### Chapter 31, Problem 065#### Problem StatementAn AC generator provides an EMF to a resistive load in a remote factory over a two-cable transmission line. At the factory, a step-down transformer reduces the voltage from its (RMS) transmission value \( V_t \) to a much lower value that is safe and convenient for use in the factory. The transmission line resistance is \(0.51 \, \Omega/\text{cable}\), and the power of the generator is \(279 \, \text{kW}\).Given:- \( V_t = 110 \, \text{kV} \)1. What is (a) the voltage decrease \( \Delta V \) along the transmission line and (b) the rate \( P_d \) at which energy is dissipated in the line as thermal energy? 2. If \( V_t = 8.1 \, \text{kV} \), what are (c) \( \Delta V \) and (d) \( P_d \)? 3. If \( V_t = 0.86 \, \text{kV} \), what are (e) \( \Delta V \) and (f) \( P_d \)?#### Solutions(a) - \(\Delta V = 2.586 \, \text{kV}\)(b) - \(P_d = 6.559 \, \text{kW}\)(c) - \(\Delta V = 35.12 \, \text{kV}\)(d) - \(P_d = 209.8 \, \text{kW}\)(e) - \(\Delta V = 330.8 \, \text{kV}\) Note: The answer marked with a red “X” indicates this value is incorrect. (f) - \(P_d = 107.300 \, \text{kW}\)#### ExplanationThis problem explores the relationship between the voltage, power dissipation, and thermal energy in a transmission line. The voltage drop \( \Delta V \) along the line affects how much energy is lost as heat, which is represented by \( P_d \). By changing the transmission voltage \( V_t \), we observe how it impacts \( \Delta V \) and \( P_d \), demonstrating the importance of voltage regulation in power transmission systems for efficient energy distribution. This

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Chapter 31, Problem 065 Your answer is partially correct. Try again. n ac generator provides emf to a resistive load in a remote factory over a two-cable transmission line. At the factory a tep-down transformer reduces the voltage from its (rms) transmission value V, to a much lower value that is safe and onvenient for use in the factory. The transmission line resistance is 0.51 2/cable, and the power of the generator is 279 W. If V = 110 kV, what are (a) the voltage decrease AV along the transmission line and (b) the rate Pa at which energy s dissipated in the line as thermal energy? If V = 8.1 kV, what are (c) AV and (d) Pg? If V = 0.86 kV, what are (e) AV nd (f) Pd? Ca) Number 12.586 Units (b) Numbel6.559 UnitsW c) Number Unit T35.12 (d) Numbel 209.8 UnitsW (e) Number Units TKV 330.8 (f) Numbel07.300 Unitsw

Chapter 31, Problem 065 Your answer is partially correct. Try again. n ac generator provides emf to a resistive load in a remote factory over a two-cable transmission line. At the factory a tep-down transformer reduces the voltage from its (rms) transmission value V, to a much lower value that is safe and onvenient for use in the factory. The transmission line resistance is 0.51 2/cable, and the power of the generator is 279 W. If V = 110 kV, what are (a) the voltage decrease AV along the transmission line and (b) the rate Pa at which energy s dissipated in the line as thermal energy? If V = 8.1 kV, what are (c) AV and (d) Pg? If V = 0.86 kV, what are (e) AV nd (f) Pd? Ca) Number 12.586 Units (b) Numbel6.559 UnitsW c) Number Unit T35.12 (d) Numbel 209.8 UnitsW (e) Number Units TKV 330.8 (f) Numbel07.300 Unitsw

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter32: Faraday’s Law Of Induction

Section: Chapter Questions

Problem 52PQ

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Concept explainers

Voltage Across Inductor

An actor is a passive electrical component that consists of a coil bent in the form of wire which uses electromagnetism to produce electric current through the coil. When the electric current flows through a conductor that is the coil, a magnetic flux is developed around the conductor. This flow of current through the coil creates a magnetic field based on Fleming's Right-hand thumb rule. If there is any decrease in the current passing through the inductor, then the magnetic field will also decrease and energy is released through the generation of electric current. There is also a secondary voltage inducing in the same coil due to the magnetic flux, since it opposes any changes in the electric current flowing through the circuit. An inductor is also called choke, coil, or solenoid. A choke is designed to block certain frequencies when the DC current passes. A winding coil is coated with insulation to give extra insulation and protect the circuit. They are usually tightly wrapped around a central core which is cylindrical in nature so that the magnetic flux can be induced. The solenoid is a three-dimension coil that is used to exhibit electromagnetism when the magnetic field is developed due to the current flowing through the coil. The sign convention of the inductor is the same as the power dissipating device. When the current flows into the positive side of the voltage across the inductor, the value is positive and the inductor dissipates power whereas when the inductor releases the power back to the circuit, the current has a negative sign convention. 

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### Chapter 31, Problem 065

#### Problem Statement

An AC generator provides an EMF to a resistive load in a remote factory over a two-cable transmission line. At the factory, a step-down transformer reduces the voltage from its (RMS) transmission value \( V_t \) to a much lower value that is safe and convenient for use in the factory. The transmission line resistance is \(0.51 \, \Omega/\text{cable}\), and the power of the generator is \(279 \, \text{kW}\).

Given:
- \( V_t = 110 \, \text{kV} \)

1. What is (a) the voltage decrease \( \Delta V \) along the transmission line and (b) the rate \( P_d \) at which energy is dissipated in the line as thermal energy?

2. If \( V_t = 8.1 \, \text{kV} \), what are (c) \( \Delta V \) and (d) \( P_d \)?

3. If \( V_t = 0.86 \, \text{kV} \), what are (e) \( \Delta V \) and (f) \( P_d \)?

#### Solutions

(a)
- \(\Delta V = 2.586 \, \text{kV}\)

(b)
- \(P_d = 6.559 \, \text{kW}\)

(c)
- \(\Delta V = 35.12 \, \text{kV}\)

(d)
- \(P_d = 209.8 \, \text{kW}\)

(e)
- \(\Delta V = 330.8 \, \text{kV}\)

Note: The answer marked with a red “X” indicates this value is incorrect.

(f)
- \(P_d = 107.300 \, \text{kW}\)

#### Explanation

This problem explores the relationship between the voltage, power dissipation, and thermal energy in a transmission line. The voltage drop \( \Delta V \) along the line affects how much energy is lost as heat, which is represented by \( P_d \). By changing the transmission voltage \( V_t \), we observe how it impacts \( \Delta V \) and \( P_d \), demonstrating the importance of voltage regulation in power transmission systems for efficient energy distribution. This

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