(I) The magnetic field inside an air-filled solenoid 36 cm

The magnetic flux through a coil of wire containing two loops changes at a constant rate from to in 0.34 s. What is the emf induced in the coil?

The north pole of the magnet in Fig.2157 is being inserted into the coil. In which direction is the induced current flowing through resistor R? Explain.

The rectangular loop in Fig. 2158 is being pushed to the right, where the magnetic field points inward. In what direction is the induced current? Explain your reasoning

If the solenoid in Fig. 2159 is being pulled away from the loop shown, in what direction is the induced current in the loop? Explain.

An 18.5-cm-diameter loop of wire is initially oriented perpendicular to a 1.5-T magnetic field. The loop is rotated so that its plane is parallel to the field direction in 0.20 s. What is the average induced emf in the loop?

(II) A fixed 10.8-cm-diameter wire coil is perpendicular to a magnetic field 0.48 T pointing up. In 0.16 s, the field is changed to 0.25 T pointing down. What is the average induced emf in the coil?

A 16-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 42 angle with the field lines. What is the angle in Eq. 211 for this situation? (c) What is the magnetic flux through the loop at this angle?

(a) If the resistance of the resistor in Fig. 2160 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? Explain your answers.

The moving rod in Fig. 2111 is 12.0 cm long and is pulled at a speed of If the magnetic field is 0.800 T, calculate (a) the emf developed, and (b) the electric field felt by electrons in the rod.

A circular loop in the plane of the paper lies in a 0.65-T magnetic field pointing into the paper. The loops diameter changes from 20.0 cm to 6.0 cm in 0.50 s. What is (a) the direction of the induced current, (b) the magnitude of the average induced emf, and (c) the average induced current if the coil resistance is ?

What is the direction of the induced current in the circular loop due to the current shown in each part of Fig. 2161? Explain why

A 600-turn solenoid, 25 cm long, has a diameter of 2.5 cm. A 14-turn coil is wound tightly around the center of the solenoid. If the current in the solenoid increases uniformly from 0 to 5.0 A in 0.60 s, what will be the induced emf in the short coil during this time?

When a car drives through the Earths magnetic field, an emf is induced in its vertical 55-cm-long radio antenna. If the Earths field points north with a dip angle of 38, what is the maximum emf induced in the antenna and which direction(s) will the car be moving to produce this maximum value? The cars speed is on a horizontal road

Part of a single rectangular loop of wire with dimensions shown in Fig. 2162 is situated inside a region of uniform magnetic field of 0.550 T. The total resistance of the loop is Calculate the force required to pull the loop from the field (to the right) at a constant velocity of Neglect gravity

In order to make the rod of Fig. 2111a move to the right at speed you need to apply an external force on the rod to the right. (a) Explain and determine the magnitude of the required force. (b) What external power is needed to move the rod? (Do not confuse this external force on the rod with the upward force on the electrons shown in Fig. 2111b.)

In Fig. 2111, the moving rod has a resistance of and moves on rails 20.0 cm apart. The stationary conductor has negligible resistance. When a force of 0.350 N is applied to the rod, it moves to the right at a constant speed of What is the magnetic field?

In Fig. 2111, the rod moves with a speed of on rails 30.0 cm apart. The rod has a resistance of The magnetic field is 0.35 T, and the resistance of the conductor is at a given instant. Calculate (a) the induced emf, (b) the current in the conductor, and (c) the external force needed to keep the rods velocity constant at that instant

A 22.0-cm-diameter coil consists of 30 turns of circular copper wire 2.6 mm in diameter. A uniform magnetic field, perpendicular to the plane of the coil, changes at a rate of Determine (a) the current in the loop, and (b) the rate at which thermal energy is produced

The magnetic field perpendicular to a single 13.2-cmdiameter circular loop of copper wire decreases uniformly from 0.670 T to zero. If the wire is 2.25 mm in diameter, how much charge moves past a point in the coil during this operation?

The generator of a car idling at 1100 rpm produces 12.7 V. What will the output be at a rotation speed of 2500 rpm, assuming nothing else changes?

A 550-loop circular armature coil with a diameter of 8.0 cm rotates at 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?

A generator rotates at 85 Hz in a magnetic field of 0.030 T. It has 950 turns and produces an rms voltage of 150 V and an rms current of 70.0 A. (a) What is the peak current produced? (b) What is the area of each turn of the coil?

A simple generator has a square armature 6.0 cm on a side. The armature has 85 turns of 0.59-mm- diameter copper wire and rotates in a 0.65-T magnetic field. The generator is used to power a lightbulb rated at 12.0 V and 25.0 W. At what rate should the generator rotate to provide 12.0 V to the bulb? Consider the resistance of the wire on the armature.

A motor has an armature resistance of If it draws 8.20 A when running at full speed and connected to a 120-V line, how large is the back emf?

The back emf in a motor is 72 V when operating at 1800 rpm. What would be the back emf at 2300 rpm if the magnetic field is unchanged?

What will be the current in the motor of Example 218 if the load causes it to run at half speed?

A transformer is designed to change 117 V into 13,500 V, and there are 148 turns in the primary coil. How many turns are in the secondary coil?

A transformer has 360 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?

Neon signs require 12 kV for their operation. To operate from a 240-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 in reverse?

A model-train transformer plugs into 120-V ac and draws 0.35 A while supplying 6.8 A to the train. (a) What voltage is present across the tracks? (b) Is the transformer step-up or step-down?

The output voltage of a 95-W transformer is 12 V, and the input current is 25 A. (a) Is this a step-up or a step-down transformer? (b) By what factor is the voltage multiplied?

