times 10^{-3}H$
$C=20\mu F=20\times 10^{-6}F$
${\omega }_r=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{8\times 10^{-3}\times 20\times 10^{-6}}}$
${\omega }_r=\frac{1}{4\times 10^{-4}}=\frac{10^4}{4}=2500rad{s}^{-1}$
$I_0=\frac{V_0}{R}=\frac{\sqrt{2}{V}_{rms}}{R}$
$=\frac{\sqrt{2}\times 220}{44}$
$=5\sqrt{2}A$