Physics Principles with Applications

Douglas C. Giancoli

Chapter 21

Electromagnetic Induction and Faraday's Law - all with Video Answers

Educators

Chapter Questions

Problem 1

(I) The magnetic flux through a coil of wire containing two loops changes from $-50 \mathrm{Wb}$ to $+38 \mathrm{Wb}$ in 0.42 $\mathrm{s}$ . What is the emf induced in the coil?

Vishal Gupta

Vishal Gupta

Numerade Educator

Problem 2

(I) The rectangular loop shown in Fig. $21-46$ is pushed into the magnetic field which points inward. In what direction is the induced current?

Vishal Gupta

Numerade Educator

Problem 3

(I) The north pole of the magnet in Fig. $21-47$ is being inserted into the coil. In which direction is the induced current flowing through the resistor $R ?$

Vishal Gupta

Numerade Educator

Problem 4

(I) A 9.6 -cm-diameter circular loop of wire is in a $1.10-\mathrm{T}$ magnetic field. The loop is removed from the field in 0.15 $\mathrm{s}$ . What is the average induced emf?

Vishal Gupta

Numerade Educator

Problem 5

(I) A 12.0 $\mathrm{cm}$ -diameter loop of wire is initially oriented perpendicular to a $1.5-\mathrm{T}$ magnetic field. The loop is rotated so that its plane is parallel to the field direction in 0.20 $\mathrm{s}$ . What is the average induced emf in the loop?

Vishal Gupta

Numerade Educator

Problem 6

(II) A 10.2 -cm-diameter wire coil is initially oriented so that its plane is perpendicular to a magnetic field of 0.63 T pointing up. During the course of 0.15 $\mathrm{s}$ , the field is changed to one of 0.25 $\mathrm{T}$ pointing down. What is the average induced emf in the coil?

Vishal Gupta

Numerade Educator

Problem 7

(II) A 15 -cm-diameter circular loop of wire is placed in a 0.50 - T magnetic field. (a) When the plane of the loop is perpendicular to the field lines, what is the magnetic flux through the loop? (b) The plane of the loop is rotated until it makes a $35^{\circ}$ angle with the field lines. What is the angle $\theta$ in Eq. $21-1$ for this situation? (c) What is the magnetic flux through the loop at this angle?

Vishal Gupta

Numerade Educator

Problem 8

(II) $(a)$ If the resistance of the resistor in Fig. $21-48$ is slowly increased, what is the direction of the current induced in the small circular loop inside the larger loop? (b) What would it be if the small loop were placed outside the larger one, to the left?

Vishal Gupta

Numerade Educator

Problem 9

(II) What is the direction of the induced current in the circular loop due to the current shown in each part of Fig. $21-49 ?$

Vishal Gupta

Numerade Educator

Problem 10

(II) If the solenoid in Fig. $21-50$ is being pulled away from the loop shown, in what direction is the induced current in the loop?

Vishal Gupta

Numerade Educator

Problem 11

(II) The magnetic field perpendicular to a circular wire loop 12.0 $\mathrm{cm}$ in diameter is changed from $+0.52 \mathrm{T}$ to $-0.45 \mathrm{T}$ in 180 $\mathrm{ms}$ , where $+$ means the field points away from an observer and - toward the observer. (a) Calculate the induced emf. (b) In what direction does the induced current flow?

Vishal Gupta

Numerade Educator

Problem 12

(II) The moving rod in Fig. $21-12$ is 12.0 $\mathrm{cm}$ long and is pulled at a speed of 15.0 $\mathrm{cm} / \mathrm{s}$ . If the magnetic field is 0.800 $\mathrm{T}$ , calculate $(a)$ the emf developed, and $(b)$ the electric field felt by electrons in the rod.

Vishal Gupta

Numerade Educator

Problem 13

(II) A circular loop in the plane of the paper lies in a $0.75-\mathrm{T}$ magnetic field pointing into the paper. If the loop's diameter changes from 20.0 $\mathrm{cm}$ to 6.0 $\mathrm{cm}$ in $0.50 \mathrm{s},(a)$ what is the direction of the induced current, (b) what is the magnitude of the average induced current, (b) what is the magnitude of the average induced emf, and $(c)$ if the coil resistance is $2.5 \Omega,$ what is the average induced current?