A transformer has 330 primary turns and 1240 secondary turns. The input voltage is 120 V and the output current is 15.0 A. What are the output voltage and input current?

If 35 MW of power at 45 kV (rms) arrives at a town from a generator via 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 line

For the transmission of electric power from power plant to home, as depicted in Fig. 2125, where the electric power sent by the plant is 100 kW, about how far away could the house be from the power plant before power loss is 50%? Assume the wires have a resistance per unit length of

For the transmission of electric power from power plant to home, as depicted in Fig. 2125, where the electric power sent by the plant is 100 kW, about how far away could the house be from the power plant before power loss is 50%? Assume the wires have a resistance per unit length of

For the electric power transmission system shown in Fig. 2125, what is the ratio for (a) the step-up transformer, (b) the step-down transformer next to the home?

Suppose 2.0 MW is to arrive at a large shopping mall over two lines. Estimate how much power is saved if the voltage is stepped up from 120 V to 1200 V and then down again, rather than simply transmitting at 120 V. Assume the transformers are each 99% efficient.

Design a dc transmission line that can transmit 925 MW of electricity 185 km with only a 2.5% loss. The wires are to be made of aluminum and the voltage is 660 kV.

If the current in a 160-mH coil changes steadily from 25.0 A to 10.0 A in 350 ms, what is the magnitude of the induced emf?

What is the inductance of a coil if the coil produces an emf of 2.50 V when the current in it changes from to in 14.0 ms?

Determine the inductance L of a 0.60-m-long air-filled solenoid 2.9 cm in diameter containing 8500 loops.

How many turns of wire would be required to make a 130-mH inductor out of a 30.0-cm-long air-filled solenoid with a diameter of 5.8 cm?

An air-filled cylindrical inductor has 2600 turns, and it is 2.5 cm in diameter and 28.2 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.

A coil has resistance and 112-mH inductance. If the current is 3.00 A and is increasing at a rate of what is the potential difference across the coil at this moment?

A physics professor wants to demonstrate the large size of the henry unit. On the outside of a 12-cm- diameter plastic hollow tube, she wants to wind an air-filled solenoid with self-inductance of 1.0 H using copper wire with a 0.81-mm diameter. The solenoid is to be tightly wound with each turn touching its neighbor (the wire has a thin insulating layer on its surface so the neighboring turns are not in electrical contact). How long will the plastic tube need to be and how many kilometers of copper wire will be required? What will be the resistance of this solenoid?

A long thin solenoid of length and cross-sectional area A contains closely packed turns of wire. Wrapped tightly around it is an insulated coil of turns, Fig. 2163. Assume all the flux from coil 1 (the solenoid) passes through coil 2, and calculate the mutual inductance.

The magnetic field inside an air-filled solenoid 36 cm long and 2.0 cm in diameter is 0.72 T. Approximately how much energy is stored in this field?

At the current through a 45.0-mH inductor is 50.0 mA and is increasing at the rate of What is the initial energy stored in the inductor, and how long does it take for the energy to increase by a factor of 5.0 from the initial value?

Assuming the Earths magnetic field averages about near Earths surface, estimate the total energy stored in this field in the first 10 km above Earths surface.

It takes 2.56 ms for the current in an LR circuit to increase from zero to 0.75 its maximum value. Determine (a) the time constant of the circuit, (b) the resistance of the circuit if L = 31.0 mH.

How many time constants does it take for the potential difference across the resistor in an LR circuit like that in Fig. 2137 to drop to 2.5% of its original value, after the switch is moved to the upper position, removing from the circuit?

Determine at (when the battery is connected) for the LR circuit of Fig. 2137 and show that if I continued to increase at this rate, it would reach its maximum value in one time constant

After how many time constants does the current in Fig. 2137 reach within (a) 10%, (b) 1.0%, and (c) 0.1% of its maximum value?

(I) What is the reactance of a capacitor at a frequency of a \(6.20-\mu \mathrm F\) (a) 60.0 Hz, (b) 1.00 MHz?

At what frequency will a 32.0-mH inductor have a reactance of 660 ?

At what frequency will a capacitor have a reactance of 6.10 k?

Calculate the reactance of, and rms current in, a 260-mH radio coil connected to a 240-V (rms) 10.0- kHz ac line. Ignore resistance.

An inductance coil operates at 240 V and 60.0 Hz. It draws 12.2 A. What is the coils inductance?

What is the reactance of a well-insulated capacitor connected to a 2.0-kV (rms) 720-Hz line? (b) What will be the peak value of the current?

For a 120-V rms 60-Hz voltage, an rms current of 70 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?

A resistor is in series with a 55-mH inductor and an ac source. Calculate the impedance of the circuit if the source frequency is (a) 50 Hz, and 3.0 * 104 Hz

A resistor and a capacitor are connected in series to an ac source. Calculate the impedance of the circuit if the source frequency is (a) 60 Hz, and (b) 60,000 Hz

Determine the resistance of a coil if its impedance is 225 and its reactance is 115 .

Determine the total impedance, phase angle, and rms current in an LRC circuit connected to a 10.0- kHz, 725-V (rms) source if and C = 6250 pF

An ac voltage source is connected in series with a capacitor and a resistor. Using a digital ac voltmeter, the amplitude of the voltage source is measured to be 4.0 V rms, while the voltages across the resistor and across the capacitor are found to be 3.0 V rms and 2.7 V rms, respectively. Determine the frequency of the ac voltage source. Why is the voltage measured across the voltage source not equal to the sum of the voltages measured across the resistor and across the capacitor?

