An alternating voltage source is connected across a series combination of a 0.5 H inductor, a 2 μ F capacitor, and a 50 resistor. At what frequency of the AC source will the current amplitude in the circuit be maximum?

Question

Quantrex Academy · Accepted Answer

Correct answer: B. (500)/(π) Hz

The current amplitude in a series LCR circuit is maximum at the resonant frequency.

The resonant frequency is given by

f = \dfrac{1}{2\pi\sqrt{LC}}

Given

L = 0.5 \text{ H}

and

C = 2 \text{ \mu F} = 2 \times 10^{-6} \text{ F}

Substituting the values:

f = \dfrac{1}{2\pi\sqrt{0.5 \times 2 \times 10^{-6}}}

f = \dfrac{1}{2\pi\sqrt{10^{-6}}}

f = \dfrac{1}{2\pi \times 10^{-3}}

f = \dfrac{1000}{2\pi} = \dfrac{500}{\pi} \text{ Hz}

Answer:

\dfrac{500}{\pi} \text{ Hz}

An alternating voltage source is connected across a series...

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