Supratim Pal

Numerade Educator

Problem 14

(II) The moving rod in Fig. $21-12$ is 13.2 $\mathrm{cm}$ long and generates an emf of 120 $\mathrm{mV}$ while moving in a $0.90-\mathrm{T}$ magnetic field. ( $a$ ) What is its speed? (b) What is the electric field in the rod?

Vishal Gupta

Numerade Educator

Problem 15

(II) Part of a single rectangular loop of wire with dimensions shown in Fig. $21-51$ is situated inside a region of uniform magnetic field of 0.550 $\mathrm{T}$ . The total resistance of the loop is 0.230$\Omega$ . Calculate the force required to pull the loop from the field (to the right) at a constant velocity of 3.40 $\mathrm{m} / \mathrm{s}$ . Neglect gravity.

Vishal Gupta

Numerade Educator

Problem 16

(II) A 500 -turn solenoid, 25 $\mathrm{cm}$ long, has a diameter of $2.5 \mathrm{cm} .$ A 10 -turn coil is wound tightly around the center of the solenoid. If the current in the solenoid increases uniformly from 0 to 5.0 $\mathrm{A}$ in $0.60 \mathrm{s},$ what will be the induced emf in the short coil during this time?

Vishal Gupta

Numerade Educator

Problem 17

(II) In Fig. $21-12,$ the rod moves with a speed of 1.6 $\mathrm{m} / \mathrm{s}$ , is 30.0 $\mathrm{cm}$ long. and has a resistance of 2.5$\Omega$ . The magnetic field is 0.35 $\mathrm{T}$ , and the resistance of the U-shaped conductor is 25.0$\Omega$ at a given instant. Calculate (a) the induced emf, ( $b$ ) the current in the U-shaped conductor, and $(c)$ the external force needed to keep the rod's velocity constant at that instant.

Vishal Gupta

Numerade Educator

Problem 18

(III) A 22.0 -cm-diameter coil consists of 20 turns of circular copper wire 2.6 $\mathrm{mm}$ in diameter. A uniform magnetic field, perpendicular to the plane of the coil, changes at a rate of $8.65 \times 10^{-3} \mathrm{T} / \mathrm{s}$ . Determine (a) the current in the loop, and (b) the rate at which thermal energy is produced.

Supratim Pal

Numerade Educator

Problem 19

(III) The magnetic field perpendicular to a single 13.2 -cm-diameter circular loop of copper wire decreases uniformly from 0.750 $\mathrm{T}$ to zero. If the wire is 2.25 $\mathrm{mm}$ in diameter, how much charge moves past a point in the coil during this operation?

Vishal Gupta

Numerade Educator

Problem 20

(I) A simple generator is used to generate a peak output voltage of 24.0 $\mathrm{V}$ . The square armature consists of windings that are 6.0 $\mathrm{cm}$ on a side and rotates in a field of 0.420 $\mathrm{T}$ at a rate of 60.0 $\mathrm{rev} / \mathrm{s}$ . How many loops of wire should be wound on the square armature?

Vishal Gupta

Numerade Educator

Problem 21

(II) The generator of a car idling at 1100 rpm produces 12.4 $\mathrm{V}$ . What will the output be at a rotation speed of 2500 $\mathrm{rpm}$ , assuming nothing else changes?

Vishal Gupta

Numerade Educator

Problem 22

(II) Show that the rms output (Section $18-7 )$ of an ac generator is $V_{\mathrm{rms}}=N A B \omega / \sqrt{2},$ where $\omega=2 \pi f$

Vishal Gupta

Numerade Educator

Problem 23

(II) A simple generator has a 320 -loop square coil 21.0 $\mathrm{cm}$ on a side. How fast must it turn in a $0.650-\mathrm{T}$ field to produce a $120-\mathrm{V}$ peak output?

Vishal Gupta

Numerade Educator

Problem 24

(II) A 450 -loop circular armature coil with a diameter of 8.0 $\mathrm{cm}$ rotates at 120 $\mathrm{rev} / \mathrm{s}$ in a uniform magnetic field of strength 0.55 T. $(a)$ What is the rms voltage output of the
generator? (b) What would you do to the rotation frequency in order to double the rms voltage output?

