/*! 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} Q61P A coil is connected in series wi... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

A coil is connected in series with a 10.0kΩresistor. An ideal 50.0 Vbattery is applied across the two devices, and the current reaches a value of 2.00 mAafter 5.00 ms.(a) Find the inductance of the coil. (b) How much energy is stored in the coil at this same moment?

Short Answer

Expert verified

a) L=97.9H

b)Ub=0.196mJ

Step by step solution

01

Given

R=10kΩ=10×103ΩE=50.0VI=2.00mA=2.00×10-3At=5.00ms=5×10-3s

02

Understanding the concept

Here we have to use the formula for current through RL circuit to find inductance. Then by using formula for energy stored by inductor’s magnetic field, we can calculate the energy stored in the coil.

Formula:

i=ER1-etLtUb=0.5Li2

03

(a) Find the inductance of the coil

Here, the rise of current for RL circuit is as follows:

i=ER1-e-tLti=ER1-e-t×RL2.00×10-3=5010×1031-e-5×10-3×10×103L0.4=1-e50-L0.6=e-50/LL=-50In0.6L=97.9H

04

(b) Calculate how much energy is stored in the coil at this same moment

The inductor’s magnetic field stores energy and is given by

Ub=0.5Li2Ub=0.5×97.9×(2.00×10-3)2

Ub=0.196mJ

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 91Ó°ÊÓ!

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

Figure 30-74 shows a uniform magnetic field confined to a cylindrical volume of radius R. The magnitude of is decreasing at a constant rate of 10m Ts. In unit-vector notation, what is the initial acceleration of an electron released at (a) point a (radial distance r=0.05m ), (b) point b (r =0 ), and (c) point c (r =0.05m)?

Figure 30-39 shows a closed loop of wire that consists of a pair of equal semicircles, of radius3.7 cm, lying in mutually perpendicular planes. The loop was formed by folding a flat circular loop along a diameter until the two halves became perpendicular to each other. A uniform magnetic fieldB→of magnitude 76 mTis directed perpendicular to the fold diameter and makes equal angles (of45°) with the planes of the semicircles. The magnetic field is reduced to zero at a uniform rate during a time interval of4.5 ms. During this interval, what are the (a) magnitude and (b) direction (clockwise or counterclockwise when viewed along the direction of B→) of the emf induced in the loop?

A loop antenna of area2.00cm2and resistance 5.21 mis perpendicular to a uniform magnetic field of magnitude 17.0 mT. The field magnitude drops to zero in 2.96 ms. How much thermal energy is produced in the loop by the change in field?

If the circular conductor in Fig. 30-21 undergoes thermal expansion while it is in a uniform magnetic field, a current is induced clockwise around it. Is the magnetic field directed into or out of the page?

Two identical long wires of radius a=1.53mmare parallel and carry identical currents in opposite directions. Their center-to-center separation is d=4.2cm.Neglect the flux within the wires but consider the flux in the region between the wires. What is the inductance per unit length of the wires?

See all solutions

Recommended explanations on Physics Textbooks

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.