PHYS 2212 Module 11 Self Assessment Practice Problems

Module 11 Self Assessment Practice Problems

An RLC series circuit with R = 600 Ω, L = 30 mH, and C = 0.050 µF is driven by an ac source whose frequency and voltage amplitude are 500 Hz and 50 V, respectively.
(a) What is the impedance of the circuit?
(b) What is the amplitude of the current in the circuit?
(c) What is the phase angle between the emf of the source and the current?
Answer:  (a) 6300 Ω (b) 7.9 mA (c) -85°
Calculate the rms currents for an ac source is given by v(t) = V0sin(ωt), where V0 = 100 V and ω = 200π rad/s when connected across
(a) a 20-µF capacitor
(b) a 20-mH inductor
(c) a 50-Ω resistor
Answer:  (a) 0.89 A (b) 5.63 A (c) 1.41 A
A 700-pF capacitor is connected across an ac source with a voltage amplitude of 160 V and a frequency of 20 kHz.
(a) Determine the capacitive reactance of the capacitor and the amplitude of the output current of the source.
(b) If the frequency is changed to 60 Hz while keeping the voltage amplitude at 160 V, what are the capacitive reactance and the current amplitude?
Answer:   (a) 11.4 kΩ, 14 mA   (b) 3.79 x 106 Ω, 4.2 x 10-5 A 
A 20-mH inductor is connected across an AC source with a variable frequency and a constant-voltage amplitude of 9.0 V. 
(a) Determine the reactance of the circuit and the maximum current through the inductor when the frequency is set at 20 kHz.
(b) Do the same calculations for a frequency of 60 Hz.
Answer:  (a) 2.5 kΩ, 3.6 mA  (b) 7.54 Ω, 1.19 A
In a series R-L-C circuit, the phase angle is 43.5°, with the source voltage leading the current. The reactance of the capacitor is 395 Ω and the resistance of the resistor is 190 Ω. The average power delivered by the source is 175 W.
(a) Find the reactance of the inductor.
(b) Find the rms current.
(c) Find the rms voltage of the source.
Answer:  (a) 575 Ω (b) 0.96 A (c) 251 V
An ac source of voltage amplitude 100 V and frequency 1.0 kHz drives an RLC series circuit with R = 20 Ω, L = 4.0 mH, and C = 50 µF.
(a) Determine the rms current through the circuit.
(b) What are the rms voltages across the three elements?
(c) What is the phase angle between the emf and the current?
(d) What is the power output of the source?
(e) What is the power dissipated in the resistor?
Answer:  (a) 2.38 A  (b) R: 47.6 V, L: 59.8 V, C: 7.57 V  (c) 47.7°  (d) max = 227 W, avg: 113 W  (e) 113 W
In a series R-L-C circuit, R = 300 Ω, XC = 340 Ω and XL = 580 Ω. The average power consumed in the resistor is 60.0 W.
(a) What is the power factor of the circuit?
(b) What is the rms voltage of the source?
Answer:  (a) 0.78  (b) 172
An RLC series circuit consists of a 10-Ω resistor, an 8.0-µF capacitor, and a 50-mH inductor. A 110-V (rms) source of variable frequency is connected across the combination. What is the power output of the source when its frequency is set to one-half the resonant frequency of the circuit?
Answer: 8.5 W
A power plant generator produces 100 A at 15 kV (rms). A transformer is used to step up the transmission line voltage to 150 kV (rms).
(a) What is rms current in the transmission line?
(b) If the resistance per unit length of the line is 8.6 x 10-8 Ω/m, what is the power loss per meter in the line?
(c) What would the power loss per meter be if the line voltage were 15 kV (rms)?
Answer:   (a) 10 A  (b) 8.6 µW/m  (c) 860 µW/m
Neon signs require 12 kV for their operation. A transformer is to be used to change the voltage from 220-V (rms) ac to 12-kV (rms) ac. 
(a) What must the ratio be of turns in the secondary winding to the turns in the primary winding?
(b) What is the maximum rms current the neon lamps can draw if the fuse in the primary winding goes off at 0.5 A?
(c) How much power is used by the neon sign when it is drawing the maximum current allowed by the fuse in the primary winding?
Answer:  (a) 55  (b) 9.1 mA  (c) 110 W