Integrated Concepts A very large, superconducting solenoid such as one used in MRI

How do the multiple-loop coils and iron ring in the version of Faradays apparatus shown in Figure 23.3 enhance the observation of induced emf?

When a magnet is thrust into a coil as in Figure 23.4(a), what is the direction of the force exerted by the coil on the magnet? Draw a diagram showing the direction of the current induced in the coil and the magnetic field it produces, to justify your response. How does the magnitude of the force depend on the resistance of the galvanometer?

Explain how magnetic flux can be zero when the magnetic field is not zero

Is an emf induced in the coil in Figure 23.54 when it is stretched? If so, state why and give the direction of the induced current.

A person who works with large magnets sometimes places her head inside a strong field. She reports feeling dizzy as she quickly turns her head. How might this be associated with induction?

A particle accelerator sends high-velocity charged particles down an evacuated pipe. Explain how a coil of wire wrapped around the pipe could detect the passage of individual particles. Sketch a graph of the voltage output of the coil as a single particle passes through it.

Why must part of the circuit be moving relative to other parts, to have usable motional emf? Consider, for example, that the rails in Figure 23.11 are stationary relative to the magnetic field, while the rod moves.

A powerful induction cannon can be made by placing a metal cylinder inside a solenoid coil. The cylinder is forcefully expelled when solenoid current is turned on rapidly. Use Faradays and Lenzs laws to explain how this works. Why might the cylinder get live/hot when the cannon is fired?

An induction stove heats a pot with a coil carrying an alternating current located beneath the pot (and without a hot surface). Can the stove surface be a conductor? Why wont a coil carrying a direct current work?

Explain how you could thaw out a frozen water pipe by wrapping a coil carrying an alternating current around it. Does it matter whether or not the pipe is a conductor? Explain.

Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation.

Explain how electromagnetic induction can be used to detect metals? This technique is particularly important in detecting buried landmines for disposal, geophysical prospecting and at airports.

Using RHR-1, show that the emfs in the sides of the generator loop in Figure 23.23 are in the same sense and thus add

The source of a generators electrical energy output is the work done to turn its coils. How is the work needed to turn the generator related to Lenzs law?

Suppose you find that the belt drive connecting a powerful motor to an air conditioning unit is broken and the motor is running freely. Should you be worried that the motor is consuming a great deal of energy for no useful purpose? Explain why or why not

Explain what causes physical vibrations in transformers at twice the frequency of the AC power involved.

Does plastic insulation on live/hot wires prevent shock hazards, thermal hazards, or both?

Why are ordinary circuit breakers and fuses ineffective in preventing shocks?

A GFI may trip just because the live/hot and neutral wires connected to it are significantly different in length. Explain why.

How would you place two identical flat coils in contact so that they had the greatest mutual inductance? The least?

How would you shape a given length of wire to give it the greatest self-inductance? The least?

Verify, as was concluded without proof in Example 23.7, that units of T m2 / A = s = H .

Presbycusis is a hearing loss due to age that progressively affects higher frequencies. A hearing aid amplifier is designed to amplify all frequencies equally. To adjust its output for presbycusis, would you put a capacitor in series or parallel with the hearing aids speaker? Explain.

Would you use a large inductance or a large capacitance in series with a system to filter out low frequencies, such as the 100 Hz hum in a sound system? Explain.

High-frequency noise in AC power can damage computers. Does the plug-in unit designed to prevent this damage use a large inductance or a large capacitance (in series with the computer) to filter out such high frequencies? Explain

Does inductance depend on current, frequency, or both? What about inductive reactance?

Explain why the capacitor in Figure 23.55(a) acts as a low-frequency filter between the two circuits, whereas that in Figure 23.55(b) acts as a high-frequency filter

If the capacitors in Figure 23.55 are replaced by inductors, which acts as a low-frequency filter and which as a highfrequency filter?

Does the resonant frequency of an AC circuit depend on the peak voltage of the AC source? Explain why or why not

Suppose you have a motor with a power factor significantly less than 1. Explain why it would be better to improve the power factor as a method of improving the motors output, rather than to increase the voltage input.

What is the peak emf generated by a 0.250 m radius, 500-turn coil is rotated one-fourth of a revolution in 4.17 ms, originally having its plane perpendicular to a uniform magnetic field. (This is 60 rev/s.)

