Explanation 1) Concept: The three-phase generator has three ac voltages that are 120 0 out of phase with each other. We can calculate the potential difference between any two wires by using trigonometric identity. 2) Formula: sin ⁡ A - sin ⁡ B = 2 sin ⁡ A - B 2 cos ⁡ A + B 2 3) Given: i) V 1 = A sin ⁡ ω d t ii) V 2 = A sin ⁡ ( ω d t - 120 0 ) iii) V 3 = A sin ⁡ ( ω d t - 240 0 ) 4) Calculations: a) We consider different combinations for potential difference: ∆ V 12 = V 1 - V 2 ∆ V 12 = A sin ⁡ ω d t - A sin ⁡ ω d t - 120 0 By using the trigonometric identity, ∆ V 12 = 2 A sin ⁡ ω d t - ω d t + 120 0 2 cos ⁡ ω d t + ω d t - 120 0 2 ∆ V 12 = 2 A sin ⁡ ( 60 0 ) cos ⁡ ( ω d t - 60 0 ) ∆ V 12 = 2 A 3 2 cos ⁡ ( ω d t - 60 0 ) ∆ V 12 = 3 A cos ⁡ ( ω d t - 60 0 ) Now, ∆ V 13 = V 1 - V 3 ∆ V 13 = A sin ⁡ ω d t - A sin ⁡ ( ω d t - 240 0 ) By using the trigonometric identity, ∆ V 13 = 2 A sin ⁡ ω d t - ω d t + 240 0 2 cos ⁡ ω d t + ω d t - 240 0 2 </

10th Edition

ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Chapter 31, Problem 77P

To determine

To show:

a) The potential difference between any two of the wires oscillates sinusoidally with the angular frequency ωd

b) The potential difference between any two of the wires has an amplitude of A3

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Chapter 31, Problem 76P

Chapter 31, Problem 78P

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Chapter 31 Solutions

Fundamentals of Physics Extended

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Knowledge Booster

a) The potential difference between any two of the wires oscillates sinusoidally with the angular frequency ω d b) The potential difference between any two of the wires has an amplitude of A 3

Solution Summary: The author explains that the three-phase generator has three ac voltages that are 1200 out of phase with each other. They can calculate the potential difference between any two wires by using trigon

To show:

a) The potential difference between any two of the wires oscillates sinusoidally with the angular frequency ωd

b) The potential difference between any two of the wires has an amplitude of A3

Want to see the full answer?

Chapter 31 Solutions

a) The potential difference between any two of the wires oscillates sinusoidally with the angular frequency ω d b) The potential difference between any two of the wires has an amplitude of A 3

Solution Summary: The author explains that the three-phase generator has three ac voltages that are 1200 out of phase with each other. They can calculate the potential difference between any two wires by using trigon

To show: a) The potential difference between any two of the wires oscillates sinusoidally with the angular frequency ωd b) The potential difference between any two of the wires has an amplitude of A3

Want to see the full answer?

Chapter 31 Solutions

To show:

a) The potential difference between any two of the wires oscillates sinusoidally with the angular frequency ωd

b) The potential difference between any two of the wires has an amplitude of A3