(a) What is the rms current in an LR circuit when a 60.0-Hz 120-V rms ac voltage is applied, where and (b) What is the phase angle between voltage and current? (c) How much power is dissipated? (d) What are the rms voltage readings across R and L?

(a) What is the rms current in an RC circuit if and the rms applied voltage is 120 V at 60.0 Hz? (b) What is the phase angle between voltage and current? (c) What are the voltmeter readings across R and C?

Suppose circuit B in Fig. 2142a consists of a resistance The filter capacitor has capacitance Will this capacitor act to eliminate 60-Hz ac but pass a high-frequency signal of frequency 6.0 kHz? To check this, determine the voltage drop across R for a 130-mV signal of frequency (a) 60 Hz; (b) 6.0 kHz.

A 3500-pF capacitor is connected in series to a coil of resistance What is the resonant frequency of this circuit?

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

An LRC circuit has and (a) What value must C have to produce resonance at 3600 Hz? (b) What will be the maximum current at resonance if the peak external voltage is 150 V?

A resonant circuit using a 260-nF capacitor is to resonate at 18.0 kHz. The air-core inductor is to be a solenoid with closely packed coils made from 12.0 m of insulated wire 1.1 mm in diameter. How many loops will the inductor contain?

A 2200-pF capacitor is charged to 120 V and then quickly connected to an inductor. The frequency of oscillation is observed to be 19 kHz. Determine (a) the inductance, (b) the peak value of the current, and (c) the maximum energy stored in the magnetic field of the inductor.

Suppose you are looking at two wire loops in the plane of the page as shown in Fig. 2164. When switch S is closed 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? (d) Suppose the right-hand loop also has a switch like the left-hand loop. The switch in the left-hand loop has been closed a long time when the switch in the right-hand loop is closed. What happens in this case? Explain each answer.

A square loop 24.0 cm on a side has a resistance of It is initially in a 0.665-T magnetic field, with its plane perpendicular to but is removed from the field in 40.0 ms. Calculate the electric energy dissipated in this process

A high-intensity desk lamp is rated at 45 W but requires only 12 V. It contains a transformer that converts 120-V household voltage. (a) Is the transformer step-up or stepdown? (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?

A flashlight can be made that is powered by the induced current from a magnet moving through a coil of wire. The coil and magnet are inside a plastic tube that can be shaken causing the magnet to move back and forth through the coil. Assume the magnet has a maximum field strength of 0.05 T. Make reasonable assumptions and specify the size of the coil and the number of turns necessary to light a standard 1-watt, 3-V flashlight bulb

Conceptual Example 21–9 states that an overloaded motor may burn out due to high currents. Suppose you have a blender with an internal resistance of \(3.0\ \Omega\) (a) At 120 V, what is the initial current through the blender? (b) The blender is rated at 2.0 A for continuous use.What is the back emf of the blender? (c)At what rate is heat dissipated in the blender during normal use? (d) If the blender jams and stops turning, at what rate is heat dissipated in the motor coils?

Power is generated at 24 kV at a generating plant located 56 km from a town that requires 55 MW of power at 12 kV. Two transmission lines from the plant to the town each have a resistance of \(0.10\ \Omega/km\). 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?

The primary windings of a transformer which has an 88% efficiency are connected to 110-V ac. The secondary windings are connected across a 75-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.

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

Two resistanceless rails rest 32 cm apart on a 6.0° ramp. They are joined at the bottom by a \(0.60-\Omega\) resistor. At the top a copper bar of mass 0.040 kg (ignore its resistance) is laid across the rails. Assuming a vertical 0.45-T magnetic field, what is the terminal (steady) velocity of the bar as it slides frictionlessly down the rails?

. Show that the power loss in transmission lines, is given by where is the power transmitted to the user, V is the delivered voltage, and is the resistance of the power lines.

A coil with 190 turns, a radius of 5.0 cm, and a resistance of surrounds a solenoid with and a radius of 4.5 cm (Fig. 2165). The current in the solenoid changes at a constant rate from 0 to 2.0 A in 0.10 s. Calculate the magnitude and direction of the induced current in the outer coil.

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 mA in the first The device has resistance and is designed to operate at 55 mA. How would you protect this device?

A 35-turn 12.5-cm-diameter coil is placed between the pole pieces of an electromagnet. When the electromagnet is turned on, the flux through the coil changes, inducing an emf. At what rate (in ) must the magnetic field change if the emf is to be 120 V?

Calculate the peak output voltage of a simple generator whose square armature windings are 6.60 cm on a side; the armature contains 125 loops and rotates in a field of 0.200 T at a rate of 120 rev/s.

Typical large values for electric and magnetic fields attained in laboratories are about and 2.0 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-T magnetic field?

Determine the inductance L of the primary of a transformer whose input is 220 V at 60.0 Hz if the current drawn is 6.3 A. Assume no current in the secondary

A 130-mH coil whose resistance is \(15.8 \ \Omega\) 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?

. 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?

The Q factor of a resonant ac circuit (Section 2115) 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 (b) At a resonant frequency what must be the values of L and R to produce a Q factor of 650? Assume that C = 0.010 mF.

Problem 1COQ In the photograph above, the bar magnet is inserted down into the coil of wire, and is left there for 1 minute; then it is pulled up and out from the coil. What would an observer watching the galvanometer see? (a) No change (pointer stays on zero): without a battery there is no current to detect. (b) A small current flows while the magnet is inside the coil of wire. (c) A current spike as the magnet enters the coil, and then nothing. (d) A current spike as the magnet enters the coil, and then a steady small current. (e) A current spike as the magnet enters the coil, then nothing (pointer at zero), then a current spike in the opposite direction as the magnet exits the coil.