(a) A bicycle generator rotates at 1875 rad/s, producing an 18.0 V peak emf. It has a 1.00 by 3.00 cm rectangular coil in a 0.640 T field. How many turns are in the coil? (b) Is this number of turns of wire practical for a 1.00 by 3.00 cm coil?

Integrated Concepts This problem refers to the bicycle generator considered in the previous problem. It is driven by a 1.60 cm diameter wheel that rolls on the outside rim of the bicycle tire. (a) What is the velocity of the bicycle if the generators angular velocity is 1875 rad/s? (b) What is the maximum emf of the generator when the bicycle moves at 10.0 m/s, noting that it was 18.0 V under the original conditions? (c) If the sophisticated generator can vary its own magnetic field, what field strength will it need at 5.00 m/s to produce a 9.00 V maximum emf?

(a) A car generator turns at 400 rpm when the engine is idling. Its 300-turn, 5.00 by 8.00 cm rectangular coil rotates in an adjustable magnetic field so that it can produce sufficient voltage even at low rpms. What is the field strength needed to produce a 24.0 V peak emf? (b) Discuss how this required field strength compares to those available in permanent and electromagnets.

Show that if a coil rotates at an angular velocity , the period of its AC output is 2/ .

A 75-turn, 10.0 cm diameter coil rotates at an angular velocity of 8.00 rad/s in a 1.25 T field, starting with the plane of the coil parallel to the field. (a) What is the peak emf? (b) At what time is the peak emf first reached? (c) At what time is the emf first at its most negative? (d) What is the period of the AC voltage output?

(a) If the emf of a coil rotating in a magnetic field is zero at t = 0 , and increases to its first peak at t = 0.100 ms , what is the angular velocity of the coil? (b) At what time will its next maximum occur? (c) What is the period of the output? (d) When is the output first one-fourth of its maximum? (e) When is it next one-fourth of its maximum?

Unreasonable Results A 500-turn coil with a 0.250 m2 area is spun in the Earths 5.00105 T field, producing a 12.0 kV maximum emf. (a) At what angular velocity must the coil be spun? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?

Suppose a motor connected to a 120 V source draws 10.0 A when it first starts. (a) What is its resistance? (b) What current does it draw at its normal operating speed when it develops a 100 V back emf?

A motor operating on 240 V electricity has a 180 V back emf at operating speed and draws a 12.0 A current. (a) What is its resistance? (b) What current does it draw when it is first started?

What is the back emf of a 120 V motor that draws 8.00 A at its normal speed and 20.0 A when first starting?

The motor in a toy car operates on 6.00 V, developing a 4.50 V back emf at normal speed. If it draws 3.00 A at normal speed, what current does it draw when starting?

Integrated Concepts The motor in a toy car is powered by four batteries in series, which produce a total emf of 6.00 V. The motor draws 3.00 A and develops a 4.50 V back emf at normal speed. Each battery has a 0.100 internal resistance. What is the resistance of the motor?

A plug-in transformer, like that in Figure 23.29, supplies 9.00 V to a video game system. (a) How many turns are in its secondary coil, if its input voltage is 120 V and the primary coil has 400 turns? (b) What is its input current when its output is 1.30 A?

An American traveler in New Zealand carries a transformer to convert New Zealands standard 240 V to 120 V so that she can use some small appliances on her trip. (a) What is the ratio of turns in the primary and secondary coils of her transformer? (b) What is the ratio of input to output current? (c) How could a New Zealander traveling in the United States use this same transformer to power her 240 V appliances from 120 V?

A cassette recorder uses a plug-in transformer to convert 120 V to 12.0 V, with a maximum current output of 200 mA. (a) What is the current input? (b) What is the power input? (c) Is this amount of power reasonable for a small appliance?

(a) What is the voltage output of a transformer used for rechargeable flashlight batteries, if its primary has 500 turns, its secondary 4 turns, and the input voltage is 120 V? (b) What input current is required to produce a 4.00 A output? (c) What is the power input?

(a) The plug-in transformer for a laptop computer puts out 7.50 V and can supply a maximum current of 2.00 A. What is the maximum input current if the input voltage is 240 V? Assume 100% efficiency. (b) If the actual efficiency is less than 100%, would the input current need to be greater or smaller? Explain.

