JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Alternating Current

In a series LCR circuit, a resistor of

300Ω

, 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

____

\times 1 0^{4}

radians

s^{- 1}

Answer: 2

Solution

Current in a series LCR circuit is maximum at resonance, where the inductive and capacitive reactances cancel:

ω = \frac{1}{L C}

With

L = 100 mH = 0.1 H

and

C = 25 nF = 25 \times 1 0^{- 9} F

L C = 0.1 \times 25 \times 1 0^{- 9} = 2.5 \times 1 0^{- 9}

ω = \frac{1}{2.5 \times 1 0 ^{- 9}} = \frac{1}{5 \times 1 0 ^{- 5}} = 2 \times 1 0^{4} rad/s

The angular frequency is

2 \times 1 0^{4} rad s^{- 1}

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Integer answer