Vishal Gupta

Numerade Educator

Problem 25

(II) A generator rotates at 85 $\mathrm{Hz}$ in a magnetic field of 0.030 $\mathrm{T}$ . It has 1000 turns and produces an rms voltage of 150 $\mathrm{V}$ and an $\mathrm{rms}$ current of 70.0 $\mathrm{A}$ . (a) What is the peak current produced? (b) What is the area of each turn of the coil?

Anand Jangid

Numerade Educator

Problem 26

(I) A motor has an armature resistance of 3.25$\Omega$ . If it draws 8.20 A when running at full speed and connected to a $120-\mathrm{V}$ line, how large is the back emf?

Vishal Gupta

Numerade Educator

Problem 27

(I) The back emf in a motor is 72 $\mathrm{V}$ when operating at 1800 $\mathrm{rpm}$ . What would be the back emf at 2500 $\mathrm{rpm}$ if the magnetic field is unchanged?

Vishal Gupta

Numerade Educator

Problem 28

(II) The back emf in a motor is 95 $\mathrm{V}$ when the motor is operating at 1000 $\mathrm{rpm}$ . How would you change the motor's magnetic field if you wanted to reduce the back emf to 65 $\mathrm{V}$ when the motor was running at 2500 $\mathrm{rpm} ?$

Vishal Gupta

Numerade Educator

Problem 29

(II) What will be the current in the motor of Example $21-9$ if the load causes it to run at half speed?

Vishal Gupta

Numerade Educator

Problem 30

(I) A transformer is designed to change 120 $\mathrm{V}$ into $10,000 \mathrm{V}$ , and there are 164 turns in the primary coil. How many turns are in the secondary coil?

Vishal Gupta

Numerade Educator

Problem 31

(I) A transformer has 320 turns in the primary coil and 120 in the secondary coil. What kind of transformer is this, and by what factor does it change the voltage? By what factor does it change the current?

Vishal Gupta

Numerade Educator

Problem 32

(I) A step-up transformer increases 25 $\mathrm{V}$ to 120 $\mathrm{V}$ . What is the current in the secondary coil as compared to the primary coil?

Vishal Gupta

Numerade Educator

Problem 33

(I) Neon signs require 12 $\mathrm{kV}$ for their operation. To operate from a $240-\mathrm{V}$ line, what must be the ratio of secondary to primary turns of the transformer? What would the voltage output be if the transformer were connected backward?

Bruce Edelman

Numerade Educator

Problem 34

(II) A model-train transformer plugs into $120-\mathrm{V}$ ac and draws 0.35 $\mathrm{A}$ while supplying 7.5 $\mathrm{A}$ to the train. (a) What voltage is present across the tracks? (b) Is the trans- former step-up or step-down?

Vishal Gupta

Numerade Educator

Problem 35

(II) The output voltage of a $95-\mathrm{W}$ transformer is 12 $\mathrm{V}$ , and the input current is 22 $\mathrm{A}$ . $(a)$ Is this a step-up or a step-down transformer? $(b)$ By what factor is the voltage multiplied?

Vishal Gupta

Numerade Educator

Problem 36

(II) A transformer has 330 primary turns and 1340 secondary turns. The input voltage is 120 $\mathrm{V}$ and the output current is 15.0 $\mathrm{A}$ . What are the output voltage and input current?

Vishal Gupta

Numerade Educator

Problem 37

(II) If 30 $\mathrm{MW}$ of power at 45 $\mathrm{kV}$ (rms) arrives at a town from a generator via $4.0 \Omega$ transmission lines, calculate (a) the emf at the generator end of the lines, and (b) the fraction of the power generated that is wasted in the lines.

Vishal Gupta

Numerade Educator

Problem 38

(III) 65 $\mathrm{k} \mathrm{W}$ is to arrive at a town over two $0.100-\Omega$ lines. Estimate how much power is saved if the voltage is stepped up from 120 $\mathrm{V}$ to 1200 $\mathrm{V}$ and then down again, rather than simply transmitting at 120 $\mathrm{V}$ . Assume the transformers are each 99$\%$ efficient.

Vishal Gupta

Numerade Educator

Problem 39

(I) If the current in a 180 -mH coil changes steadily from 25.0 $\mathrm{A}$ to 10.0 $\mathrm{A}$ in 350 $\mathrm{ms}$ , what is the magnitude of the induced emf?

