In a series circuit, the inductance is 10 mH, capacitance is 1 and resistance R is 100 . The frequency at which resonance occurs is [2023]

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Solution

Q.
In a series $L C R$ circuit, the inductance $L$ is 10 mH, capacitance $C$ is 1 $µ F$ and resistance R is 100 $Ω$ . The frequency at which resonance occurs is [2023]

1 1.59 rad/s

2 1.59 kHz

3 15.9 rad/s

4 15.9 kHz

Ans.
(2)

Given, $L = 10$ $mH = 10 \times 10^{- 3}$ $H$

$C = 1$ $μ F = 1 \times 10^{- 6}$ $F$

$R = 100 Ω$

Resonance frequency,

$υ_{0} = \frac{1}{2 π} \sqrt{\frac{1}{L C}} = \frac{1}{2 \times 3.14} \sqrt{\frac{1}{10 \times 10^{- 3} \times 10^{- 6}}}$

$= \frac{1}{2 \times 3.14} \sqrt{\frac{10^{8}}{1}} = \frac{10^{4}}{2 \times 3.14} = 1592.3 = 1.59$ $kHz$

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