Physics

Physics

Problem

Two identical series LCR circuits are excited at angular frequencies ω1\omega_1 and ω2\omega_2 such that ω1<ω0<ω2\omega_1 < \omega_0 < \omega_2, where ω0\omega_0 is the circuit’s resonant frequency. Which statement correctly describes the sign of (XL−XC)(X_L - X_C) and the effective nature of the circuit at these two frequencies? a) At ω1\omega_1 the circuit is capacitive with (XL−XC)<0(X_L-X_C)<0; at ω2\omega_2 it is inductive with (XL−XC)>0(X_L-X_C)>0. b) At ω1\omega_1 the circuit is inductive with (XL−XC)>0(X_L-X_C)>0; at ω2\omega_2 it is capacitive with (XL−XC)<0(X_L-X_C)<0. c) Both ω1\omega_1 and ω2\omega_2 make (XL−XC)(X_L-X_C) positive so the circuit is inductive at both frequencies. d) (XL−XC)=0(X_L-X_C)=0 at both ω1\omega_1 and ω2\omega_2, so the circuit behaves purely resistive in each case.

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