NEET 2023, Physics Q1: LR, CR, LCR Circuits

NEET2023Physics

In a series LCR 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:

A
$15.9$ kHz
B
$1.59$ rad/s
C
$1.59$ kHz
D
$15.9$ rad/s

Solution

At resonance the inductive and capacitive reactances are equal, giving the resonant angular frequency $ω_{0} = \frac{1}{L C}$ and frequency $f_{0} = \frac{1}{2 π L C}$ .

Substituting $L = 1 0^{- 2}$ H and $C = 1 0^{- 6}$ F:

$f_{0} = \frac{1}{2 π 1 0 ^{- 2} \times 1 0 ^{- 6}} = \frac{1}{2 π \times 1 0 ^{- 4}} \approx 1.59 \times 1 0^{3}$ Hz $= 1.59$ kHz.

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NEET 2023, Physics Q1: LR, CR, LCR Circuits

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