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The field coils of a six-poles D. C. Generator, each having 600 turns, are connected in series. On the excitation of the field, there is a magnetic flux of 0.024 Wb/pole. If the field circuit is opened in 0.24 seconds and residual magnetism is 0.0024 wb/pole, calculate the average voltage induced across field terminals.

The field coils of a six-poles D. C. Generator, each having 600 turns, are connected in series. On the excitation of the field, there is a magnetic flux of 0.024 Wb/pole. If the field circuit is opened in 0.24 seconds and residual magnetism is 0.0024 wb/pole, calculate the average voltage induced across field terminals.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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**Problem Statement:** The field coils of a six-poles D.C. Generator, each having 600 turns, are connected in series. On the excitation of the field, there is a magnetic flux of 0.024 Wb/pole. If the field circuit is opened in 0.24 seconds and residual magnetism is 0.0024 Wb/pole, calculate the average voltage induced across field terminals. **Solution Explanation:** To calculate the average voltage induced across the field terminals when the circuit is opened, we use the formula for the average induced emf (electromotive force) in a coil, which is derived from Faraday's Law of Electromagnetic Induction: \[ \text{Average emf} = -N \left(\frac{\Delta \Phi}{\Delta t}\right) \] Where: - \( N \) is the total number of turns in the coil. - \( \Delta \Phi \) is the change in magnetic flux. - \( \Delta t \) is the time interval during which the change occurs. **Given:** - Number of poles (\( P \)) = 6 - Number of turns per pole = 600 - Initial magnetic flux per pole = 0.024 Wb - Residual magnetic flux per pole = 0.0024 Wb - Time interval (\( \Delta t \)) = 0.24 s **Calculation:** 1. **Calculate Total Number of Turns:** \[ N_{\text{total}} = P \times \text{Turns per pole} = 6 \times 600 = 3600 \] 2. **Calculate Change in Magnetic Flux (\( \Delta \Phi \)):** \[ \Delta \Phi = (\text{Initial Flux} - \text{Residual Flux}) \times P = (0.024 - 0.0024) \times 6 = 0.1296 \text{ Wb} \] 3. **Calculate Average Induced EMF:** \[ \text{Average emf} = -3600 \times \left(\frac{0.1296}{0.24}\right) \] \[ \text{Average emf} = -3600 \times 0.54 = -1944 \text{ V} \] The negative sign indicates the direction of the induced emf as per Lenz's law
Transcribed Image Text:**Problem Statement:** The field coils of a six-poles D.C. Generator, each having 600 turns, are connected in series. On the excitation of the field, there is a magnetic flux of 0.024 Wb/pole. If the field circuit is opened in 0.24 seconds and residual magnetism is 0.0024 Wb/pole, calculate the average voltage induced across field terminals. **Solution Explanation:** To calculate the average voltage induced across the field terminals when the circuit is opened, we use the formula for the average induced emf (electromotive force) in a coil, which is derived from Faraday's Law of Electromagnetic Induction: \[ \text{Average emf} = -N \left(\frac{\Delta \Phi}{\Delta t}\right) \] Where: - \( N \) is the total number of turns in the coil. - \( \Delta \Phi \) is the change in magnetic flux. - \( \Delta t \) is the time interval during which the change occurs. **Given:** - Number of poles (\( P \)) = 6 - Number of turns per pole = 600 - Initial magnetic flux per pole = 0.024 Wb - Residual magnetic flux per pole = 0.0024 Wb - Time interval (\( \Delta t \)) = 0.24 s **Calculation:** 1. **Calculate Total Number of Turns:** \[ N_{\text{total}} = P \times \text{Turns per pole} = 6 \times 600 = 3600 \] 2. **Calculate Change in Magnetic Flux (\( \Delta \Phi \)):** \[ \Delta \Phi = (\text{Initial Flux} - \text{Residual Flux}) \times P = (0.024 - 0.0024) \times 6 = 0.1296 \text{ Wb} \] 3. **Calculate Average Induced EMF:** \[ \text{Average emf} = -3600 \times \left(\frac{0.1296}{0.24}\right) \] \[ \text{Average emf} = -3600 \times 0.54 = -1944 \text{ V} \] The negative sign indicates the direction of the induced emf as per Lenz's law
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