Question

For the series $ LCR $ circuit shown in the 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\text{ }rad-{{s}^{-1}}and\text{ }5\text{ }A $
• C. $ 2500\text{ }rad-{{s}^{-1}}and\,\frac{5}{\sqrt{2}}\text{ }A $
• D. $ 250\,rad-{{s}^{-1}}and\,5\sqrt{2}A $
• E. $ 25\,rad-{{s}^{-1}}and\,5\sqrt{2}A $

Answer 1

Answer: (B)

Resonance frequency, $ \omega =\frac{1}{\sqrt{LC}} $
$ =\frac{1}{\sqrt{8\times {{10}^{-3}}\times 20\times {{10}^{-6}}}} $
$ =\frac{1}{4\times {{10}^{-4}}}=\frac{{{10}^{4}}}{4} $
$ \approx 2500\,rad/s $ Amplitude of current, $ {{I}_{0}}=\frac{V}{R}=\frac{220}{44} $
$ =5A $