15.5 Resonance in an AC Circuit

In the circuit of the reference, $L = 2.0 \times 10^{−3} \text{H},$ $C = 5.0 \times 10^{−4} \text{F},$ and $R = 40 \Omega .$ (a) What is the resonant frequency? (b) What is the impedance of the circuit at resonance? (c) If the voltage amplitude is 10 V, what is i(t) at resonance? (d) The frequency of the AC generator is now changed to 200 Hz. Calculate the phase difference between the current and the emf of the generator.

What happens to the resonant frequency of an RLC series circuit when the following quantities are increased by a factor of 4: (a) the capacitance, (b) the self-inductance, and (c) the resistance?

The resonant angular frequency of an RLC series circuit is $4.0 \times 10^{2} \text{rad}/\text{s} .$ An ac source operating at this frequency transfers an average power of $2.0 \times 10^{−2} \text{W}$ to the circuit. The resistance of the circuit is $0.50 \Omega .$ Write an expression for the emf of the source.

The resonant frequency of an RLC series circuit is $2.0 \times 10^{3} \text{Hz} .$ If the self-inductance in the circuit is 5.0 mH, what is the capacitance in the circuit?

For an RLC series circuit, $R = 100 \Omega$, $L = 150 \text{mH}$, and $C = 0.25 \mu \text{F} .$ (a) If an ac source of variable frequency is connected to the circuit, at what frequency is maximum power dissipated in the resistor? (b) What is the quality factor of the circuit?

(a) What is the resonant frequency of a resistor, capacitor, and inductor connected in series if $R = 100 \Omega,$ $L = 2.0 \text{H}$, and $C = 5.0 \mu \text{F}$? (b) If this combination is connected to a 100-V source operating at the resonant frequency, what is the power output of the source? (c) What is the Q of the circuit? (d) What is the bandwidth of the circuit?