Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 33, Problem 33.59AP

Review. The voltage phasor diagram for a certain series RLC circuit is shown in Figure P33.59. The resistance of the circuit is 75.0 Ω, and the frequency is 60.0 Hz. Find (a) the maximum voltage ΔVmax, (b) the phase angle ϕ, (c) the maximum current, (d) the impedance, (e) the capacitance and (f) the inductance of the circuit, and (g) the average power delivered to the circuit.

Chapter 33, Problem 33.59AP, Review. The voltage phasor diagram for a certain series RLC circuit is shown in Figure P33.59. The

(a)

Expert Solution
Check Mark
To determine

 The maximum voltage.

Answer to Problem 33.59AP

The maximum voltage is 22.4V .

Explanation of Solution

Given info: The resistance of the circuit is 75.0Ω , the frequency is 60.0Hz . The voltage drop across the resistor is 20.0V , the voltage drop across the inductor is 25.0V and the voltage drop across the capacitor is 15.0V .

The expression for maximum value of the voltage is,

ΔVmax=(ΔVR)2+(ΔVLΔVC)2

Here,

ΔVR is the voltage drop across the resistor.

ΔVL is the voltage drop across the inductor.

ΔVC is the voltage drop across the capacitor.

Substitute 20.0V for ΔVR , 25.0V for ΔVL and 15.0V for ΔVC in the above expression.

ΔVmax=(20.0V)2+(25.0V15.0V)2=22.36V22.4V

Conclusion:

Therefore, the maximum voltage is 22.4V .

(b)

Expert Solution
Check Mark
To determine

 The phase angle.

Answer to Problem 33.59AP

 The phase angle is 26.6° .

Explanation of Solution

Given info: The resistance of the circuit is 75.0Ω , the frequency is 60.0Hz . The voltage drop across the resistor is 20.0V , the voltage drop across the inductor is 25.0V and the voltage drop across the capacitor is 15.0V .

The expression for the phase angle is,

ϕ=sin1(ΔVLΔVCΔVmax)

Substitute 22.4V for ΔVmax , 25.0V for ΔVL and 15.0V for ΔVC in the above expression.

ϕ=sin1(25.0V15.0V22.4V)=26.5°26.6°

Conclusion:

Therefore, the phase angle is 26.6° .

(c)

Expert Solution
Check Mark
To determine

 The maximum current.

Answer to Problem 33.59AP

The maximum current is 0.267A .

Explanation of Solution

Given info: The resistance of the circuit is 75.0Ω , the frequency is 60.0Hz . The voltage drop across the resistor is 20.0V , the voltage drop across the inductor is 25.0V and the voltage drop across the capacitor is 15.0V .

The expression for maximum current is,

Imax=ΔVRR

Here,

R is the resistance.

Substitute 20.0V for ΔVR and 75.0Ω for R in the above expression.

Imax=20.0V75.0Ω=0.267A

Conclusion:

Therefore, the maximum current is 0.267A .

(d)

Expert Solution
Check Mark
To determine

 The impedance.

Answer to Problem 33.59AP

 The impedance is 83.9Ω .

Explanation of Solution

Given info: The resistance of the circuit is 75.0Ω , the frequency is 60.0Hz . The voltage drop across the resistor is 20.0V , the voltage drop across the inductor is 25.0V and the voltage drop across the capacitor is 15.0V .

The expression for the impedance is,

Z=Rcosϕ

Substitute 75.0Ω for R and 26.6° for ϕ in the above expression.

Z=75.0Ωcos(26.6°)=83.87Ω83.9Ω

Conclusion:

Therefore, the impedance is 83.9Ω .

(e)

Expert Solution
Check Mark
To determine

 The capacitance.

Answer to Problem 33.59AP

 The capacitance is 47.2μF .

Explanation of Solution

Given info: The resistance of the circuit is 75.0Ω , the frequency is 60.0Hz . The voltage drop across the resistor is 20.0V , the voltage drop across the inductor is 25.0V and the voltage drop across the capacitor is 15.0V .

The circuit is series RLC circuit, therefore the value of current throughout the circuit is same.

The expression capacitive reactance is,

XC=ΔVCImax

Substitute 15.0V for ΔVC and 0.267A for Imax in the above expression.

XC=15.0V0.267A=56.18Ω

The expression capacitive reactance in terms of the capacitance is,

XC=12πfC

Here,

f is the frequency.

C is the capacitance.

Rearrange the above equation for the value of capacitance.

C=12πfXC

Substitute 56.18Ω for XC and 60.0Hz for f in the above expression.

C=12π(60.0Hz)(56.18Ω)=47.2×106F=47.2μF

Conclusion:

Therefore, the capacitance is 47.2μF .

(f)

Expert Solution
Check Mark
To determine

 The inductance of the circuit.

Answer to Problem 33.59AP

 The inductance of the circuit 0.248H .

Explanation of Solution

Given info: The resistance of the circuit is 75.0Ω , the frequency is 60.0Hz . The voltage drop across the resistor is 20.0V , the voltage drop across the inductor is 25.0V and the voltage drop across the capacitor is 15.0V .

The circuit is series RLC circuit, therefore the value of current throughout the circuit is same.

The expression inductive reactance is,

XL=ΔVLImax

Substitute 25.0V for ΔVC and 0.267A for Imax in the above expression.

XL=25.0V0.267A=93.63Ω

Thus the value of inductive reactance is 93.63Ω .

The expression inductive reactance in terms of the inductance is,

XL=2πfL

Here,

f is the frequency.

L is the capacitance.

Rearrange the above equation for the value of inductance.

L=XL2πf

Substitute 93.63Ω for XC and 60.0Hz for f in the above expression.

C=93.63Ω2π(60.0Hz)=0.248H0.248H

Conclusion:

Therefore, the inductance is 0.248H .

(g)

Expert Solution
Check Mark
To determine

 The average power delivered to circuit.

Answer to Problem 33.59AP

 The average power delivered to circuit is 2.67W .

Explanation of Solution

Given info: The resistance of the circuit is 75.0Ω , the frequency is 60.0Hz . The voltage drop across the resistor is 20.0V , the voltage drop across the inductor is 25.0V and the voltage drop across the capacitor is 15.0V .

The expression for R.M.S value of the current is,

IRMS=Imax2

The expression for the average power delivered is,

Pavg=(IRMS)2R

Substitute Imax2 for IRMS in the above equation.

Pavg=(Imax2)2R=(Imax)22R

Substitute 0.267A for Imax and 75.0Ω for R in the above equation.

Pavg=(0.267A)2275.0Ω=2.67W

Conclusion:

Therefore, the average power delivered to circuit is 2.67W .

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Chapter 33 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

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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