A multipurpose transformer has a secondary coil with several points at which a voltage can be extracted, giving outputs of 5.60, 12.0, and 480 V. (a) The input voltage is 240 V to a primary coil of 280 turns. What are the numbers of turns in the parts of the secondary used to produce the output voltages? (b) If the maximum input current is 5.00 A, what are the maximum output currents (each used alone)?

A large power plant generates electricity at 12.0 kV. Its old transformer once converted the voltage to 335 kV. The secondary of this transformer is being replaced so that its output can be 750 kV for more efficient cross-country transmission on upgraded transmission lines. (a) What is the ratio of turns in the new secondary compared with the old secondary? (b) What is the ratio of new current output to old output (at 335 kV) for the same power? (c) If the upgraded transmission lines have the same resistance, what is the ratio of new line power loss to old?

If the power output in the previous problem is 1000 MW and line resistance is 2.00 , what were the old and new line losses?

Unreasonable Results The 335 kV AC electricity from a power transmission line is fed into the primary coil of a transformer. The ratio of the number of turns in the secondary to the number in the primary is Ns / Np = 1000 . (a) What voltage is induced in the secondary? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?

Construct Your Own Problem Consider a double transformer to be used to create very large voltages. The device consists of two stages. The first is a transformer that produces a much larger output voltage than its input. The output of the first transformer is used as input to a second transformer that further increases the voltage. Construct a problem in which you calculate the output voltage of the final stage based on the input voltage of the first stage and the number of turns or loops in both parts of both transformers (four coils in all). Also calculate the maximum output current of the final stage based on the input current. Discuss the possibility of power losses in the devices and the effect on the output current and power.

Integrated Concepts A short circuit to the grounded metal case of an appliance occurs as shown in Figure 23.60. The person touching the case is wet and only has a 3.00 k resistance to earth/ ground. (a) What is the voltage on the case if 5.00 mA flows through the person? (b) What is the current in the short circuit if the resistance of the earth/ground wire is 0.200 ? (c) Will this trigger the 20.0 A circuit breaker supplying the appliance?

Two coils are placed close together in a physics lab to demonstrate Faradays law of induction. A current of 5.00 A in one is switched off in 1.00 ms, inducing a 9.00 V emf in the other. What is their mutual inductance?

If two coils placed next to one another have a mutual inductance of 5.00 mH, what voltage is induced in one when the 2.00 A current in the other is switched off in 30.0 ms?

The 4.00 A current through a 7.50 mH inductor is switched off in 8.33 ms. What is the emf induced opposing this?

A device is turned on and 3.00 A flows through it 0.100 ms later. What is the self-inductance of the device if an induced 150 V emf opposes this?

Starting with emf2 = M I1 t , show that the units of inductance are (V s)/A = s .

Camera flashes charge a capacitor to high voltage by switching the current through an inductor on and off rapidly. In what time must the 0.100 A current through a 2.00 mH inductor be switched on or off to induce a 500 V emf?

A large research solenoid has a self-inductance of 25.0 H. (a) What induced emf opposes shutting it off when 100 A of current through it is switched off in 80.0 ms? (b) How much energy is stored in the inductor at full current? (c) At what rate in watts must energy be dissipated to switch the current off in 80.0 ms? (d) In view of the answer to the last part, is it surprising that shutting it down this quickly is difficult?

(a) Calculate the self-inductance of a 50.0 cm long, 10.0 cm diameter solenoid having 1000 loops. (b) How much energy is stored in this inductor when 20.0 A of current flows through it? (c) How fast can it be turned off if the induced emf cannot exceed 3.00 V?

A precision laboratory resistor is made of a coil of wire 1.50 cm in diameter and 4.00 cm long, and it has 500 turns. (a) What is its self-inductance? (b) What average emf is induced if the 12.0 A current through it is turned on in 5.00 ms (one-fourth of a cycle for 50 Hz AC)? (c) What is its inductance if it is shortened to half its length and counterwound (two layers of 250 turns in opposite directions)?

The heating coils in a hair dryer are 0.800 cm in diameter, have a combined length of 1.00 m, and a total of 400 turns. (a) What is their total self-inductance assuming they act like a single solenoid? (b) How much energy is stored in them when 6.00 A flows? (c) What average emf opposes shutting them off if this is done in 5.00 ms (one-fourth of a cycle for 50 Hz AC)?