Problem 1MCQ A coil rests in the plane of the page while a magnetic field is directed into the page. A clockwise current is induced (a) when the magnetic field gets stronger. (b) when the size of the coil decreases. (c) when the coil is moved sideways across the page. (d) when the magnetic field is tilted so it is no longer perpendicular to the page.

Problem 1P (I) The magnetic flux through a coil of wire containing two loops changes at a constant rate from -58 Wb to +38 Wb in 0.34 s. What is the emf induced in the coil?

What would be the advantage, in Faraday’s experiments (Fig. 21–1), of using coils with many turns?

Problem 2MCQ A wire loop moves at constant velocity without rotation through a constant magnetic field. The induced current in the loop will be (a) clockwise. (b) counterclockwise. (c) zero. (d)We need to know the orientation of the loop relative to the magnetic field.

(I) The north pole of the magnet in Fig.21–57 is being inserted into the coil. In which direction is the induced current flowing through resistor ? Explain. FIGURE 21–57 Problem 2

While demonstrating Faraday's law to her class, a physics professor inadvertently moves the gold ring on her finger from a location where a -T magnetic field points along her finger to a zero-field location in . The diameter ring has a resistance and mass of \(55 \mu \Omega\) and , respectively. (a) Estimate the thermal energy produced in the ring due to the flow of induced current. ( ) Find the temperature rise of the ring, assuming all of the thermal energy produced goes into increasing the ring's temperature. The specific heat of gold is \(129 J / k g . C^{0}\). Equation transcription: Text transcription: 55 mu Omega 129 J / k g . C^{0}

A square loop moves to the right from an area where \(\vec{B}\)= 0, completely through a region containing a uniform magnetic field directed into the page (Fig. 21–52), and then out to after point L. A current is induced in the loop (a) only as it passes line J. (d) as it passes line J or line L. (b) only as it passes line K. (e) as it passes all three lines. (c) only as it passes line L. FIGURE 21–52 MisConceptual Question 3. Equation transcription: Text transcription: vec{B}

(I) The rectangular loop in Fig. 21–58 is being pushed to the right, where the magnetic field points inward. In what direction is the induced current? Explain your reasoning. FIGURE 21–58 Problem 3.

Problem 3Q Suppose you are holding a circular ring of wire in front of you and (a) suddenly thrust a magnet, south pole first, away from you toward the center of the circle. Is a current induced in the wire? (b) Is a current induced when the magnet is held steady within the ring? (c) Is a current induced when you withdraw the magnet? For each yes answer, specify the direction. Explain your answers.

Problem 3SL A small electric car overcomes a 250-N friction force when Traveling 35 km/h. The electric motor is powered by ten 12-V batteries connected in series and is coupled directly to the wheels whose diameters are 58 cm. The 290 armature coils are rectangular, 12 cm by 15 cm, and rotate in a 0.65-T magnetic field. (a) How much current does the motor draw to produce the required torque? (b) What is the back emf? (c) How much power is dissipated in the coils? (d) What percent of the input power is used to drive the car? [Hint: Check Sections 6–10, 18–5, 20–9, 20–10, and 21–6.]

Two loops of wire are moving in the vicinity of a very long straight wire carrying a steady current (Fig. 21–53). Find the direction of the induced current in each loop. For C: (a) clockwise. (b) counterclockwise. (c) zero. (d) alternating (ac). For D: (a) clockwise. (b) counterclockwise. (c) zero. (d) alternating (ac). FIGURE 21–53 MisConceptual Question 4.

(I) If the solenoid in Fig. 21–59 is being pulled away from the loop shown, in what direction is the induced current in the loop? Explain.

(a) A wire loop is pulled away from a current-carrying wire (Fig. 21–47). What is the direction of the induced current in the loop: clockwise or counterclockwise? (b) What if the wire loop stays fixed as the current I decreases? Explain your answers.

Problem 4SL Explain the advantage of using ac rather than dc current when electric power needs to be transported long distances. (See Section 21–7.)

Problem 5MCQ If there is induced current in Question 18 (see Fig. 21–51), wouldn’t that cost energy? Where would that energy come from in case (a)? (a) Induced current doesn’t need energy. (b) Energy conservation is violated. (c) There is less kinetic energy. (d) There is more gravitational potential energy.

Problem 5P (II) An 18.5-cm-diameter loop of wire is initially oriented perpendicular to a 1.5-T magnetic field. The loop is rotated so that its plane is parallel to the field direction in 0.20 s. What is the average induced emf in the loop?

(a) If the north pole of a thin flat magnet moves on a table toward a loop also on the table (Fig. 21–48), in what direction is the induced current in the loop? Assume the magnet is the same thickness as the wire. (b) What if the magnet is four times thicker than the wire loop? Explain your answers.

