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Chapter 30: Q46P (page 899)

The current i through a 4.6 Hinductor varies with time t as shown by the graph of Figure, where the vertical axis scale is set by is=8.0A and the horizontal axis scale is set by ts=6.0ms . The inductor has a resistance of12惟.(a) Find the magnitude of the induced emf 蔚 during time intervals 0 to 2 ms. (b) Find the magnitude of the induced emf 蔚 during time intervals 2 ms to 5 ms. (c) Find the magnitude of the induced emf 蔚during time intervals 5 ms to 6 ms. (Ignore the behavior at the ends of the intervals.)

Short Answer

Expert verified
  1. 蔚=1.6x104V
  2. 蔚=3.1x103V
  3. 蔚=2.3x104V

Step by step solution

01

Given

is=8Ats=6ms

02

Understanding the concept

According to Faraday鈥檚 law, the emf induced in a circuit is proportional to the time rate of change of the magnetic flux linking that circuit.

Formulae:

Induced emfis given by

蔚=Ldidt

03

(a) Calculate the induced emf for a time interval  0 to 2 ms

Induced emf 蔚 is given by

o,=Ldidti=0to7A蔚=Ldidt=4.6脳7-02-0脳10-3蔚=1.6脳104V

04

(b) Calculate the induced emf for time interval  2ms to5ms

For time interval 2ms to 5ms

1=7t05A蔚=Ldidt=4.6脳5-75-2脳10-3蔚=3.1脳103鈥�V

05

(c) Calculate the induced emf for time interval  5ms to 6ms

For time interval 5ms to 6ms

1=0to5A蔚=Ldidt=4.6脳5-06-5脳10-3蔚=2.3脳104V

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Most popular questions from this chapter

A solenoid that is 85 cm long has a cross-sectional area of 17.0cm2. There are 950of wire carrying a current of 6.60 A. (a) Calculate the energy density of the magnetic field inside the solenoid. (b) Find the total energy stored in the magnetic field there (neglect end effects).

In Figure,R=15惟,L=5.0Hthe ideal battery has 蔚=10V, and the fuse in the upper branch is an ideal3.0 A fuse. It has zero resistance as long as the current through it remains less than3.0 A . If the current reaches3.0 A , the fuse 鈥渂lows鈥� and thereafter has infinite resistance. Switch S is closed at timet = 0 . (a) When does the fuse blow? (Hint: Equation 30-41 does not apply. Rethink Eq. 30-39.) (b) Sketch a graph of the current i through the inductor as a function of time. Mark the time at which the fuse blows.

In Fig. 30-23, a long straight wire with current ipasses (without touching) three rectangular wire loops with edge lengths L, 1.5L, and 2L. The loops are widely spaced (so as not to affect one another). Loops 1 and 3 are symmetric about the long wire. Rank the loops according to the size of the current induced in them if current iis (a) constant and (b) increasing, greatest first.

Figure 30-25 shows a circular region in which a decreasing uniform magnetic field is directed out of the page, as well as four concentric circular paths. Rank the paths according to the magnitude of 鈭�E鈫�.dS鈫�evaluated along them, greatest first.

The switch in the circuit of Fig. 30-15 has been closed on a for a very long time when it is then thrown to b. The resulting current through the inductor is indicated in Fig. 30-28 for four sets of values for the resistance R and inductance L: (1) R=R0, (2) 2R0=R, (3) R0and2L0 , (4) 2R0and2L0. Which set goes with which curve?
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