When the 20.0 A current through an inductor is turned off in 1.50 ms, an 800 V emf is induced, opposing the change. What is the value of the self-inductance?

How fast can the 150 A current through a 0.250 H inductor be shut off if the induced emf cannot exceed 75.0 V?

Integrated Concepts A very large, superconducting solenoid such as one used in MRI scans, stores 1.00 MJ of energy in its magnetic field when 100 A flows. (a) Find its self-inductance. (b) If the coils go normal, they gain resistance and start to dissipate thermal energy. What temperature increase is produced if all the stored energy goes into heating the 1000 kg magnet, given its average specific heat is 200 J/kgC ?

Unreasonable Results A 25.0 H inductor has 100 A of current turned off in 1.00 ms. (a) What voltage is induced to oppose this? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?

If you want a characteristic RL time constant of 1.00 s, and you have a 500 resistor, what value of selfinductance is needed?

Your RL circuit has a characteristic time constant of 20.0 ns, and a resistance of 5.00 M. (a) What is the inductance of the circuit? (b) What resistance would give you a 1.00 ns time constant, perhaps needed for quick response in an oscilloscope?

A large superconducting magnet, used for magnetic resonance imaging, has a 50.0 H inductance. If you want current through it to be adjustable with a 1.00 s characteristic time constant, what is the minimum resistance of system?

Verify that after a time of 10.0 ms, the current for the situation considered in Example 23.9 will be 0.183 A as stated.

Suppose you have a supply of inductors ranging from 1.00 nH to 10.0 H, and resistors ranging from 0.100 to 1.00 M. What is the range of characteristic RL time constants you can produce by connecting a single resistor to a single inductor?

(a) What is the characteristic time constant of a 25.0 mH inductor that has a resistance of 4.00 ? (b) If it is connected to a 12.0 V battery, what is the current after 12.5 ms?

What percentage of the final current I0 flows through an inductor L in series with a resistor R , three time constants after the circuit is completed?

The 5.00 A current through a 1.50 H inductor is dissipated by a 2.00 resistor in a circuit like that in Figure 23.44 with the switch in position 2. (a) What is the initial energy in the inductor? (b) How long will it take the current to decline to 5.00% of its initial value? (c) Calculate the average power dissipated, and compare it with the initial power dissipated by the resistor

(a) Use the exact exponential treatment to find how much time is required to bring the current through an 80.0 mH inductor in series with a 15.0 resistor to 99.0% of its final value, starting from zero. (b) Compare your answer to the approximate treatment using integral numbers of . (c) Discuss how significant the difference is.

(a) Using the exact exponential treatment, find the time required for the current through a 2.00 H inductor in series with a 0.500 resistor to be reduced to 0.100% of its original value. (b) Compare your answer to the approximate treatment using integral numbers of . (c) Discuss how significant the difference is.

At what frequency will a 30.0 mH inductor have a reactance of 100 ?

What value of inductance should be used if a 20.0 k reactance is needed at a frequency of 500 Hz?

What capacitance should be used to produce a 2.00 M reactance at 60.0 Hz?

At what frequency will an 80.0 mF capacitor have a reactance of 0.250 ?

(a) Find the current through a 0.500 H inductor connected to a 60.0 Hz, 480 V AC source. (b) What would the current be at 100 kHz?

(a) What current flows when a 60.0 Hz, 480 V AC source is connected to a 0.250 F capacitor? (b) What would the current be at 25.0 kHz?

A 20.0 kHz, 16.0 V source connected to an inductor produces a 2.00 A current. What is the inductance?

A 20.0 Hz, 16.0 V source produces a 2.00 mA current when connected to a capacitor. What is the capacitance?

(a) An inductor designed to filter high-frequency noise from power supplied to a personal computer is placed in series with the computer. What minimum inductance should it have to produce a 2.00 k reactance for 15.0 kHz noise? (b) What is its reactance at 60.0 Hz?

