Physics for Scientists and Engineers, Volume 1, Chapters 1-22
8th Edition
ISBN: 9781439048382
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 33, Problem 33.70AP
(a) Sketch a graph of the phase angle for an RLC series circuit as a function of angular frequency from zero to a frequency much higher than the resonance frequency. (b) Identify the value of ϕ at the resonance angular frequency ω0. (c) Prove that the slope of the graph of ϕ versus ω at the resonance point is 2Q/ω0.
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(a) Sketch a graph of the phase angle for an RLC series circuit as a function of angular frequency from zero to a frequency much higher than the resonance frequency. (b) Identify the value of φ at the resonance angular frequency ω0. (c) Prove that the slope of the graph of φ versus ω at the resonance point is 2Q/ω0.
In a series RLC circuit, The source voltage Vs = 120Vac. The values of the components are: R1= 50.0 ohm, L1= 3.0 H, and C1= 6.0 x 10-6 F. If the angular frequency of the source equals the resonance frequency of the circuit, what is the average output power from the source?
Electronics students are learning to use phasor diagrams to analyze RLC series circuits. They are given the following phasor diagram, and they are told that the AC power source has a frequency of 60.0 Hz and the resistor has a resistance of 50.0 Ω.
The students are then asked to determine the following.
(a)the maximum voltage ΔVmax (in V) across the series RLC combination
V
(b)the phase angle ? (in degrees)
°
(c)the maximum current (in A) in the circuit
A
(d)the total impedance (in Ω) of the circuit
Ω
(e)the capacitance (in µF)
µF
(f)the inductance (in H)
H
(g)the average power (in W) delivered to the circuit
Chapter 33 Solutions
Physics for Scientists and Engineers, Volume 1, Chapters 1-22
Ch. 33 - Consider the voltage phasor in Figure 32.4, shown...Ch. 33 - Consider the AC circuit in Figure 32.8. The...Ch. 33 - Consider the AC circuit in Figure 32.11. The...Ch. 33 - Consider the AC circuit in Figure 32.12. The...Ch. 33 - Label each part of Figure 32.16, (a), (b), and...Ch. 33 - An AC source drives an RLC circuit with a fixed...Ch. 33 - What is the impedance of a series RLC circuit at...Ch. 33 - An inductor and a resistor are connected in series...Ch. 33 - (i) When a particular inductor is connected to a...Ch. 33 - A capacitor and a resistor are connected in series...
Ch. 33 - Prob. 33.4OQCh. 33 - Prob. 33.5OQCh. 33 - A sinusoidally varying potential difference has...Ch. 33 - A series RLCcircuit contains a 20.0- resistor, a...Ch. 33 - A resistor, a capacitor, and an inductor are...Ch. 33 - (a) Why does a capacitor act as a short circuit at...Ch. 33 - What is the plia.se angle in a series RLC circuit...Ch. 33 - Prob. 33.11OQCh. 33 - A 6.00-V battery is connected across the primary...Ch. 33 - Do AC ammeters and voltmeters read (a)...Ch. 33 - (a) Explain how the quality factor is related to...Ch. 33 - (a) Explain how the mnemonic ELI the ICE man can...Ch. 33 - Why is the sum of the maximum voltages across each...Ch. 33 - (a) Does the phase angle in an RLC series circuit...Ch. 33 - Prob. 33.5CQCh. 33 - As shown in Figure CQ33.6, a person pulls a vacuum...Ch. 33 - Prob. 33.7CQCh. 33 - Will a transformer operate if a battery is used...Ch. 33 - Prob. 33.9CQCh. 33 - Prob. 33.10CQCh. 33 - When an AC source is connected across a 12.0-...Ch. 33 - (a) What is the resistance of a lightbulb that...Ch. 33 - An AC power supply produces a maximum voltage Vmax...Ch. 33 - A certain lightbulb is rated at 60.0 W when...Ch. 33 - The current in the circuit shown in Figure P32.3...Ch. 33 - In the AC circuit shown in Figure P32.3, R = 70.0 ...Ch. 33 - An audio amplifier, represented by the AC I source...Ch. 33 - Figure P32.4 shows three lightbulbs connected to a...Ch. 33 - An inductor has a .54.0- reactance when connected...Ch. 33 - In a purely inductive AC circuit as shown in...Ch. 33 - Prob. 33.11PCh. 33 - An inductor is connected to an AC power supply...Ch. 33 - An AC source has an output rms voltage of 78.0 V...Ch. 33 - A 20.0-mH inductor is connected to a North...Ch. 33 - Review. Determine the maximum magnetic flux...Ch. 33 - The output voltage of an AC source is given by v =...Ch. 33 - A 1.00-mF capacitor is connected to a North...Ch. 33 - An AC source with an output rms voltage of 86.0 V...Ch. 33 - (a) For what frequencies does a 22.0-F capacitor...Ch. 33 - A source delivers an AC voltage of the form =...Ch. 33 - What maximum current is delivered by an AC source...Ch. 33 - A capacitor C is connected to a power supply that...Ch. 33 - What is the maximum current in a 2.20-F capacitor...Ch. 33 - An AC source with Vmax = 150 V and f = 50.0 Hz is...Ch. 33 - In addition to phasor diagrams showing voltages...Ch. 33 - A sinusoidal voltage = 40.0 sin 100t, where is...Ch. 33 - A