Essential College Physics

Andrew F. Rex, Richard Wolfson

Chapter 19

Electromagnetic Induction and Alternating Current - all with Video Answers

Educators

Chapter Questions

Problem 1

Show that with SI units on the right side of Faraday's law (Equation 19.2 ), the emf comes out in volts.

Ajay Singhal

Ajay Singhal

Numerade Educator

Problem 2

Explain why magnetic flux decreases as the angle $\theta$ increases from 0 to $90^{\circ}$

Ajay Singhal

Numerade Educator

Problem 3

Is the magnetic flux through a horizontal loop larger at the equator or the North Pole?

Ajay Singhal

Numerade Educator

Problem 4

Explain why the magnetic brake shown in Figure 19.10 works equally well when the metal plate is moving into or out of the magnetic field but doesn't work when the plate is entirely within the uniform magnetic field.

Ajay Singhal

Numerade Educator

Problem 5

In the dropping-magnet demonstration (Conceptual Example 19.4 ), the magnet has very little kinetic energy when it exits the tube. What happened to most of the gravitational potential energy it had at the top?

Ajay Singhal

Numerade Educator

Problem 6

Suppose in Figure 19.7 that the magnetic field is out of the page instead of in. What are (a) the direction of the induced current, (b) the induced emf, and (c) the direction of the force on the sliding bar?

Ajay Singhal

Numerade Educator

Problem 7

Suppose the bar in Figure 19.7 moves leftward instead of rightward. What are (a) the direction of the induced current,
(b) the induced emf, and (c) the direction of the force on the sliding bar?

Ajay Singhal

Numerade Educator

Problem 8

In an $R L$ circuit, is there more energy in the inductor just after the switch is closed or much later?

Ajay Singhal

Numerade Educator

Problem 9

How is an $L C$ circuit like a simple harmonic oscillator?

Ajay Singhal

Numerade Educator

Problem 10

How is an $R L C$ circuit like a damped harmonic oscillator?

Ajay Singhal

Numerade Educator

Problem 11

Suppose you know the resistance, inductive reactance, and capacitive reactance for a series $R L C$ circuit. Is the total impedance for the circuit equal to the sum of these three quantities? Why or why not?

Ajay Singhal

Numerade Educator

Problem 12

For which of the following AC circuits does impedance depend on frequency? A circuit with (a) only a resistor,
(b) a resistor and inductor, (c) a resistor and capacitor.

Ajay Singhal

Numerade Educator

Problem 13

For which of the following AC circuits does impedance depend on frequency? A circuit with (a) only a resistor,
(b) a resistor and inductor, (c) a resistor and capacitor.

Ajay Singhal

Numerade Educator

Problem 14

A series $R L C$ circuit has $X_{C}>X_{L}$. To bring the circuit into resonance, should you increase or decrease the capacitance?

Ajay Singhal

Numerade Educator

Problem 15

An $R L C$ circuit has power factor $0.90 .$ From this information, can you tell whether the current leads or lags the emf?

Ajay Singhal

Numerade Educator

Problem 16

A 2.3-T magnetic field lies perpendicular to a $35-\mathrm{cm}$ -diameter circular wire loop. The magnetic flux through the loop is
(a) $0.07 \mathrm{~T} \cdot \mathrm{m}^{2}$
(b) $0.14 \mathrm{~T} \cdot \mathrm{m}^{2}$
(c) $0.22 \mathrm{~T} \cdot \mathrm{m}^{2}$
(d) $0.28 \mathrm{~T} \cdot \mathrm{m}^{2}$

Ajay Singhal

Numerade Educator

Problem 17

A 1.9-T magnetic field makes a $60^{\circ}$ angle with a square loop $50 \mathrm{~cm}$ on a side. The magnetic flux through the loop is
(a) $0.24 \mathrm{~T} \cdot \mathrm{m}^{2}$
(b) $0.41 \mathrm{~T} \cdot \mathrm{m}^{2}$
(c) $0.48 \mathrm{~T} \cdot \mathrm{m}^{2}$
(d) $0.75 \mathrm{~T} \cdot \mathrm{m}^{2}$

Ajay Singhal

Numerade Educator

Problem 18

A 130 -turn circular coil has diameter $5.2 \mathrm{~cm}$. A magnetic field perpendicular to the coil is changing at $0.75 \mathrm{~T} / \mathrm{s}$. The induced emf in the coil is (a) $0.07 \mathrm{~V} ;$ (b) $0.14 \mathrm{~V} ;$ (c) $0.21 \mathrm{~V} ;$ (d) $0.28 \mathrm{~V}$.

