/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 51 The current in a \(0.080-\mathrm... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 20: Problem 51

The current in a \(0.080-\mathrm{H}\) solenoid increases from \(20.0 \mathrm{mA}\) to \(160.0 \mathrm{mA}\) in \(7.0 \mathrm{s} .\) Find the average emf in the solenoid during that time interval.

Short Answer

Expert verified
Answer: The average electromotive force (emf) in the solenoid during the given time interval is -1.6 V.

Step by step solution

01

Convert values to proper units

To work with the given values, let's convert all currents to amperes (A) and make sure all other units are in SI units. Initial current: \(I_1 = 20.0 \mathrm{mA} = 20.0 \times 10^{-3} A\) Final current: \(I_2 = 160.0 \mathrm{mA} = 160.0 \times 10^{-3} A\) Inductance: \(L = 0.080 H\) Time interval: \(\Delta t = 7.0 s\)
02

Calculate change in current

Calculate the change in current by subtracting the initial current from the final current: \(\Delta I = I_2 - I_1 = (160.0 - 20.0) \times 10^{-3} A = 140 \times 10^{-3} A\)
03

Plug values into Faraday's law formula

Plug the given values into Faraday's law formula to find the average emf: \(\text{average emf} = \frac{-L \Delta I}{\Delta t} = \frac{-(0.080 H)(140 \times 10^{-3} A)}{7.0 s}\)
04

Calculate the average emf

Now calculate the average emf: \(\text{average emf} = \frac{-(0.080 H)(140 \times 10^{-3} A)}{7.0 s} = -1.6 V\) The average electromotive force (emf) in the solenoid during the given time interval is \(-1.6 V\). The negative sign indicates that the emf is acting against the change in current.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

When the armature of an ac generator rotates at $15.0 \mathrm{rad} / \mathrm{s},\( the amplitude of the induced emf is \)27.0 \mathrm{V}$ What is the amplitude of the induced emf when the armature rotates at $10.0 \mathrm{rad} / \mathrm{s} ?$ (tutorial: generator)

The armature of an ac generator is a circular coil with 50 turns and radius \(3.0 \mathrm{cm} .\) When the armature rotates at 350 rpm, the amplitude of the emf in the coil is \(17.0 \mathrm{V}\) What is the strength of the magnetic field (assumed to be uniform)?
The outside of an ideal solenoid $\left(N_{1} \text { turns, length } L\right.\( radius \)r)\( is wound with a coil of wire with \)N_{2}$ turns. (a) What is the mutual inductance? (b) If the current in the solenoid is changing at a rate \(\Delta I_{1} / \Delta t,\) what is the magnitude of the induced emf in the coil?
The alternator in an automobile generates an emf of amplitude $12.6 \mathrm{V}\( when the engine idles at \)1200 \mathrm{rpm}$. What is the amplitude of the emf when the car is being driven on the highway with the engine at 2800 rpm?
In this problem, you derive the expression for the self inductance of a long solenoid [Eq. \((20-15 a)] .\) The solenoid has \(n\) turns per unit length, length \(\ell,\) and radius \(r\) Assume that the current flowing in the solenoid is \(I\) (a) Write an expression for the magnetic field inside the solenoid in terms of \(n, \ell, r, I,\) and universal constants. (b) Assume that all of the field lines cut through each turn of the solenoid. In other words, assume the field is uniform right out to the ends of the solenoid-a good approximation if the solenoid is tightly wound and sufficiently long. Write an expression for the magnetic flux through one turn. (c) What is the total flux linkage through all turns of the solenoid? (d) Use the definition of self-inductance [Eq. \((20-14)]\) to find the self inductance of the solenoid.
See all solutions

Recommended explanations on Physics Textbooks

Thermodynamics

Read Explanation

Oscillations

Read Explanation

Space Physics

Read Explanation

Quantum Physics

Read Explanation

Translational Dynamics

Read Explanation

Electromagnetism

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.