The capacitor in Figure 23.55(a) is designed to filter lowfrequency signals, impeding their transmission between circuits. (a) What capacitance is needed to produce a 100 k reactance at a frequency of 120 Hz? (b) What would its reactance be at 1.00 MHz? (c) Discuss the implications of your answers to (a) and (b)

The capacitor in Figure 23.55(b) will filter high-frequency signals by shorting them to earth/ground. (a) What capacitance is needed to produce a reactance of 10.0 m for a 5.00 kHz signal? (b) What would its reactance be at 3.00 Hz? (c) Discuss the implications of your answers to (a) and (b).

Unreasonable Results In a recording of voltages due to brain activity (an EEG), a 10.0 mV signal with a 0.500 Hz frequency is applied to a capacitor, producing a current of 100 mA. Resistance is negligible. (a) What is the capacitance? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?

Construct Your Own Problem Consider the use of an inductor in series with a computer operating on 60 Hz electricity. Construct a problem in which you calculate the relative reduction in voltage of incoming high frequency noise compared to 60 Hz voltage. Among the things to consider are the acceptable series reactance of the inductor for 60 Hz power and the likely frequencies of noise coming through the power lines.

An RL circuit consists of a 40.0 resistor and a 3.00 mH inductor. (a) Find its impedance Z at 60.0 Hz and 10.0 kHz. (b) Compare these values of Z with those found in Example 23.12 in which there was also a capacitor.

An RC circuit consists of a 40.0 resistor and a 5.00 F capacitor. (a) Find its impedance at 60.0 Hz and 10.0 kHz. (b) Compare these values of Z with those found in Example 23.12, in which there was also an inductor.

An LC circuit consists of a 3.00 mH inductor and a 5.00 F capacitor. (a) Find its impedance at 60.0 Hz and 10.0 kHz. (b) Compare these values of Z with those found in Example 23.12 in which there was also a resistor.

What is the resonant frequency of a 0.500 mH inductor connected to a 40.0 F capacitor?

To receive AM radio, you want an RLC circuit that can be made to resonate at any frequency between 500 and 1650 kHz. This is accomplished with a fixed 1.00 H inductor connected to a variable capacitor. What range of capacitance is needed?

Suppose you have a supply of inductors ranging from 1.00 nH to 10.0 H, and capacitors ranging from 1.00 pF to 0.100 F. What is the range of resonant frequencies that can be achieved from combinations of a single inductor and a single capacitor?

What capacitance do you need to produce a resonant frequency of 1.00 GHz, when using an 8.00 nH inductor?

What inductance do you need to produce a resonant frequency of 60.0 Hz, when using a 2.00 F capacitor?

The lowest frequency in the FM radio band is 88.0 MHz. (a) What inductance is needed to produce this resonant frequency if it is connected to a 2.50 pF capacitor? (b) The capacitor is variable, to allow the resonant frequency to be adjusted to as high as 108 MHz. What must the capacitance be at this frequency?

An RLC series circuit has a 2.50 resistor, a 100 H inductor, and an 80.0 F capacitor.(a) Find the circuits impedance at 120 Hz. (b) Find the circuits impedance at 5.00 kHz. (c) If the voltage source has Vrms = 5.60 V , what is Irms at each frequency? (d) What is the resonant frequency of the circuit? (e) What is Irms at resonance?

An RLC series circuit has a 1.00 k resistor, a 150 H inductor, and a 25.0 nF capacitor. (a) Find the circuits impedance at 500 Hz. (b) Find the circuits impedance at 7.50 kHz. (c) If the voltage source has Vrms = 408 V , what is Irms at each frequency? (d) What is the resonant frequency of the circuit? (e) What is Irms at resonance?

An RLC series circuit has a 2.50 resistor, a 100 H inductor, and an 80.0 F capacitor. (a) Find the power factor at f = 120 Hz . (b) What is the phase angle at 120 Hz? (c) What is the average power at 120 Hz? (d) Find the average power at the circuits resonant frequency

An RLC series circuit has a 1.00 k resistor, a 150 H inductor, and a 25.0 nF capacitor. (a) Find the power factor at f = 7.50 Hz . (b) What is the phase angle at this frequency? (c) What is the average power at this frequency? (d) Find the average power at the circuits resonant frequency

An RLC series circuit has a 200 resistor and a 25.0 mH inductor. At 8000 Hz, the phase angle is 45.0 . (a) What is the impedance? (b) Find the circuits capacitance. (c) If Vrms = 408 V is applied, what is the average power supplied?

Referring to Example 23.14, find the average power at 10.0 kHz.