JEE MAIN - Physics (2022 - 29th June Evening Shift - No. 27)
An inductor of 0.5 mH, a capacitor of 200 $$\mu$$F and a resistor of 2 $$\Omega$$ are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ____________ $$\times$$ 102 Hz.
Answer
5
Explanation
Current will be in phase with emf when
$$\omega L = {1 \over {\omega C}}$$
$$ \Rightarrow \omega = {1 \over {\sqrt {LC} }} = {1 \over {\sqrt {5 \times {{10}^{ - 4}} \times 2 \times {{10}^{ - 4}}} }}$$
$$ \Rightarrow \omega = {{{{10}^4}} \over {\sqrt {10} }}$$ rad/s
$$ \Rightarrow f = {1 \over {2\pi }} \times {{{{10}^4}} \over {\sqrt {10} }}$$ Hz
$$\Rightarrow$$ f $$\simeq$$ 500 Hz
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