Ajay Singhal

Numerade Educator

Problem 19

A 50 -turn circular coil has diameter $6.2 \mathrm{~cm}$ and resistance $0.75 \Omega$. A magnetic field perpendicular to the coil is changing at $0.50 \mathrm{~T} / \mathrm{s} .$ The induced current in the coil is (a) $10 \mathrm{~mA} ;$ (b) $30 \mathrm{~mA}$
(c) $100 \mathrm{~mA} ;$ (d) $300 \mathrm{~mA}$.

Ajay Singhal

Numerade Educator

Problem 20

For the apparatus shown in Figure $19.7,$ the magnetic field strength is $4.5 \mathrm{~T}$ and the rail separation is $L=25 \mathrm{~cm} .$ What's the induced emf when the bar moves at $35 \mathrm{~cm} / \mathrm{s}$ ? (a) $0.39 \mathrm{~V} ;$ (b) $0.45 \mathrm{~V}$
(d) $0.65 \mathrm{~V}$. (c) $0.53 \mathrm{~V}$

Nick Johnson

Numerade Educator

Problem 21

A generator has a coil with area $0.12 \mathrm{~m}^{2}$, rotating at $60 \mathrm{~Hz}$ in a 0.47-T magnetic field. If the generator's peak emf is $340 \mathrm{~V}$, the number of turns in the coil is (a) $16 ;$ (b) $32 ;$ (c) $50 ;$ (d) 100 .

Ajay Singhal

Numerade Educator

Problem 22

A generator has a coil with area $0.12 \mathrm{~m}^{2}$, rotating at $60 \mathrm{~Hz}$ in a 0.47-T magnetic field. If the generator's peak emf is $340 \mathrm{~V}$, the number of turns in the coil is (a) $16 ;$ (b) $32 ;$ (c) $50 ;$ (d) 100 .

Ajay Singhal

Numerade Educator

Problem 23

You have a 320 -mH inductor. Over what time must you increase the inductor current by $2.0 \mathrm{~A}$ in order to induce a $5.0-\mathrm{V}$ emf?
(a) $0.13 \mathrm{~s}$
(c) $0.39 \mathrm{~s}$
(d) 0.52 s.
; (b) $0.26 \mathrm{~s}$

Ajay Singhal

Numerade Educator

Problem 24

A radio receiver has a $25-\mu \mathrm{H}$ inductance. The capacitance required to tune in a $1470-\mathrm{kHz}$ radio station is
(a) $0.47 \mathrm{nF}$
(b) $1.88 \mathrm{nF}$
(c) $3.76 \mathrm{nF}$
(d) $18.8 \mathrm{nF}$.

Ajay Singhal

Numerade Educator

Problem 25

An AC power source produces a $170-\mathrm{V}$ peak emf at $60 \mathrm{~Hz}$. What's the average power dissipated in a $480-\Omega$ resistor connected across this source? (a) $75 \mathrm{~W} ;$ (b) $60 \mathrm{~W} ;$ (c) $42 \mathrm{~W}$; (d) $30 \mathrm{~W}$.

Ajay Singhal

Numerade Educator

Problem 26

A variable capacitor is connected across a variable-frequency AC source. The combination that gives the highest current is:
(a) $23 \mu \mathrm{F}, 60 \mathrm{~Hz}$
(b) $33 \mu \mathrm{F}, 55 \mathrm{~Hz}$
(c) $30 \mu \mathrm{F}, 70 \mathrm{~Hz}$
(d) $25 \mu \mathrm{F}$
$50 \mathrm{~Hz}$

Ajay Singhal

Numerade Educator

Problem 27

If 1.5 -T magnetic field lies perpendicular to a 25 -cm-diameter circular wire loop. What's the magnetic flux through the loop?

Ajay Singhal

Numerade Educator

Problem 28

A 2.9-T magnetic field makes a $40^{\circ}$ angle with a square loop $25 \mathrm{~cm}$ on a side. What's the magnetic flux through the loop?

