31. Alternating Current

An inductor, a capacitor, and a resistor are in series with a $300\mathrm{Hz}$ AC source. If the capacitor is $470\mathrm{nF}$, the inductor is $24\mathrm{mH}$, and the resistor is $800\mathrm{\Omega }$, what is the impedance?

An inductor, a capacitor, and a resistor are in series with a $300\mathrm{Hz}$ AC source with peak voltage 13 V$13\mathrm{V}$. If the impedance of the circuit is $3.4\mathrm{\Omega }$, what is the peak current?

An inductor, a capacitor, and a resistor are in series with an AC source. If the capacitor is 470 nF, the inductor is $24\mathrm{mH}$, and the resistor is 800 Ω$800\mathrm{\Omega }$, what is the circuit's resonant (angular) frequency?

An inductor, a capacitor, and a resistor are in series with a $300\mathrm{Hz}$ AC source. If the capacitor is $470\text{nF}$, the inductor is $24\text{mH},$ and the resistor is $800\Omega$. what is the impedance?

An inductor, a capacitor, and a resistor are in series with an AC source. If the capacitor is $470\text{nF}$, the inductor is $24\text{mH}$, and the resistor is $800\Omega$. what is the circuit's resonant frequency?

A series RLC circuit consists of a 75 Ω resistor, a 0.12 H inductor, and a 30 μF capacitor. It is attached to a 120 V/60 Hz power line. What are (a) the peak current I,

Show that the power factor of a series RLC circuit is cos  ​ϕ=R/Z.

The tuning circuit in an FM radio receiver is a series RLC circuit with a 0.200 μH inductor. a. The receiver is tuned to a station at 104.3 MHz. What is the value of the capacitor in the tuning circuit?

FIGURE CP32.68 shows voltage and current graphs for a series RLC circuit. a. What is the resistance R?

b. Prove that the energy dissipation is a maximum at ω=ω₀.

a. Show that the peak inductor voltage in a series RLC circuit is maximum at frequency ωL=(1/ω₀²− 1/2 R²C²)^−1/2

A series RLC circuit consists of a 75 Ω resistor, a 0.12 H inductor, and a 30 μF capacitor. It is attached to a 120 V/60 Hz power line. What are (b) the phase angle ϕ, and

A series RLC circuit consists of a 75 Ω resistor, a 0.12 H inductor, and a 30 μF capacitor. It is attached to a 120 V/60 Hz power line. What are c) the average power dissipated?

A motor attached to a 120 V/60 Hz power line draws an 8.0 A current. Its average energy dissipation is 800 W. c. What is the motor's resistance?

A motor attached to a 120 V/60 Hz power line draws an 8.0 A current. Its average energy dissipation is 800 W. d. How much series capacitance needs to be added to increase the power factor to 1.0?

b. A series RLC circuit with ε​0=10.0 V consists of a 1.0 Ω resistor, a 1.0 μH inductor, and a 1.0 μF capacitor. What is Vₗ at ω=ω₀ and at ω=ωₗ?

The tuning circuit in an FM radio receiver is a series RLC circuit with a 0.200 μH inductor. b. FM radio stations are assigned frequencies every 0.2 MHz, but two nearby stations cannot use adjacent frequencies. What is the maximum resistance the tuning circuit can have if the peak current at a frequency of 103.9 MHz, the closest frequency that can be used by a nearby station, is to be no more than 0.10% of the peak current at 104.3 MHz? The radio is still tuned to 104.3 MHz, and you can assume the two stations have equal strength.