A power line carrying a sinusoidally varying current with frequency \(\(f=60 H z\)\) and peak value \(I_{0}=155 \mathrm{~A}\) runs at a height of across a farmer's land (Fig. ). The farmer constructs a vertical -m-high 2000 -turn rectangular wire coil below the power line. The farmer hopes to use the induced voltage in this coil to power 120-V electrical equipment, which requires a sinusoidally varying voltage with frequency \(f=60 H z\) and peak value \(V_{0}=170 \mathrm{~V}\). Estimate the length of the coil needed. Would this be stealing? [Hint: Consider over one-quarter of a cycle \(\left(\frac{1}{240} S\right)\). See Sections and .] \(I_{0}=155 \mathrm{~A}\) \(f=60 H z\) Equation transcription: Text transcription: V_{0}=170 \mathrm{~V} \left(\frac{1}{240} S\right) I_{0}=155 \mathrm{~A} f=60 H z

A nonconducting plastic hoop is held in a magnetic field that points out of the page (Fig. 21–54). As the strength of the field increases, (a) an induced emf will be produced that causes a clockwise current. (b) an induced emf will be produced that causes a counterclockwise current. (c) an induced emf will be produced but no current. (d) no induced emf will be produced. Equation Transcription: Text Transcription: \vec{B}

Problem 6P (II) A fixed 10.8-cm-diameter wire coil is perpendicular to a magnetic field 0.48 T pointing up. In 0.16 s, the field is changed to 0.25 T pointing down. What is the average induced emf in the coil?

Problem 6Q Suppose you are looking along a line through the centers of two circular (but separate) wire loops, one behind the other. A battery is suddenly connected to the front loop, establishing a clockwise current. (a) Will a current be induced in the second loop? (b) If so, when does this current start? (c) When does it stop? (d) In what direction is this current? (e) Is there a force between the two loops? (f ) If so, in what direction?

A ballistic galvanometer is a device that measures the total charge that passes through it in a short time. It is connected to a search coil that measures (also called a flip coil) which is a small coil with turns, each of cross-sectional area . The flip coil is placed in the magnetic field to be measured with its face perpendicular to the field. It is then quickly rotated about a diameter. Show that the total charge that flows in the induced current during this short "flip" time is proportional to the magnetic field . In particular, show that \(\)B=\frac{Q R}{2 N A} where is the total resistance of the circuit including the coil and ballistic galvanometer which measures charge . Equation transcription: Text transcription: B=frac{Q R}{2 N A}

A long straight wire carries a current I as shown in Fig. 21–55. A small loop of wire rests in the plane of the page. Which of the following will not induce a current in the loop? (a) Increasing the current in the straight wire. (b) Moving the loop in a direction parallel to the wire. (c) Rotating the loop so that it becomes perpendicular to the plane of the page. (d) Moving the loop farther from the wire without rotating it. (e) Moving the loop farther from the wire while rotating it.

Problem 7P (I) The magnetic field inside an air-filled solenoid 36 cm long and 2.0 cm in diameter is 0.72 T. Approximately how much energy is stored in this field?

Problem 7Q The battery mentioned in Question 6 is disconnected. Will a current be induced in the second loop? If so, when does it start and stop? In what direction is this current?

Two separate but nearby coils are mounted along the same axis. A power supply controls the flow of current in the first coil, and thus the magnetic field it produces. The second coil is connected only to an ammeter. The ammeter will indicate that a current is flowing in the second coil (a) whenever a current flows in the first coil. (b) only when a steady current flows in the first coil. (c) only when the current in the first coil changes. (d) only if the second coil is connected to the power supply by rewiring it to be in series with the first coil.

(II) (a) If the resistance of the resistor in Fig. 21–60 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? Explain your answers. FIGURE 21–60 Problem 8.

In Fig. 21–49, determine the direction of the induced current in resistor \(R_{A}\) (a) when coil B is moved toward coil A, (b) when coil B is moved away from A, (c) when the resistance \(R_{B}\) is increased but the coils remain fixed. Explain your answers. FIGURE 21–49 Question 8. Equation transcription: Text transcription: R{A} R{B}

Problem 9MCQ When a generator is used to produce electric current, the resulting electric energy originates from which source? (a) The generator’s magnetic field. (b)Whatever rotates the generator’s axle. (c) The resistance of the generator’s coil. (d) Back emf. (e) Empty space.

Problem 9P (II) The moving rod in Fig. 21–11 is 12.0 cm long and is pulled at a speed of 18.0 cm/s. If the magnetic field is 0.800 T, calculate (a) the emf developed, and (b) the electric field felt by electrons in the rod.

Problem 9Q In situations where a small signal must travel over a distance, a shielded cable is used in which the signal wire is surrounded by an insulator and then enclosed by a cylindrical conductor (shield) carrying the return current. Why is a “shield” necessary?

Problem 10MCQ Which of the following will not increase a generator’s voltage output? (a) Rotating the generator faster. (b) Increasing the area of the coil. (c) Rotating the magnetic field so that it is more closely parallel to the generator’s rotation axis. (d) Increasing the magnetic field through the coil. (e) Increasing the number of turns in the coil.

(II) A circular loop in the plane of the paper lies in a 0.65-T magnetic field pointing into the paper. The loop’s diameter changes from 20.0 cm to 6.0 cm in 0.50 s. What is (a) the direction of the induced current, (b) the magnitude of the average induced emf, and (c) the average induced current if the coil resistance is \(2.5\ \Omega\)?

Problem 10Q What is the advantage of placing the two insulated electric wires carrying ac close together or even twisted about each other?

Problem 11MCQ Which of the following can a transformer accomplish? (a) Changing voltage but not current. (b) Changing current but not voltage. (c) Changing power. (d) Changing both current and voltage.

(II) What is the direction of the induced current in the circular loop due to the current shown in each part of Fig. 21–61? Explain why. FIGURE 21–61 Problem 11.

Problem 11Q Explain why, exactly, the lights may dim briefly when a refrigerator motor starts up. When an electric heater is turned on, the lights may stay dimmed as long as the heater is on. Explain the difference.

