Explanation 1) Concept: For a series LCR circuit, we have the relations to find out the inductive and capacitive reactance. By using those relations, we can find out the impedance of the circuit, phase angle, and the amplitude of the current. 2) Formula: i) Capacitive reactance, χ c = 1 ω d C ii) Inductive reactance, χ L = ω d L iii) Impedance, Z = R 2 + χ L - χ C 2 iv) Phase constant or angle, ϕ = tan - 1 ⁡ ( χ L - χ C R ) v) Amplitude of current, I = ϵ m Z 3) Given: i) Resistance, R = 200 Ω ii) Capacitance, C = 70.0 μ F = 70.0 × 10 - 6 F iii) Inductance, L = 230 m H = 230 × 10 - 3 H iv) Driving frequency, f d = 60.0 H z v) Amplitude of emf ϵ m = 36.0 V 4) Calculations: a) First, let’s find out the driving angular frequency. It is given as ω d = 2 π f d ω d = 2 × 3.14 × 60.0 = 376.8 H z Capacitive reactance is given by χ c = 1 ω d C = 1 376.8 × 70.0 × 10 - 6 = 10 6 376

11th Edition

ISBN: 9781119455608

Author: Halliday

Publisher: WILEY

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Question

Chapter 31, Problem 41P

To determine

To find:

a) Impedance of the series LCR circuit, Z

b) Phase angle, ϕ

c) Amplitude of current, I

d) Construct phasor diagram

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Chapter 31, Problem 40P

Chapter 31, Problem 42P

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Chapter 31 Solutions

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Ch. 31 - Figure 31-19 shows three oscillating LC circuits...Ch. 31 - Figure 31-20 shows graphs of capacitor voltage vc...Ch. 31 - Prob. 3Q Ch. 31 - What values of phase constant in Eq. 31-12 allow...Ch. 31 - Curve a in Fig. 31-21 gives the impedance Z of a...Ch. 31 - Prob. 6Q Ch. 31 - Prob. 7Q Ch. 31 - The values of the phase constant for four...Ch. 31 - Prob. 9Q Ch. 31 - Figure 31-24 shows three situations like those of...

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a) Impedance of the series LCR circuit, Z b) Phase angle, ϕ c) Amplitude of current, I d) Construct phasor diagram

Solution Summary: The author explains how to find the impedance, phase angle, and amplitude of a series LCR circuit.

To find: a) Impedance of the series LCR circuit, Z b) Phase angle, ϕ c) Amplitude of current, I d) Construct phasor diagram

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Chapter 31 Solutions

To find:

a) Impedance of the series LCR circuit, Z

b) Phase angle, ϕ

c) Amplitude of current, I

d) Construct phasor diagram