Vishal Gupta

Numerade Educator

Problem 40

(I) What is the inductance of a coil if the coil produces an emf of 2.50 $\mathrm{V}$ when the current in it changes from $-28.0 \mathrm{mA}$ to $+31.0 \mathrm{mA}$ in 12.0 $\mathrm{ms}$ ?

Vishal Gupta

Numerade Educator

Problem 41

(I) What is the inductance $L$ of a 0.60 -m-long air-filled coil 2.9 $\mathrm{cm}$ in diameter containing $10,000$ loops?

Vishal Gupta

Numerade Educator

Problem 42

(I) How many turns of wire would be required to make a 130 -m $\mathrm{H}$ inductance out of a 30.0 -cm-long air-filled coil with a diameter of 5.2 $\mathrm{cm} ?$

Vishal Gupta

Numerade Educator

Problem 43

(II) An air-filled cylindrical inductor has 2800 turns, and it is 2.5 $\mathrm{cm}$ in diameter and 28.2 $\mathrm{cm}$ long. (a) What is its inductance? (b) How many turns would you need to generate the same inductance if the core were iron-filled instead? Assume the magnetic permeability of iron is about 1200 times that of free space.

Vishal Gupta

Numerade Educator

Problem 44

(II) A coil has $2.25-\Omega$ resistance and 440 -m $\mathrm{H}$ inductance. If the current is 3.00 $\mathrm{A}$ and is increasing at a rate of $3.50 \mathrm{A} / \mathrm{s},$ what is the potential difference across the coil at this moment?

Vishal Gupta

Numerade Educator

Problem 45

(III) A long thin solenoid of length $l$ and cross-sectional area $A$ contains $N_{1}$ closely packed turns of wire. Wrapped tightly around it is an insulated coil of $N_{2}$ turns, Fig. $21-52$ . Assume all the flux from coil 1 (the solenoid) passes through coil $2,$ and calculate the mutual inductance.

Vishal Gupta

Numerade Educator

Problem 46

(III) The wire of a tightly wound solenoid is unwound and used to make another tightly wound solenoid of twice the diameter. By what factor does the inductance change?

Vishal Gupta

Numerade Educator

Problem 47

(I) The magnetic field inside an air-filled solenoid 36 $\mathrm{cm}$ long and 2.0 $\mathrm{cm}$ in diameter is 0.80 $\mathrm{T}$ . Approximately how much energy is stored in this field?

Vishal Gupta

Numerade Educator

Problem 48

(II) At a given instant the current through an inductor is 50.0 $\mathrm{mA}$ and is increasing at the rate of 115 $\mathrm{mA} / \mathrm{s}$ . What is the initial energy stored in the inductor if the inductance is known to be $60.0 \mathrm{mH},$ and how long does it take for the energy to increase by a factor of 10 from the initial value?

Vishal Gupta

Numerade Educator

Problem 49

(II) Assuming the Earth's magnetic field averages about $0.50 \times 10^{-4} \mathrm{T}$ near the surface of the Earth, estimate the total energy stored in this field in the first 10 $\mathrm{km}$ above the Earth's surface.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 50

(II) Determine $\Delta I / \Delta t$ at $t=0$ (when the battery is connected for the $L R$ circuit of Fig. $21-33$ and show that if $I$ continued to increase at this rate, it would reach its maximum value in one time constant.

Ceren Uzun

Texas Tech University

Problem 51

(III) After how many time constants does the current in Fig. $21-33$ reach within (a) $10 \%,(b) 1.0 \%,$ and $(c) 0.1 \%$ of its maximum value?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 52

(III) Two tightly wound solenoids have the same length and circular cross-sectional area. But solenoid 1 uses wire that is half as thick as solenoid 2 . (a) What is the ratio of their inductances? (b) What is the ratio of their inductive time constants (assuming no other resistance in the circuits)?

Vishal Gupta

Numerade Educator

Problem 53

(I) What is the reactance of a $7.20-\mu \mathrm{F}$ capacitor at a frequency of $(a) 60.0 \mathrm{Hz},(b) 1.00 \mathrm{MHz}$ ?