Problem 12MCQ A laptop computer’s charger unit converts 120 V from a wall power outlet to the lower voltage required by the laptop. Inside the charger’s plastic case is a diode or rectifier (discussed in Chapter 29) that changes ac to dc plus a (a) battery. (b) motor. (c) generator. (d) transformer. (e) transmission line.

Problem 12P (II) A 600-turn solenoid, 25 cm long, has a diameter of 2.5 cm. A 14-turn coil is wound tightly around the center of the solenoid. If the current in the solenoid increases uniformly from 0 to 5.0 A in 0.60 s, what will be the induced emf in the short coil during this time?

Problem 13MCQ Which of the following statements about transformers is false? (a) Transformers work using ac current or dc current. (b) If the current in the secondary is higher, the voltage is lower. (c) If the voltage in the secondary is higher, the current is lower. (d) If no flux is lost, the product of the voltage and the current is the same in the primary and secondary coils.

Problem 13P (II) When a car drives through the Earth’s magnetic field, an emf is induced in its vertical 55-cm-long radio antenna. If the Earth’s field (5.0 X 10-5 T) points north with a dip angle of 38°, what is the maximum emf induced in the antenna and which direction(s) will the car be moving to produce this maximum value? The car’s speed is 30.3 m/s on a horizontal road.

Will an eddy current brake (Fig. 21–20) work on a copper or aluminum wheel, or must the wheel be ferromagnetic? Explain

Problem 14MCQ A 10-V, 1.0-A dc current is run through a step-up transformer that has 10 turns on the input side and 20 turns on the output side. What is the output? (a) 10 V, 0.5 A. (b) 20 V, 0.5 A. (c) 20V, 1A. (d) 10V, 1A. (e) 0V, 0A.

(II) Part of a single rectangular loop of wire with dimensions shown in Fig. 21–62 is situated inside a region of uniform magnetic field of 0.550 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 3.10 m/s Neglect gravity Equation transcription: Text transcription: 0.230 Omega

Problem 14Q A bar magnet falling inside a vertical metal tube reaches a terminal velocity even if the tube is evacuated so that there is no air resistance. Explain.

Problem 15MCQ The alternating electric current at a wall outlet is most commonly produced by (a) a connection to rechargeable batteries. (b) a rotating coil that is immersed in a magnetic field. (c) accelerating electrons between oppositely charged capacitor plates. (d) using an electric motor. (e) alternately heating and cooling a wire.

(II) In order to make the rod of Fig. 21–11a move to the right at speed \(v\), you need to apply an external force on the rod to the right. (a) Explain and determine the magnitude of the required force. (b) What external power is needed to move the rod? (Do not confuse this external force on the rod with the upward force on the electrons shown in Fig. 21–11b.) Equation transcription: Text transcription: v

Problem 15Q It has been proposed that eddy currents be used to help sort solid waste for recycling. The waste is first ground into tiny pieces and iron removed with a magnet. The waste then is allowed to slide down an incline over permanent magnets. How will this aid in the separation of nonferrous metals (Al, Cu, Pb, brass) from nonmetallic materials?

Problem 16MCQ When you swipe a credit card, the machine sometimes fails to read the card. What can you do differently? (a) Swipe the card more slowly so that the reader has more time to read the magnetic stripe. (b) Swipe the card more quickly so that the induced emf is higher. (c) Swipe the card more quickly so that the induced currents are reduced. (d) Swipe the card more slowly so that the magnetic fields don’t change so fast.

(II) In Fig. 21-11, the moving rod has a resistance of \(0.25 \Omega\) and moves on rails apart. The stationary U-shaped conductor has negligible resistance. When a force of is applied to the rod, it moves to the right at a constant speed of \(1.50 \mathrm{~m} / \mathrm{s}\). What is the magnetic field? Equation transcription: Text transcription: 0.25 Omega 1.50{~m} /{s}

The pivoted metal bar with slots in Fig. 21–50 falls much more quickly through a magnetic field than does a solid bar. Explain. FIGURE 21–50 Question 16.

Problem 17MCQ Which of the following is true about all series ac circuits? (a) The voltage across any circuit element is a maximum when the current is a maximum in that circuit element. (b) The current at any point in the circuit is always the same as the current at any other point in the circuit. (c) The current in the circuit is a maximum when the source ac voltage is a maximum. (d) Resistors, capacitors, and inductors can all change the phase of the current.

(III) In Fig. , the rod moves with a speed of \(1.6 \mathrm{~m} / \mathrm{s}\) on rails apart. The rod has a resistance of \(2.5 \Omega\). The magnetic field is , and the resistance of the -shaped conductor is \(21.0 \Omega\) at a given instant. Calculate the induced emf, (b) the current in the U-shaped conductor, and the external force needed to keep the rod's velocity constant at that instant. Equation transcription: Text transcription: 1.6{~m} /{s} 2.5 Omega 21.0 Omega

Problem 17Q If an aluminum sheet is held between the poles of a large bar magnet, it requires some force to pull it out of the magnetic field even though the sheet is not ferromagnetic and does not touch the pole faces. Explain.

Problem 18P (III) A 22.0-cm-diameter coil consists of 30 turns of circular copper wire 2.6 mm in diameter. A uniform magnetic field, perpendicular to the plane of the coil, changes at a rate of 8.65 X 10-3 T/s. Determine (a) the current in the loop, and (b) the rate at which thermal energy is produced.

A bar magnet is held above the floor and dropped (Fig. 21–51). In case (a), the magnet falls through a wire loop. In case (b), there is nothing between the magnet and the floor. How will the speeds of the magnets compare? Explain. FIGURE 21–51 Question 18 and MisConceptual Question 5.

