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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 $i_{s} = 8.0 A$ and the horizontal axis scale is set by $t_{s} = 6.0 m s$ . The inductor has a resistance of $12 惟$ .(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

$蔚 = 1.6 x 10^{4} V$
$蔚 = 3.1 x 10^{3} V$
$蔚 = 2.3 x 10^{4} V$

Step by step solution

01

Given

$i_{s} = 8 A t_{s} = 6 m s$

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

$蔚 = L \frac{d i}{d t}$

03

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

Induced emf $蔚$ is given by

$\overset{,}{o} = L \frac{d i}{d t} i = 0 t o 7 A 蔚 = L \frac{d i}{d t} = \frac{4.6 脳 (7 - 0)}{(2 - 0) 脳 10^{- 3}} 蔚 = 1.6 脳 10^{4} V$

04

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

For time interval 2ms to 5ms

$1 = 7 t 0 5 A 蔚 = L \frac{d i}{d t} = \frac{4.6 脳 (5 - 7)}{(5 - 2) 脳 10^{- 3}} 蔚 = 3.1 脳 10^{3} 鈥� V$

05

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

For time interval 5ms to 6ms

$1 = 0 t o 5 A 蔚 = L \frac{d i}{d t} = \frac{4.6 脳 (5 - 0)}{(6 - 5) 脳 10^{- 3}} 蔚 = 2.3 脳 10^{4} V$

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Most popular questions from this chapter

A coil with an inductance of 2.0H and a resistance of $10 惟$ is suddenly connected to an ideal battery with $蔚 = 100 V$ . (a) What is the equilibrium current? (b) How much energy is stored in the magnetic 铿乪ld when this current exists in the coil?

A small loop of area 6.8 ${mm}^{2}$ is placed inside a long solenoid that hasand carries a sinusoidally varying current i of amplitude1.28 A and angular frequency rad/s.The central axes of the loop and solenoid coincide. What is the amplitude of the emf induced in the loop?

A solenoid having an inductance of $6.30 渭贬$ is connected in series with a $1.20 k 惟$ resistor. (a) If a 14.0Vbattery is connected across the pair, how long will it take for the current through the resistor to reach 80.0% of its final value?

(b) What is the current through the resistor at time $t = 1.0 蟿_{L}$ ?

In Fig. 30-63, a V = 12.0 V ideal battery, a $R = 20.0 惟$ resistor, and an inductor are connected by a switch at time t = 0 .At what rate is the battery transferring energy to the inductor鈥檚 field at $t = 1.61 蟿_{L}$ ?

Figure 30-24 shows two circuits in which a conducting bar is slid at the same speed vthrough the same uniform magnetic field and along a U-shaped wire. The parallel lengths of the wire are separated by 2Lin circuit 1 and by Lin circuit 2. The current induced in circuit 1 is counter clockwise. (a) Is the magnetic field into or out of the page? (b) Is the current induced in circuit 2 clockwise or counter clockwise? (c) Is the emf induced in circuit 1 larger than, smaller than, or the same as that in circuit 2?

See all solutions

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