Vishal Gupta

Numerade Educator

Problem 54

(I) At what frequency will a $22.0-\mathrm{mH}$ inductor have a reactance of 660$\Omega ?$

Vishal Gupta

Numerade Educator

Problem 55

(I) At what frequency will a $2.40-\mu \mathrm{F}$ capacitor have a reactance of 6.70 $\mathrm{k\Omega}$ ?

Vishal Gupta

Numerade Educator

Problem 56

(II) Plot a graph of the reactance of a $1.0-\mu \mathrm{F}$ capacitor as a function of frequency from 10 to 1000 $\mathrm{Hz}$ .

Vishal Gupta

Numerade Educator

Problem 57

(II) Plot a graph of the reactance of a 1.0$\cdot \mathrm{mH}$ inductor as a function of frequency from 100 to $10,000 \mathrm{Hz}$ .

Vishal Gupta

Numerade Educator

Problem 58

(II) Calculate the reactance of, and rms current in, a 160 -m $\mathrm{H}$ tadio coil connected to a $240-\mathrm{V}$ (rms) $10.0-\mathrm{kHz}$ ac line. Ignore resistance.

Vishal Gupta

Numerade Educator

Problem 59

(II) An inductance coil operates at 240 $\mathrm{V}$ and 60.0 $\mathrm{Hz}$ . It draws 12.8 $\mathrm{A}$ . What is the coil's inductance?

Vishal Gupta

Numerade Educator

Problem 60

(II) $(a)$ What is the reactance of a well-insulated $0.030-\mu \mathrm{F}$ capacitor connected to a $2.0-\mathrm{kV}$ (rms) $720 . \mathrm{Hz}$ line? (b) What will be the peak value of the current?

Ze-Han Lee

Numerade Educator

Problem 61

(I) A $30-\mathrm{k} \Omega$ resistor is in series with a $45-\mathrm{mH}$ inductor and an ac source. Calculate the impedance of the circuit if the source frequency is $(a) 50 \mathrm{Hz}$ , and $(b) 3.0 \times 10^{4} \mathrm{Hz}$ .

Vishal Gupta

Numerade Educator

Problem 62

(I) A $3.5-\mathrm{k} \Omega$ resistor and a $4.0-\mu \mathrm{F}$ capacitor are connected in series to an ac source. Calculate the impedance of the circuit if the source frequency is $(a) 60 \mathrm{Hz}$ , and $(b) 60,000 \mathrm{Hz}$ .

Vishal Gupta

Numerade Educator

Problem 63

(I) For a $120-V$ rms $60-$ Hz voltage, an $\mathrm{rms}$ current of 70 $\mathrm{mA}$ passing through the human body for 1.0 s could be lethal. What must be the impedance of the body for this to occur?

Vishal Gupta

Numerade Educator

Problem 64

(II) What is the resistance of a coil if its impedance is 235$\Omega$ and its reactance is 135$\Omega ?$

Vishal Gupta

Numerade Educator

Problem 65

(II) What are the total impedance, phase angle, and rms current in an $L R C$ circuit connected to a 10.0 -kHz, $725-\mathrm{V}$ (rms) source if $L=22.0 \mathrm{mH}, R=8.70 \mathrm{k\Omega}$ , and $C=6250 \mathrm{pF} ?$

Vishal Gupta

Numerade Educator

Problem 66

(III) A $2.5-\mathrm{k} \Omega$ resistor in series with a 420 $\mathrm{mH}$ inductor is driven by an ac power supply. At what frequency is the impedance double that of the impedance at 60 $\mathrm{Hz}$ ?

Vishal Gupta

Numerade Educator

Problem 67

(III) $(a)$ What is the rms current in an $R L$ circuit when a 60.0 -Hz $120 . \mathrm{V}$ rms ac voltage is applied, where $R=1.80 \mathrm{k} \Omega,$ and $L=350 \mathrm{mH}$ ? $(b)$ What is the phase angle between voltage and current? (c) What are the rms voltage readings across $R$ and $L ?$

Vishal Gupta

Numerade Educator

Problem 68

(III) $(a)$ What is the rms current in an $R C$ circuit if $R=8.80 \mathrm{k} \Omega, C=1.80 \mu \mathrm{F},$ and the rms applied voltage is 120 $\mathrm{V}$ at 60.0 $\mathrm{Hz} ?$ (b) What is the phase angle between voltage and current? $(c)$ What are the voltmeter readings across $R$ and $C ?$

Vishal Gupta

Numerade Educator

Problem 69

(I) A 3500 -pF capacitor is connected to a $55.0-\mu \mathrm{H}$ coil of resistance 3.00$\Omega$ . What is the resonant frequency of this circuit?