Ajay Singhal

Numerade Educator

Problem 29

At one location, Earth's magnetic field has a magnitude of $5.4 \times 10^{-5} \mathrm{~T}$ with an inclination of $72^{\circ}$ to the horizontal. Find
the magnetic flux through a horizontal rectangular roof measuring $35 \mathrm{~m}$ by $20 \mathrm{~m}$.

Ajay Singhal

Numerade Educator

Problem 30

At one location, Earth's magnetic field has a magnitude of $5.4 \times 10^{-5} \mathrm{~T}$ with an inclination of $72^{\circ}$ to the horizontal. Find the magnetic flux through a horizontal rectangular roof measuring $35 \mathrm{~m}$ by $20 \mathrm{~m}$.

Ajay Singhal

Numerade Educator

Problem 31

A 150 -turn circular coil has diameter $5.25 \mathrm{~cm}$ and resistance $1.30 \Omega$. A magnetic field perpendicular to the coil is changing at $1.15 \mathrm{~T} / \mathrm{s} .$ Find the induced current in the coil.

Ajay Singhal

Numerade Educator

Problem 32

In A circular loop of wire with area $0.015 \mathrm{~m}^{2}$ lies in the $x-y$ plane. Initially there's a magnetic field of $4.0 \mathrm{~T}$ in the $-z$ -direction. The field remains constant for $10 \mathrm{~s}$, then decreases gradually to zero in $10 \mathrm{~s},$ and then remains zero for $10 \mathrm{~s}$. Find the magnitude and direction of the induced emf in the loop for each of the three $10-\mathrm{s}$ intervals.

Ajay Singhal

Numerade Educator

Problem 33

A square wire loop $15 \mathrm{~cm}$ on a side lies in the $x$ - $y$ plane. Its resistance is $0.55 \Omega$. A magnetic field points in the $+z$ -direction and increases at $15 \mathrm{mT} / \mathrm{s}$. (a) What's the direction of the induced current in the loop? (b) Find the magnitudes of the induced emf and induced current in the loop.

Ajay Singhal

Numerade Educator

Problem 34

A 75 -turn circular coil has diameter $4.0 \mathrm{~cm}$ and resistance $2.6 \Omega$. This coil is placed inside a solenoid, with coil and solenoid axes aligned. The solenoid has 5000 turns of wire and is $24 \mathrm{~cm}$ long. If the solenoid current increases steadily from 0 to $10 \mathrm{~A}$ in $2.5 \mathrm{~s},$ find the induced $\mathrm{emf}$ and induced current in the coil.

Ajay Singhal

Numerade Educator

Problem 35

A circular wire coil with resistance $1.4 \Omega$ and area $5.0 \times$ $10^{-3} \mathrm{~m}^{2}$ lies perpendicular to a magnetic field that's increasing at $2.0 \mathrm{~T} / \mathrm{s} .$ If the induced current is $250 \mathrm{~mA},$ how many turns are in the coil?

Ajay Singhal

Numerade Educator

Problem 36

In Figure 19.7 , take $B=3.5 \mathrm{~T}$ and $L=12 \mathrm{~cm}$. Find the induced emf when the bar moves at $0.25 \mathrm{~m} / \mathrm{s}$.

Ajay Singhal

Numerade Educator

Problem 37

In Figure $19.7,$ take $B=1.8 \mathrm{~T}, R=2.3 \Omega,$ and $L=12 \mathrm{~cm}$ Suppose the bar moves at $0.80 \mathrm{~m} / \mathrm{s}$ to the left. (a) Find the magnitude and direction of the induced current. (b) At what rate is electric power generated?

Ajay Singhal

Numerade Educator

Problem 38

Suppose the rectangular wire loop with a resistance of $3.5 \Omega$ enters the magnetic field as shown in Figure $\mathrm{P} 19.38$, moving to the right at $25 \mathrm{~cm} / \mathrm{s}$. (a) What are the magnitude and direction of the induced current? (b) Later the loop is fully in the field, still moving at $25 \mathrm{~cm} / \mathrm{s}$. What are the magnitude and direction of the induced current? (c) Eventually the loop begins to emerge from the field, still at $25 \mathrm{~cm} / \mathrm{s}$. What are the magnitude and direction of the induced current?

