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Ch 31: Alternating Current
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 31: Alternating CurrentProblem 24
Chapter 31, Problem 24

An L-R-C series circuit is connected to a 120-Hz ac source that has Vrms = 80.0 V. The circuit has a resistance of 75.0 Ω and an impedance at this frequency of 105 Ω. What average power is delivered to the circuit by the source?

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Start by understanding the concept of average power in an AC circuit, which is given by the formula: \( P_{avg} = I_{rms}^2 \times R \), where \( I_{rms} \) is the root mean square current and \( R \) is the resistance.
To find \( I_{rms} \), use the relationship between voltage, current, and impedance in an AC circuit: \( V_{rms} = I_{rms} \times Z \), where \( Z \) is the impedance. Rearrange this formula to solve for \( I_{rms} \): \( I_{rms} = \frac{V_{rms}}{Z} \).
Substitute the given values into the formula: \( V_{rms} = 80.0 \) V and \( Z = 105 \) Ω to calculate \( I_{rms} \).
Once \( I_{rms} \) is calculated, substitute it into the average power formula: \( P_{avg} = I_{rms}^2 \times R \), using \( R = 75.0 \) Ω.
Calculate \( P_{avg} \) using the values obtained from the previous steps to find the average power delivered to the circuit.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Impedance in AC Circuits

Impedance is the total opposition a circuit presents to the flow of alternating current (AC) and is a combination of resistance, inductive reactance, and capacitive reactance. In an L-R-C circuit, impedance determines how much voltage is required to drive a certain current through the circuit. It is crucial for calculating power in AC circuits.
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Impedance in AC Circuits

RMS Voltage

RMS (Root Mean Square) voltage is a measure of the effective value of an alternating voltage, which is equivalent to a DC voltage that would deliver the same power to a load. It is used in AC circuits to calculate power because it accounts for the varying nature of AC voltage over time.
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Average Power in AC Circuits

Average power in AC circuits is calculated using the formula P_avg = V_rms * I_rms * cos(φ), where φ is the phase angle between the voltage and current. This formula accounts for the fact that not all the power in an AC circuit is used effectively due to phase differences, making it essential for determining the actual power delivered to the circuit.
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Related Practice
Textbook Question

In an L-R-C series circuit, the components have the following values: L = 20.0 mH, C = 140 nF, and R = 350 Ω.The generator has an rms voltage of 120 V and a frequency of 1.25 kHz. Determine (a) the power supplied by the generator and (b) the power dissipated in the resistor.

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Textbook Question

Off to Europe! You plan to take your hair dryer to Europe, where the electrical outlets put out 240 V instead of the 120 V seen in the United States. The dryer puts out 1600 W at 120 V. (b) What current will your dryer draw from a European outlet? (c) What resistance will your dryer appear to have when operated at 240 V?

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Textbook Question

Off to Europe! You plan to take your hair dryer to Europe, where the electrical outlets put out 240 V instead of the 120 V seen in the United States. The dryer puts out 1600 W at 120 V. What could you do to operate your dryer via the 240 V line in Europe?

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Textbook Question

A series ac circuit contains a 250-Ω resistor, a 15-mH inductor, a 3.5-μF capacitor, and an ac power source of voltage amplitude 45 V operating at an angular frequency of 360 rad/s.What is the power factor of this circuit?

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Textbook Question

An L-R-C series circuit with L = 0.120 H, R = 240 Ω, and C = 7.30 μF carries an rms current of 0.450 A with a frequency of 400 Hz. What are the phase angle and power factor for this circuit?

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Textbook Question

The power of a certain CD player operating at 120 V rms is 20.0 W. Assuming that the CD player behaves like a pure resistor, find the maximum instantaneous power.

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