A parallel RLC circuit has an inductance of 1 H and a capacitance of 1 µF. What is the resonant frequency (f0 )? 

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  1. \(\rm \frac{1}{\pi \times 10^{-3}}Hz\)
  2. \(\rm \frac{1}{\pi}Hz\)
  3. \(\rm \frac{1}{2\pi}Hz\)
  4. \(\rm \frac{1}{2\pi \times 10^{-3}}Hz\)

Answer (Detailed Solution Below)

Option 4 : \(\rm \frac{1}{2\pi \times 10^{-3}}Hz\)
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Detailed Solution

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Concept

The resonant frequency of a parallel RLC circuit is given by:

\(f_o={1\over 2\pi \sqrt{LC}}\)

where, fo = Resonant frequency

L = Inductance

C = Capacitance

Calculation

Given, L = 1 H

C = 1 μF = 1 × 10-6 F

\(f_o={1\over 2\pi \sqrt{1\times 1\times 10^{-6}}}\)

\(f_o=\rm \frac{1}{2\pi \times 10^{-3}}Hz\)

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