Vishal Gupta

Numerade Educator

Problem 39

The apparatus in Figure 19.7 is rotated $90^{\circ}$, so the bar falls vertically while maintaining electrical contact with the rails. The rail spacing is $L=30 \mathrm{~cm},$ and the field strength is $B=1.2 \mathrm{~T}$. If the bar drops from rest, what's the magnitude of the induced emf after it's been falling for (a) $0.5 \mathrm{~s}$ and (b) $1.0 \mathrm{~s}$ ? (You may assume that the magnetic force on the falling bar is much less than the bar's weight.)

Ajay Singhal

Numerade Educator

Problem 40

In the rail gun of Figure $19.12,$ the field strength is $3.0 \mathrm{~T}$ and the rail spacing is $50 \mathrm{~cm}$. A discharging capacitor supplies a current of $100 \mathrm{kA}$. (a) What's the acceleration of the $0.25-\mathrm{kg}$ bar?
(b) What's the bar speed at the end of the $2.75-\mathrm{m}$ track? a horizontal metal bar of length $L$ falls vertically through a horizontal magnetic field of strength $B$.
(a) Show that if the bar falls with speed $v,$ the induced emf between its ends is $\mathcal{E}=B L v .$ (b) Suppose $B=0.25 \mathrm{~T}$ and $L=0.50 \mathrm{~m} .$ What's the induced emf 1.0 s after the bar is dropped from rest?

Ajay Singhal

Numerade Educator

Problem 41

A horizontal metal bar of length $L$ falls vertically through a horizontal magnetic field of strength $B$.
(a) Show that if the bar falls with speed $v,$ the induced emf between its ends is $\mathcal{E}=B L v$
(b) Suppose $B=0.25 \mathrm{~T}$ and $L=0.50 \mathrm{~m} .$ What's the induced emf $1.0 \mathrm{~s}$ after the bar is dropped from rest?

Ajay Singhal

Numerade Educator

Problem 42

In airplane flies due north in a region where Earth's magnetic field has magnitude $5.3 \times 10^{-5} \mathrm{~T},$ declination $0^{\circ},$ and inclination $75^{\circ} .$ What's the induced emf between the wingtips, $35 \mathrm{~m}$ apart, when the plane flies at $220 \mathrm{~m} / \mathrm{s}$ ? Hint: See the preceding problem.

Ajay Singhal

Numerade Educator

Problem 43

(a) A 20-turn generator coil with area $0.016 \mathrm{~m}^{2}$ rotates at $50 \mathrm{~Hz}$ in a 0.75-T magnetic field. Find the peak induced emf. (b) Graph the induced emf as a function of time from $t=0$ to $t=40 \mathrm{~ms}$.

Ajay Singhal

Numerade Educator

Problem 44

A 10 -turn generator coil with area $0.150 \mathrm{~m}^{2}$ rotates in a $1.25-\mathrm{T}$ magnetic field. At what frequency should the coil rotate to produce a peak emf of $150 \mathrm{~V} ?$

Ajay Singhal

Numerade Educator

Problem 45

A generator has a 150 -turn square coil, $5 \mathrm{~cm}$ on a side. Find the peak emf in this coil when it's rotating at $100 \mathrm{~Hz}$ (a) in Earth's field, $B=5 \times 10^{-5} \mathrm{~T},$ and $(\mathrm{b})$ in a strong $6.4-\mathrm{T}$ field.

Ajay Singhal

Numerade Educator

Problem 46

- Figure $\mathrm{P} 19.46$ shows the induced emf in a 5 -turn square coil, $8 \mathrm{~cm}$ on a side, rotating in a uniform magnetic field. Find (a) the rotation frequency, (b) the angular velocity, and (c) the magnetic field strength.

Ajay Singhal

Numerade Educator

Problem 47

(a) A $120-\mathrm{V}$ emf is across a transformer's 200 -turn primary coil. How many turns should the secondary have in order to produce a $30-\mathrm{V}$ emf? (b) A $240-\mathrm{V}$ emf is across a transformer's $140-$ turn primary coil. What's the emf in the 250 -turn secondary coil?

Ajay Singhal

Numerade Educator

Problem 48

A home receives $1.5 \mathrm{~kW}$ of electric power from a transformer on a nearby pole. The line from the substation to the transformer is at $10 \mathrm{kV}$ and has $0.13 \Omega$ resistance. What fraction of the power is lost in this transmission line?