Problem 19P (III) The magnetic field perpendicular to a single 13.2-cmdiameter circular loop of copper wire decreases uniformly from 0.670 T to zero. If the wire is 2.25 mm in diameter, how much charge moves past a point in the coil during this operation?

Problem 19Q A metal bar, pivoted at one end, oscillates freely in the absence of a magnetic field; but in a magnetic field, its oscillations are quickly damped out. Explain. (This magnetic damping is used in a number of practical devices.)

Problem 20P (II) The generator of a car idling at 1100 rpm produces 12.7 V. What will the output be at a rotation speed of 2500 rpm, assuming nothing else changes?

An enclosed transformer has four wire leads coming from it. How could you determine the ratio of turns on the two coils without taking the transformer apart? How would you know which wires paired with which?

EXERCISE A Return to the Chapter-Opening Question, page 590, and answer it again now. Try to explain why you may have answered differently the first time.

EXERCISE C In what direction will the electrons flow in Fig. 21–11 if the rod moves to the left, decreasing the area of the current loop?

EXERCISE F The capacitor C in Fig. 21–42a is often called a “high-pass” filter, and the one in Fig. 21–42b a “low-pass” filter. Explain why.

Problem 21ED A bicycle headlight is powered by a generator that is turned by the bicycle wheel. (a) If you speed up, how does the power to the light change? (b) Does the generator resist being turned as the bicycle’s speed increases, and if so how?

Problem 21EE How many turns would you want in the secondary coil of a transformer having NP = 400 turns if it were to reduce the voltage from 120-V ac to 3.0-V ac?

EXERCISE F The capacitor C in Fig. 21–42a is often called a “high-pass” filter, and the one in Fig. 21–42b a “low-pass” filter. Explain why.

Problem 21P (II) A 550-loop circular armature coil with a diameter of 8.0 cm rotates at 120 rev/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?

Problem 21Q The use of higher-voltage lines in homes—say, 600 V or 1200V—would reduce energy waste.Why are they not used?

Problem 22P (II) A generator rotates at 85 Hz in a magnetic field of 0.030 T. It has 950 turns and produces an rms voltage of 150V and an rms current of 70.0 A. (a) What is the peak current produced? (b) What is the area of each turn of the coil?

Problem 22Q A transformer designed for a 120-V ac input will often “burn out” if connected to a 120-V dc source. Explain. [Hint: The resistance of the primary coil is usually very low.]

Problem 23P (III) A simple generator has a square armature 6.0 cm on a side. The armature has 85 turns of 0.59-mm-diameter copper wire and rotates in a 0.65-T magnetic field. The generator is used to power a lightbulb rated at 12.0 V and 25.0W. At what rate should the generator rotate to provide 12.0 V to the bulb? Consider the resistance of the wire on the armature.

Problem 23Q How would you arrange two flat circular coils so that their mutual inductance was (a) greatest, (b) least (without separating them by a great distance)? Explain.

Problem 24P (I) A motor has an armature resistance of 3.65? If it draws 8.20 A when running at full speed and connected to a 120-V line, how large is the back emf?

Does the emf of the battery in Fig. 21–37 affect the time needed for the LR circuit to reach (a) a given fraction of its maximum possible current, (b) a given value of current? Explain.

(I) The back emf in a motor is 72 V when operating at 1800 rpm. What would be the back emf at 2300 rpm if the magnetic field is unchanged?

Problem 25Q In an LRC circuit, can the rms voltage across (a) an inductor, (b) a capacitor, be greater than the rms voltage of the ac source? Explain.

\(\text { (II) }\) What will be the current in the motor of Example 21–8 if the load causes it to run at half speed? Equation Transcription: Text Transcription: (II)

Problem 26Q Describe briefly how the frequency of the source emf affects the impedance of (a) a pure resistance, (b) a pure capacitance, (c) a pure inductance, (d) an LRC circuit near resonance (R small), (e) an LRC circuit far from resonance (R small).

Problem 27P (I) A transformer is designed to change 117 V into 13,500 V, and there are 148 turns in the primary coil. How many turns are in the secondary coil?

Problem 27Q Describe how to make the impedance in an LRC circuit a minimum.

Problem 28P (I) A transformer has 360 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?

Problem 28Q An LRC resonant circuit is often called an oscillator circuit. What is it that oscillates?

Problem 29P (I) A step-up transformer increases 25 V to 120 V. What is the current in the secondary coil as compared to the primary coil?

Problem 29Q Is the ac current in the inductor always the same as the current in the resistor of an LRC circuit? Explain.

Problem 30P (I) Neon signs require 12 kV for their operation. To operate from a 240-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 in reverse?

Problem 31P (II) A model-train transformer plugs into 120-V ac and draws 0.35 A while supplying 6.8 A to the train. (a) What voltage is present across the tracks? (b) Is the transformer step-up or step-down?

Problem 32P (II) The output voltage of a 95-W transformer is 12 V, and the input current is 25 A. (a) Is this a step-up or a step-down transformer? (b) By what factor is the voltage multiplied?

Problem 33P (II) A transformer has 330 primary turns and 1240 secondary turns. The input voltage is 120 V and the output current is 15.0 A. What are the output voltage and input current?

If 35 MW of power at 45 kV (rms) arrives at a town from a generator via 4.6-\(\Omega\) 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.

