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An AC source operating at 60. Hz with a maximum voltage of 170 V is connected in series with a resistor ( R = 1.2 kΩ) and an inductor ( L = 2.8 H). (a) What is the maximum value of the current in the circuit? (b) What are the maximum values of the potential difference across the resistor and the inductor? (c) When the current is at a maximum, what are the magnitudes of the potential differences across the resistor, the inductor, and the AC source? (d) When the current is zero, what are the magnitudes of the potential difference across the resistor, the inductor, and the AC source?

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College Physics

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781285737027

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Chapter
Section
BuyFindarrow_forward

College Physics

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781285737027
Chapter 21, Problem 24P
Textbook Problem
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An AC source operating at 60. Hz with a maximum voltage of 170 V is connected in series with a resistor (R = 1.2 kΩ) and an inductor (L = 2.8 H). (a) What is the maximum value of the current in the circuit? (b) What are the maximum values of the potential difference across the resistor and the inductor? (c) When the current is at a maximum, what are the magnitudes of the potential differences across the resistor, the inductor, and the AC source? (d) When the current is zero, what are the magnitudes of the potential difference across the resistor, the inductor, and the AC source?

(a)

To determine
The maximum current in the circuit.

Explanation of Solution

Given Info: The resistance of the resistor is 1.2 . The inductance of the inductor is 2.8H . The frequency of the ac circuit is 60Hz . Maximum voltage of the source is 170V .

The inductive reactance of the circuit is,

XL=2πfL

  • f is the frequency of the ac source
  • L is the inductance of the inductor

Substitute 60Hz for f , 2.8H for L to determine the inductive reactance,

XL=2π(60Hz)(2.8H)=1.1×103Ω

The formula to calculate the impedance of the circuit where the components are in series is given by,

Z=R2+(XLXC)2

  • R is the resistance of the resistor
  • XL is the inductive reactance
  • XC is the capacitive reactance

Substitute 1.2 for R , 1.1×103Ω for XL , 0 for XC to determine the impedance of the circuit,

Z=(1

b)

To determine
The maximum voltage across the resistor and inductor.

c)

To determine
The potential difference across the resistor, inductor, and the ac source when the current is at its maximum.

d)

To determine
The potential difference across the resistor, inductor, and the ac source when the current is at it is zero.

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