Ajay Singhal

Numerade Educator

Problem 49

A typical coal-fired power plant produces $1000 \mathrm{MW}$ of electrical energy. Seven percent of the power is lost in a $500-\mathrm{kV}$ transmission line. (a) What's the line's resistance? (Note: This is actually the equivalent resistance of all the parallel lines in the network, so your answer should be quite small.) (b) What would be the power loss if the line were at $100 \mathrm{kV} ?$

Nick Johnson

Numerade Educator

Problem 50

A 240 -turn coil carries $350 \mathrm{~mA}$. If the magnetic flux through the coil due to this current is $0.75 \mathrm{~Wb}$, what's the coil's inductance?

Ajay Singhal

Numerade Educator

Problem 51

If A 240 -turn coil carries $350 \mathrm{~mA}$. If the magnetic flux through the coil due to this current is $0.75 \mathrm{~Wb}$, what's the coil's inductance?

Ajay Singhal

Numerade Educator

Problem 52

A solenoid has diameter $2.5 \mathrm{~cm}$, length $30 \mathrm{~cm}$, and inductance $1.34 \mathrm{mH}$. (a) How many turns of wire does it have?
(b) What's the energy stored in the solenoid when it carries a 6.0 - A current?

Ajay Singhal

Numerade Educator

Problem 53

A solenoid has the following dimensions: diameter $=5.0 \mathrm{~cm}$ $n=45$ turns $/ \mathrm{cm},$ length $=23 \mathrm{~cm}$
(a) What's its inductance?
(b) Find the current when the solenoid stores $0.50 \mathrm{~J}$ of energy.

Ajay Singhal

Numerade Educator

Problem 54

Find the inductance required to store $1.0 \mathrm{~J}$ of energy with current of 10 A through the inductor.

Ajay Singhal

Numerade Educator

Problem 55

In $48-\mathrm{V}$ battery is in series with a switch, a $0.50-\mathrm{H}$ inductor, and a $10-\Omega$ resistor. (a) What's the maximum current in this circuit? (b) What's the current at $t=0.10 \mathrm{~s}$ after the switch is closed? (c) When does the current reach half the maximum value?
(d) What's the current at time $t=2 \tau ?$

Vishal Gupta

Numerade Educator

Problem 56

In $12.0-\mathrm{V}$ battery is in series with a switch, a $0.25-\mathrm{H}$ inductor, and a $20-\Omega$ resistor. (a) What's the time constant $\tau ?$ (b) Find the potential differences across the inductor and resistor at $t=\tau$ and $t=2 \tau$.

Vishal Gupta

Numerade Educator

Problem 57

A $10.0-\mathrm{mH}$ inductor is in series with a capacitor that can be varied from $200 \mathrm{nF}$ to $400 \mathrm{nF}$. What's the range of possible oscillation frequencies?

Ajay Singhal

Numerade Educator

Problem 58

You have a variable capacitor ranging from $5.9 \mathrm{pF}$ to $8.8 \mathrm{pF}$. What inductor should be used with this capacitor in an FM radio receiver covering the entire FM band, $88 \mathrm{MHz}$ to $108 \mathrm{MHz} ?$

Ajay Singhal

Numerade Educator

Problem 59

In A charged, $250-\mu \mathrm{F}$ capacitor is connected across a $450-\mathrm{mH}$ inductor. (a) What's the oscillation period? (b) How should you change the capacitance in order to double the period?

Ajay Singhal

Numerade Educator

Problem 60

A $14700-\mu \mathrm{F}$ capacitor is charged to $9.0 \mathrm{~V}$ and then connected across a $1.50-\mathrm{H}$ inductor. (a) What's the energy in this circuit?
(b) What's the maximum current? (c) At what time after the circuit is connected are there equal energies in both components?

Ajay Singhal

Numerade Educator

Problem 61

A $500-\mu \mathrm{F}$ capacitor is connected across a $1.25-\mathrm{H}$ inductor. $\mathrm{At}$ a certain time, the charge on the capacitor is zero and the current is 0.342 A. (a) How much later will the capacitor charge reach its peak? (b) What's the total energy in the circuit?
(c) What is the peak charge on the capacitor?

Vishal Gupta

Numerade Educator

Problem 62

an (a) Consider the circuit shown in Figure $\mathrm{P} 19.62 .$ Initially here's no current in the circuit. Find the current in each resistor mmediately after the switch is closed and a long time later.
b) After the switch has been closed for a long time, it's opened. Find the current in each resistor immediately after it opens.