Vishal Gupta

Numerade Educator

Problem 70

(I) The variable capacitor in the tuner of an AM radio has a capacitance of 2800 $\mathrm{pF}$ when the radio is tuned to a station at 580 $\mathrm{kHz}$ . $(a)$ What must be the capacitance for a station at 1600 $\mathrm{kHz}$ ( $b$ ) What is the inductance (assumed constant)?

Vishal Gupta

Numerade Educator

Problem 71

(II) An LRC circuit has $L=14.8 \mathrm{mH}$ and $R=4.40 \Omega$ . (a) What value must $C$ have to produce resonance at 3600 $\mathrm{Hz}$ ? (b) What will be the maximum current at resonance if the peak external voltage is 150 $\mathrm{V}$ ?

Vishal Gupta

Numerade Educator

Problem 72

Suppose you are looking at two current loops in the plane of the page as shown in Fig. $21-53 .$ When switch $\mathrm{S}$ is thrown in the left-hand coil, $(a)$ what is the direction of the induced current in the other loop? (b) What is the situation after a "long" time? (c) What is the direction of the induced current in the right-hand loop if that loop is quickly pulled horizontally to the right?

Vishal Gupta

Numerade Educator

Problem 73

A square loop 24.0 $\mathrm{cm}$ on a side has a resistance of 5.20$\Omega$ . It is initially in a $0.665-$ T magnetic field, with its plane perpendicular to $\overrightarrow{\mathbf{B}}$ , but is removed from the field in 40.0 $\mathrm{ms}$ . Calculate the electric energy dissipated in this process.

Vishal Gupta

Numerade Educator

Problem 74

A high-intensity desk lamp is rated at 45 $\mathrm{W}$ but requires only 12 $\mathrm{V}$ . It contains a transformer that converts $120-\mathrm{V}$ household voltage. $(a)$ Is the transformer step-up or step-down? $(b)$ What is the current in the secondary coil when the lamp is on? $(c)$ What is the current in the primary coil? $(d)$ What is the resistance of the bulb when on?

Vishal Gupta

Numerade Educator

Problem 75

Power is generated at 24 $\mathrm{kV}$ at a generating plant located 118 $\mathrm{km}$ from a town that requires 50 $\mathrm{MW}$ of power at 12 $\mathrm{kV}$ . Two transmission lines from the plant to the town each have a resistance of 0.10$\Omega / \mathrm{km}$ . What should the output voltage of the transformer at the generating plant be for an overall transmission efficiency of 98.5$\%$ assuming a perfect transformer?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 76

The primary windings of a transformer which has an 80$\%$ efficiency are connected to $110-V$ ac. The secondary windings are connected across a $2.4-\Omega, 75-\mathrm{W}$ lightbulb. (a) Calculate the current through the primary windings of the transformer. (b) Calculate the ratio of the number of primary windings of the transformer to the number of secondary windings of the transformer.

Vishal Gupta

Numerade Educator

Problem 77

A pair of power transmission lines each have a $0.80-\Omega$ resistance and carry 740 A over 9.0 $\mathrm{km}$ . If the rms input voltage is 42 $\mathrm{kV}$ , calculate $(a)$ the voltage at the other end, (b) the power input, (c) power loss in the lines, and (d) the power output.

Vishal Gupta

Numerade Educator

Problem 78

Two resistanceless rails rest 32 $\mathrm{cm}$ apart on a $6.0^{\circ}$ ramp. They are joined at the bottom by a $0.60-\Omega$ resistor. At the top a copper bar of mass 0.040 $\mathrm{kg}$ (ignore its resistance) is laid across the rails. The whole apparatus is immersed in a vertical $0.55-\mathrm{T}$ field. What is the terminal (steady) velocity of the bar as it slides frictionlessly down the rails?

