An LCR series circuit of capacitance 62.5 nF and resistance 50 Ω is connected to an A.C. source of frequency 2.0 kHz. For maximum amplitude of current in the circuit, the value of inductance i s ___ mH. (Take π² = 10)
Physics · Ac Cirucuits · series combination of ac circuit and L-C-R circuit
JEE Mains 25 January 2023 Morning Shift

Question

An LCR series circuit of capacitance 62.5 nF and resistance 50 Ω is connected to an A.C. source of frequency 2.0 kHz. For maximum amplitude of current in the circuit, the value of inductance i s ___ mH. (Take π² = 10)

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

G1 Physics · Accepted Answer

At resonance, f = 1/(2π√(LC)). Hence L = 1/(4π²f²C). Using π² = 10, f = 2000 Hz and C = 62.5×10⁻⁹ F gives L = 0.1 H = 100 mH.