Zachary Warner

Numerade Educator

Problem 63

An AC power supply operates with peak emf $340 \mathrm{~V}$ and frequency $120 \mathrm{~Hz} .$ A $3.50-\mathrm{k} \Omega$ resistor is connected across the supply. Find (a) the rms current and (b) the average power dissipated in the resistor. (c) Graph the potential difference across and current through the resistor, both as functions of time.

Ajay Singhal

Numerade Educator

Problem 65

A capacitor is connected to a 200-V (peak), 50 -Hz power supply. If the maximum current is $400 \mathrm{~mA}$, what is the capacitance?

Ajay Singhal

Numerade Educator

Problem 66

$\mathbf{I}=$ When a $750-\Omega$ resistor is connected across an AC power supply, the resistor dissipates energy at a rate of $12.5 \mathrm{~W}$. (a) Find the rms current and maximum current through the resistor.
(b) What is the rms value of the power supply's emf?

Ajay Singhal

Numerade Educator

Problem 67

An AC power supply delivers $120 \mathrm{~V} \mathrm{rms}$. The time interval between peak emf in one direction and the opposite direction is $10.2 \mathrm{~ms} .$ Find (a) the peak emf and (b) the frequency. (c) Write an expression for the power supply's emf as a function of time, including all appropriate numerical values.

Ajay Singhal

Numerade Educator

Problem 68

A resistor connected across an AC power supply has a current given by $I=(1.20 \mathrm{~A}) \cos (300 t)$ when connected to a power supply with emf $100 \mathrm{~V} \mathrm{rms}$. Find (a) the rms current,
(b) the resistance, and (c) the average power delivered to the resistor.

Ajay Singhal

Numerade Educator

Problem 69

(a) At what frequency does a $100-\mu \mathrm{F}$ capacitor have $50-\Omega$ reactance? What would be its reactance if the frequency were tripled?
(b) At what frequency does a $100-\mathrm{mH}$ inductor have $50-\Omega$ reactance? What would be the reactance of this inductor if the frequency were tripled?

Ajay Singhal

Numerade Educator

Problem 70

A $240-\mathrm{V}$ (rms), 50 -Hz power supply is connected to a $4700-\mu \mathrm{F}$ capacitor. Find (a) the capacitor's reactance and (b) the peak current. (c) What's the peak current if the power supply's frequency is changed to $60 \mathrm{~Hz} ?$

Vishal Gupta

Numerade Educator

Problem 71

A solenoid has resistance $13.5 \Omega$ and inductance $410 \mathrm{mH}$ When it's connected across a $50-\mathrm{Hz}$ AC power supply, what's the circuit's impedance?

Ajay Singhal

Numerade Educator

Problem 72

$\operatorname{An} R C$ series circuit has $R=75.0 \Omega$ and $C=580 \mathrm{nF}$. The series combination is connected across a $200-\mathrm{V}(\mathrm{rms}), 60-\mathrm{Hz}$

Ajay Singhal

Numerade Educator

Problem 73

An $R C$ series circuit has $R=500 \Omega$ and $C=200 \mu \mathrm{F}$. The series combination is connected across a $120-\mathrm{V}(\mathrm{rms})$ power supply. Find the peak current when the frequency is (a) $60 \mathrm{~Hz}$ and
(b) $120 \mathrm{~Hz}$

Ajay Singhal

Numerade Educator

Problem 74

An $R L$ series circuit has $R=75.0 \Omega$ and $L=1.90 \mathrm{mH} .$ The series combination is connected across a $150-\mathrm{V}(\mathrm{rms}), 60-\mathrm{Hz}$ power supply. Find (a) the phase angle,
(b) the impedance of the $R L$ combination, and (c) the peak current.

Ajay Singhal

Numerade Educator

Problem 75

An $R L C$ series circuit has $R=1.35 \mathrm{k} \Omega, L=225 \mathrm{mH}$
$C=2.50 \mu \mathrm{F}$ and is connected across a $60-\mathrm{Hz}$ power supply. Find (a) the reactances of the capacitor and inductor and (b) the impedance of the circuit. (c) To what value should you change the capacitance in order to bring the circuit into resonance?