series AC circuit contains a resistor, an...Ch. 33 - At what frequency does the inductive reactance of...Ch. 33 - An RLC circuit consists of a 150- resistor, a...Ch. 33 - Prob. 33.30PCh. 33 - An inductor (L = 400 mH), a capacitor (C = 4.43...Ch. 33 - A 60.0-ft resistor is connected in series with a...Ch. 33 - Review. In an RLC series circuit that includes a...Ch. 33 - Prob. 33.34PCh. 33 - A series RLC circuit has a resistance of 45.0 and...Ch. 33 - An AC voltage of the form = 100 sin 1 000t, where...Ch. 33 - A series RLC circuit has a resistance of 22.0 and...Ch. 33 - An AC voltage of the form v = 90.0 sin 350t, where...Ch. 33 - ln a certain series RLC circuit, Irms = 9.00 A,...Ch. 33 - Prob. 33.40PCh. 33 - Prob. 33.41PCh. 33 - A series RLC circuit has components with the...Ch. 33 - An RLC circuit is used in a radio to tune into an...Ch. 33 - The LC circuit of a radar transmitter oscillates...Ch. 33 - A 10.0- resistor, 10.0-mH inductor, and 100-F...Ch. 33 - A resistor R, inductor L, and capacitor C are...Ch. 33 - Review. A radar transmitter contains an LC circuit...Ch. 33 - A step-down transformer is used for recharging the...Ch. 33 - The primary coil of a transformer has N1 = 350...Ch. 33 - A transmission line that has a resistance per unit...Ch. 33 - In the transformer shown in Figure P33.51, the...Ch. 33 - A person is working near the secondary of a...Ch. 33 - The RC high-pass filter shown in Figure P33.53 has...Ch. 33 - Consider the RC high-pass filler circuit shown in...Ch. 33 - Prob. 33.55PCh. 33 - Consider the Filter circuit shown in Figure...Ch. 33 - A step-up transformer is designed to have an...Ch. 33 - Prob. 33.58APCh. 33 - Review. The voltage phasor diagram for a certain...Ch. 33 - Prob. 33.60APCh. 33 - Energy is to be transmitted over a pair of copper...Ch. 33 - Energy is to be transmitted over a pair of copper...Ch. 33 - A 400- resistor, an inductor, and a capacitor are...Ch. 33 - Show that the rms value for the sawtooth voltage...Ch. 33 - A transformer may be used to provide maximum power...Ch. 33 - A capacitor, a coil, and two resistors of equal...Ch. 33 - Marie Cornu, a physicist at the Polytechnic...Ch. 33 - A series RLC circuit has resonance angular...Ch. 33 - Review. One insulated conductor from a household...Ch. 33 - (a) Sketch a graph of the phase angle for an RLC...Ch. 33 - In Figure P33.71, find the rms current delivered...Ch. 33 - Review. In the circuit shown in Figure P32.44,...Ch. 33 - Prob. 33.73APCh. 33 - A series RLC circuit is operating at 2.00 103 Hz....Ch. 33 - A series RLC circuit consists of an 8.00-...Ch. 33 - A series RLC circuit in which R = l.00 , L = 1.00...Ch. 33 - The resistor in Figure P32.49 represents the...Ch. 33 - An 80.0- resistor and a 200-mH inductor are...Ch. 33 - Prob. 33.79CPCh. 33 - P33.80a shows a parallel RLC circuit. The...Ch. 33 - Prob. 33.81CP
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- For an RLC series circuit, the voltage amplitude and frequency of the source are 100 V and 500 Hz, respectively; R=500 ; and L = 0.20H . Find the average power dissipated in the resistor for the following values for the capacitance: (a) C=2.0F and (b) C=2.0F .arrow_forwardWhat is the impedance of a series combination of a 50resistor, a 5.0F capacitor, and a 10F capacitor at a frequency of 2.0 kHz?arrow_forwardCalculate the rms currents for an ac source is given by v(t)=v0sint , where V0=100V and =200rad/s when connected across (a) a 20F capacitor, (b) a 20-mH inductor, and (c) a 50 resistor.arrow_forward
- A 40-mH inductor is connected to a 60-Hz AC source whose voltage amplitude is 50 V. If an AC voltmeter is placed across the inductor, what does it read?arrow_forwardIn the AC circuit shown in Figure P32.3, R = 70.0 and the output voltage of the AC source is Vmax sin t. (a) If VR = 0.250 Vmax for the first time at t = 0.0100 s, what is the angular frequency of the source? (b) What is the next value of t for which VR = 0.250 Vmax? Figure P32.6 Problem 3 and 5.arrow_forwardA 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.arrow_forward
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- A 1.5k resistor and 30-mH inductor are connected in series, as below, across a120-V(rms)ac power source oscillating at 60-Hz frequency. (a) Find the current in the circuit. (b) Find the voltage drops across the resistor and inductor. (C) Find the impedance of the circuit. (d) Find the power dissipated in the resistor. (e) Find the power dissipated in the inductor. (1) Find the power produced by the source.arrow_forwardIn an ideal AC circuit with capacitance, there is no resistance. Is any energy dissipated? How about in a real AC circuit with capacitance?arrow_forwardCalculate the reactance of a 5.0F capacitor at (a) 60 Hz, (b) 600 Hz, and (c) 6000 Hz.arrow_forward
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