In a series LCR circuit, a resistor of 300 \Omega , a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is \underline\hspace2cm\times 10^4 radians s^-1

Alternating Current PYQ — JEE Main 2025 · 23 Jan · Shift 2 · Q72 with Solution

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Correct answer: 2

Condition for maximum current in a series LCR circuit

In a series LCR circuit, current is maximum at resonance.

The resonant angular frequency is
$\omega_0 = \frac{1}{\sqrt{LC}}.$
Given values
- Inductance: $L = 100\,\text{mH} = 0.1\,\text{H}$
- Capacitance: $C = 25\,\text{nF} = 25 \times 10^{-9}\,\text{F}$
The resistance does not affect the value of resonant frequency.
Calculate $LC$
$LC = 0.1 \times 25 \times 10^{-9}$ $LC = 2.5 \times 10^{-9}$
Calculate $\sqrt{LC}$
$\sqrt{LC} = \sqrt{2.5 \times 10^{-9}}$ $\sqrt{2.5 \times 10^{-9}} = 5 \times 10^{-5}$
Find resonant angular frequency
$\omega_0 = \frac{1}{5 \times 10^{-5}} = 2 \times 10^4\,\text{rad s}^{-1}$
Required integer

The question asks for:
$\omega_0 = \underline{\hspace{1cm}} \times 10^4\,\text{rad s}^{-1}$
Hence the required integer is
$2.$
Comparison with stored answer

Stored correct answer = 2

Our derived answer also = 2, so they agree.