Nick Johnson

Numerade Educator

Problem 76

A $120-V$ (rms), 60 -Hz power supply is connected to an $R L C$ series circuit with $R=150 \Omega, L=1.20 \mathrm{mH},$ and $C=33.5 \mu \mathrm{F}$ Find (a) the reactance of the capacitor and inductor, (b) the circuit impedance, and (c) the peak current.

Ajay Singhal

Numerade Educator

Problem 77

For the circuit in the preceding problem, find (a) the phase angle, (b) the power factor, and (c) the average power consumption.

Ajay Singhal

Numerade Educator

Problem 78

An $R L C$ series circuit is in resonance at $60 \mathrm{~Hz}$. If you triple both the inductance and capacitance, what's the new resonance frequency?

Ajay Singhal

Numerade Educator

Problem 79

In An RLC series circuit has $R=920 \Omega, L=15.0 \mathrm{mH},$ and $C=250 \mu \mathrm{F}$. (a) What's its resonance frequency? (b) If the circuit is connected to a 100 -V rms power source at the resonance frequency, what's the average power consumption?

Ajay Singhal

Numerade Educator

Problem 80

An $R L C$ series circuit has $R=1.10 \mathrm{k} \Omega, L=190 \mathrm{mH},$ and $C=4.50 \mu \mathrm{F}$. (a) What frequencies will give a power factor of(a) $0.5 ;$ (b) 0.75 (c) $1.0 ?$

Donald Albin

Numerade Educator

Problem 81

A car alternator produces about $14 \mathrm{~V}$ peak output to charge the car's $12-\mathrm{V}$ battery. If an alternator coil is $15 \mathrm{~cm}$ in diameter and is spinning at 1200 revolutions per minute in a $0.15-\mathrm{T}$ magnetic field, how many turns must it have to produce a $14-\mathrm{V}$ peak output?

Ajay Singhal

Numerade Educator

Problem 82

A square loop $3.0 \mathrm{~m}$ on a side is perpendicular to a uniform 2.0-T magnetic field as shown in Figure GP1 9.82. A 6.0-V lightbulb is in series with the loop. The magnetic field is reduced steadily to zero during a time interval $\Delta t .$ (a) Find $\Delta t$ such that the bulb will shine at full brightness during this time. (b) In which direction does the loop current flow?

Ajay Singhal

Numerade Educator

Problem 83

Opening switches in highly inductive circuits can be dangerous, even with low-voltage power sources. To see why, consider a 6-V battery supplying 3.0 A to an electromagnet with inductance $2.5 \mathrm{H}$. A switch in this circuit opens and the current drops to zero in a mere $6.8 \mathrm{~ms}$. What's the emf induced in the electro-
magnet during this time?

Ajay Singhal

Numerade Educator

Problem 84

An MRI scanner uses a large solenoid with inductance $0.53 \mathrm{H}$, carrying $2.4 \mathrm{kA}$ of current. (a) What's the energy stored in the solenoid? (b) The solenoid coils are normally superconducting (zero resistance), but if superconductivity fails they revert to a resistance of $0.31 \mathrm{~m} \Omega$. (b) Given that the current can't change instantaneously, find the power dissipation in the solenoid immediately after a sudden loss of superconductivity.

Ajay Singhal

Numerade Educator

Problem 85

A 3.2 -cm-diameter circular coil with 30 turns of wire has resistance $1.3 \Omega$. This coil is placed inside a solenoid, with coil and solenoid axes aligned. The solenoid has 3000 turns and is $25 \mathrm{~cm}$ long. (a) At what rate must the current in the solenoid be increased to induce a $1.0-\mathrm{mA}$ current in the coil? (b) Is the induced current in the same direction or opposite the solenoid current?

Ajay Singhal

Numerade Educator

Problem 86

An electric toothbrush rests on a stand containing a 50 -turn coil connected across the $120-\mathrm{V} \mathrm{rms}$ AC power line. Inside the brush handle is another coil whose induced current charges a 6-V battery. How many turns should this coil contain if its peak $\mathrm{emf}$ is to be $7.1 \mathrm{~V} ?$

Ajay Singhal

Numerade Educator

Problem 87

Earth's magnetic field has an approximate value of $50 \mu \mathrm{T}$
(a) Estimate the total magnetic energy contained in the first $100 \mathrm{~km}$ above Earth's surface. (b) If we could tap this energy, how long would it supply humankind's power demand of 15 TW?

Vishal Gupta

Numerade Educator