For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 nF. If resistance of 200 Ω and 100 mH inductor is being used in the given circuit. The frequency of ac source i s _____ × 10³ Hz. (given π² = 10)
Physics · Ac Cirucuits · series combination of ac circuit and L-C-R circuit
JEE Mains 2024 06 Apr Evening Shift

Question

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 nF. If resistance of 200 Ω and 100 mH inductor is being used in the given circuit. The frequency of ac source i s _____ × 10³ Hz. (given π² = 10)

Physics · Ac Cirucuits · series combination of ac circuit and L-C-R circuit

JEE Mains 2024 06 Apr Evening Shift

G1 Physics · Accepted Answer

Maximum current occurs at resonance. Resonant frequency: f₀ = 1/[2π√(LC)] Given: L = 100 mH = 0.1 H C = 2.5 nF = 2.5 × 10⁻⁹ F Therefore: LC = 2.5 × 10⁻¹⁰ √(LC) = 0.5 × 10⁻⁴ So: f₀ = 1/[2π × 0.5 × 10⁻⁴] = 10⁴/π Hz Using π² = 10, the source obtains approximately: f₀ = 10 × 10³ Hz Hence: answer = 10