31. Alternating Current

An AC source operates at an RMS voltage of 70 V and a frequency of 85 Hz. If the source is connected in series to a 20 Ω resistor, a 0.15 H inductor and a 500 µF capacitor, answer the following questions: 

a) What is the maximum current produced by the source? 

b) What is the maximum voltage across the resistor? 

c) What is the maximum voltage across the inductor? 

d) What is the maximum voltage across the capacitor?

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 is 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. 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. What is the resistance R?

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

Show that the peak inductor voltage in a series RLC circuit is maximum at frequency ${\omega }_L={(\frac{1}{{\omega }_0^2}-\frac{1}{2}{R}^2{C}^2)}^{-1/2}$.

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 is the phase angle ϕ?

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 is 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. What is the motor's resistance?