Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

A series LCR circuit containing $5.0\text{ H}$ inductor, $80\text{ }\mu\text{F}$ capacitor and $40\text{ }\Omega$ resistor is connected to $230\text{ V}$ variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be

$25\text{ rad/s}$ and $75\text{ rad/s}$

$50\text{ rad/s}$ and $25\text{ rad/s}$

$46\text{ rad/s}$ and $54\text{ rad/s}$

$42\text{ rad/s}$ and $58\text{ rad/s}$

Step-by-Step Solution

The resonance frequency of LCR series circuit is given as $\omega_0 = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{5 \times 80 \times 10^{-6}}} = 50\text{ rad/s}$ . Now half power frequencies are given as $\omega = \omega_0 \pm \frac{R}{2L}$ . i.e., $\omega_L = 50 - \frac{40}{2 \times 5} = 46\text{ rad/s}$ and $\omega_H = 50 + \frac{40}{2 \times 5} = 54\text{ rad/s}$ .

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