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 </

11th Edition

ISBN: 9781119286240

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: WILEY

See similar textbooks

Question

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 31, Problem 76P

Chapter 31, Problem 78P

Students have asked these similar questions

No chatgpt pls will upvote

Solve and answer the problem correctly please. Thank you!!

Chapter 31 Solutions

Fundamentals Of Physics

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...

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