Question 105: AC fundamentals

Question

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 ____________ $$	imes$$ 102 Hz.

Accepted Answer

Current will be in phase with emf when
$$\omega L = {1 \over {\omega C}}$$
$$ \Rightarrow \omega  = {1 \over {\sqrt {LC} }} = {1 \over {\sqrt {5 	imes {{10}^{ - 4}} 	imes 2 	imes {{10}^{ - 4}}} }}$$
$$ \Rightarrow \omega  = {{{{10}^4}} \over {\sqrt {10} }}$$ rad/s
$$ \Rightarrow f = {1 \over {2\pi }} 	imes {{{{10}^4}} \over {\sqrt {10} }}$$ Hz
$$\Rightarrow$$ f $$\simeq$$ 500 Hz

AC fundamentals

An inductor of 0.5 mH, a capacitor of 200 $\muF and a resistor of 2 \Omega are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ____________ \times$ 102 Hz.

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