### Problem StatementA generator produces 18.0 V when turning at 920 rev/min. What emf does it produce when turning at 520 rev/min?[Input box for answer] V#### Additional Materials- [eBook link icon] eBook### ExplanationThe problem involves calculating the electromotive force (emf) produced by a generator when its rotational speed changes. The emf produced by a generator is directly proportional to its speed of rotation. This means if we denote the emf as $ E $ and the speed as $ \omega $, the relationship can be expressed as:\[ E_1 / E_2 = \omega_1 / \omega_2 \]Where:- $ E_1 $ is the initial emf (18.0 V)- $ \omega_1 $ is the initial speed (920 rev/min)- $ E_2 $ is the emf at the new speed- $ \omega_2 $ is the new speed (520 rev/min)The formula can be rearranged to solve for $ E_2 $:\[ E_2 = E_1 \times (\omega_2 / \omega_1) \]Substitute the provided values:\[ E_2 = 18.0 \times (520 / 920) \]Calculate $ E_2 $ to find the emf at the new speed.

Let, E1=18.0 Vf1=920 rev/minf2 = 520 rev/min To determine: E2

Answered: A generator produces 18.0 V when…

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A generator produces 18.0 V when turning at 920 rev/min. What emf does it produce when turning at 520 rev/min? V

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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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. 

Question

### Problem Statement

A generator produces 18.0 V when turning at 920 rev/min. What emf does it produce when turning at 520 rev/min?

[Input box for answer] V

#### Additional Materials
- [eBook link icon] eBook

### Explanation

The problem involves calculating the electromotive force (emf) produced by a generator when its rotational speed changes. The emf produced by a generator is directly proportional to its speed of rotation. This means if we denote the emf as $ E $ and the speed as $ \omega $, the relationship can be expressed as:

\[ E_1 / E_2 = \omega_1 / \omega_2 \]

Where:
- $ E_1 $ is the initial emf (18.0 V)
- $ \omega_1 $ is the initial speed (920 rev/min)
- $ E_2 $ is the emf at the new speed
- $ \omega_2 $ is the new speed (520 rev/min)

The formula can be rearranged to solve for $ E_2 $:

\[ E_2 = E_1 \times (\omega_2 / \omega_1) \]

Substitute the provided values:

\[ E_2 = 18.0 \times (520 / 920) \]

Calculate $ E_2 $ to find the emf at the new speed.

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