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  • An inductor of , a capacitor of <img alt="\mathrm{200 \; \mu \mathrm{F}}" src="/latex-imag

An inductor of \mathrm{0.5 \mathrm{mH}}, a capacitor of \mathrm{200 \; \mu \mathrm{F}} and a resistor of \mathrm{2\; \Omega} are connected in series with a \mathrm{220 \mathrm{~V}} ac source. If the current is in phase with the emf, the frequency of ac source will be __________\times 10^{2} \mathrm{~Hz}

Option: 1

5


Option: 2

4


Option: 3

3


Option: 4

6


Answers (1)

best_answer

Current will be in phase with emf when

\mathrm{x_{L}=x_{C}} \\

\mathrm{\omega L=\frac{1}{\omega C}} \\

\mathrm{\omega=\frac{1}{\sqrt{L C}}=\frac{1}{\sqrt{0.5 \times 10^{3} \times 200 \times 10^{-6}}}} \\

\mathrm{\omega=\frac{10^{4}}{\sqrt{10}} \mathrm{rad} / \mathrm{s}}

\mathrm{f=\frac{\omega}{2 \pi}=\frac{10^{4}}{2 \pi \times \sqrt{10}}} \\

\mathrm{f=500 \mathrm{~Hz}}

Hence answer is 5 

Posted by

Rishabh

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