Vishal Gupta

Numerade Educator

Problem 79

Show that the power loss in transmission lines, $P_{\mathrm{L}},$ is given by $P_{\mathrm{L}}=\left(P_{\mathrm{T}}\right)^{2} R_{\mathrm{L}} / V^{2}$ , where $P_{\mathrm{T}}$ is the power transmitted to the user, $V$ is the delivered voltage, and $R_{\mathrm{L}}$ is the resistance of the power lines.

Nolan Smyth

Numerade Educator

Problem 80

A coil with 150 turns, a radius of $5.0 \mathrm{cm},$ and a resistance of 12$\Omega$ surrounds a solenoid with 230 turns/cm and a radius of $4.5 \mathrm{cm} ;$ see Fig. $21-54$ . The current in the solenoid changes at a constant rate from 0 to 2.0 $\mathrm{A}$ in 0.10 $\mathrm{s}$ . Calcu- late the magnitude and direction of the induced current in the coil.

Bruce Edelman

Numerade Educator

Problem 81

A certain electronic device needs to be protected against sudden surges in current. In particular, after the power is turned on the current should rise no more than 7.5 $\mathrm{mA}$ in the first 120$\mu \mathrm{s}$ . The device has resistance 150$\Omega$ and is designed to operate at 55 $\mathrm{mA}$ . How would you protect this device?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 82

A 25 -turn 12.5 -cm-diameter coil is placed between the pole pieces of an electromagnet. When the magnet is turned on, the flux through the coil changes, inducing an emf. At what rate (in $\mathrm{T} / \mathrm{s} )$ must the field produced by the magnet change if the emf is to be 120 $\mathrm{V}$ ?

Vishal Gupta

Numerade Educator

Problem 83

Calculate the peak output voltage of a simple generator whose square armature windings are 6.60 $\mathrm{cm}$ on a side; the armature contains 155 loops and rotates in a field of 0.200 $\mathrm{T}$ at a rate of 120 $\mathrm{rev} / \mathrm{s}$ .

Vishal Gupta

Numerade Educator

Problem 84

Typical large values for electric and magnetic fields attained in laboratories are about $1.0 \times 10^{4} \mathrm{V} / \mathrm{m}$ and $2.0 \mathrm{T} .(a)$ Determine the energy density for each field and
compare. $(b)$ What magnitude electric field would be needed to produce the same energy density as the $2.0-\mathrm{T}$ magnetic field?

Ceren Uzun

Texas Tech University

Problem 85

What is the inductance $L$ of the primary of a transformer whose input is 220 $\mathrm{V}$ at 60.0 $\mathrm{Hz}$ if the current drawn is 5.8 $\mathrm{A} ?$ Assume no current in the secondary.

Vishal Gupta

Numerade Educator

Problem 86

A $130-\mathrm{mH}$ coil whose resistance is 18.5$\Omega$ is connected to a capacitor $C$ and a 1360 -Hz source voltage. If the current and voltage are to be in phase, what value must $C$ have?

Vishal Gupta

Numerade Educator

Problem 87

An inductance coil draws 2.5$\cdot \mathrm{A}$ de when connected to a $36-\mathrm{V}$ battery. When connected to a $60-\mathrm{Hz} 120-\mathrm{V}$ (rms) source, the current drawn is 3.8 $\mathrm{A}$ (rms). Determine the inductance and resistance of the coil.

Vishal Gupta

Numerade Educator

Problem 88

A $135-\mathrm{mH}$ inductor with $2.0-\Omega$ resistance is connected in series to a $20-\mu \mathrm{F}$ capacitor and a $60-\mathrm{Hz}, 45-\mathrm{V}$ source. Calculate $(a)$ the rms current, and $(b)$ the phase angle.

Vishal Gupta

Numerade Educator

Problem 89

The $Q$ factor of a resonance circuit can be defined as the ratio of the voltage across the capacitor (or inductor) to the voltage across the resistor, at resonance. The larger the $Q$ factor, the sharper the resonance curve will be and the sharper the tuning. $(a)$ Show that the $Q$ factor is given by the equation $Q=(1 / R) \sqrt{L / C} .(b)$ At a resonant frequency $f_{0}=1.0 \mathrm{MHz}$ , what must be the values of $L$ and $R$ to produce a $Q$ factor of 550$?$ Assume that $C=0.010 \mu \mathrm{F} .$

Vishal Gupta

Numerade Educator