\(\text { (II) }\) For the transmission of electric power from power plant to home, as depicted in Fig. 21–25, where the electric power sent by the plant is 100 kW, about how far away could the house be from the power plant before power loss is \(50 \%\)? Assume the wires have a resistance per unit length of \(5 \times 10^{-5} \Omega / \mathrm{m}\). Equation Transcription: Text Transcription: (II) 50% 5 x 10-5 \Omega /m

\(\text { (II) }\) For the electric power transmission system shown in Fig. 21–25, what is the ratio \(N_{S} / N_{P}\) for \(\text { (a) }\) the step-up transformer, \(\text { (b) }\) the step-down transformer next to the home? Equation Transcription: Text Transcription: (II) NS/NP (a) (b)

Problem 37P (III) Suppose 2.0 MW is to arrive at a large shopping mall over two 0.100-? lines. Estimate how much power is saved if the voltage is stepped up from 120 V to 1200 V and then down again, rather than simply transmitting at 120 V. Assume the transformers are each 99% efficient.

Problem 38P (III) Design a dc transmission line that can transmit 925MW of electricity 185 km with only a 2.5% loss. The wires are to be made of aluminum and the voltage is 660 kV.

Problem 39P (I) If the current in a 160-mH coil changes steadily from 25.0 A to 10.0 A in 350 ms, what is the magnitude of the induced emf?

Problem 40P (I) What is the inductance of a coil if the coil produces an emf of 2.50 V when the current in it changes from -28.0 mA to +31.0 mA in 14.0 ms?

Problem 41P (I) Determine the inductance L of a 0.60-m-long air-filled solenoid 2.9 cm in diameter containing 8500 loops.

Problem 42P (I) How many turns of wire would be required to make a 130-mH inductor out of a 30.0-cm-long air-filled solenoid with a diameter of 5.8 cm?

Problem 43P (II) An air-filled cylindrical inductor has 2600 turns, and it is 2.5 cm in diameter and 28.2 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.

Problem 44P (II) A coil has 2.25-? resistance and 112-mH inductance. If the current is 3.00 A and is increasing at a rate of 3.80 A/s, what is the potential difference across the coil at this moment?

Problem 45P (III) A physics professor wants to demonstrate the large size of the henry unit. On the outside of a 12-cm-diameter plastic hollow tube, she wants to wind an air-filled solenoid with self-inductance of 1.0 H using copper wire with a 0.81-mm diameter. The solenoid is to be tightly wound with each turn touching its neighbor (the wire has a thin insulating layer on its surface so the neighboring turns are not in electrical contact). How long will the plastic tube need to be and how many kilometers of copper wire will be required? What will be the resistance of this solenoid?

\((I I I)\) 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. 21–63. Assume all the flux from coil 1 (the solenoid) passes through coil 2, and calculate the mutual inductance. FIGURE 21–63 Problem 46. Equation Transcription: Text Transcription: (III) l A N1 N2

Problem 47P (I) The magnetic field inside an air-filled solenoid 36 cm long and 2.0 cm in diameter is 0.72 T. Approximately how much energy is stored in this field?

Problem 48P (II) At t =0, the current through a 45.0-mH inductor is 50.0 mA and is increasing at the rate of 115 mA/s. What is the initial energy stored in the inductor, and how long does it take for the energy to increase by a factor of 5.0 from the initial value?

Problem 50P (II) It takes 2.56 ms for the current in an LR circuit to increase from zero to 0.75 its maximum value. Determine (a) the time constant of the circuit, (b) the resistance of the circuit if L =31.0 mH.

Problem 50P (II) It takes 2.56 ms for the current in an LR circuit to increase from zero to 0.75 its maximum value. Determine (a) the time constant of the circuit, (b) the resistance of the circuit if L =31.0 mH.

Problem 51P (II) How many time constants does it take for the potential difference across the resistor in an LR circuit like that in Fig. 21–37 to drop to 2.5% of its original value, after the switch is moved to the upper position, removing V0 from the circuit?

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

(III) After how many time constants does the current in Fig. 21–37 reach within (a) 10%, (b) 1.0%, and (c) 0.1% of its maximum value?

Problem 54P (I) What is the reactance of a 6.20-µF capacitor at a frequency of (a) 60.0 Hz, (b) 1.00 MHz?

Problem 55P (I) At what frequency will a 32.0-mH inductor have a reactance of 660 ??

(I) At what frequency will a \(2.40-\mu F\) capacitor have a reactance of \(6.10\ k\Omega\)?

(II) Calculate the reactance of, and rms current in, a 260-mH radio coil connected to a 240-V (rms) 10.0-kHz ac line. Ignore resistance.

Problem 58P (II) An inductance coil operates at 240 V and 60.0 Hz. It draws 12.2 A. What is the coil’s inductance?

Problem 59P (II) (a) What is the reactance of a well-insulated 0.030-µF capacitor connected to a 2.0-kV (rms) 720-Hz line? (b)What will be the peak value of the current?

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

Problem 21ED A bicycle headlight is powered by a generator that is turned by the bicycle wheel. (a) If you speed up, how does the power to the light change? (b) Does the generator resist being turned as the bicycle’s speed increases, and if so how?

Problem 62P (II) A 3.5-k? resistor and a 3.0-µF capacitor are connected in series to an ac source. Calculate the impedance of the circuit if the source frequency is (a) 60 Hz, and (b) 60,000 Hz.

Problem 63P (II) Determine the resistance of a coil if its impedance is 235 ? and its reactance is 115 ?.

Problem 64P (II) Determine the total impedance, phase angle, and rms current in an LRC circuit connected to a 10.0-kHz, 725-V (rms) source if L =28.0 mH, R =8.70 k?, and C =6250 pF.

(II) An ac voltage source is connected in series with a \(1.0-\mu F\) capacitor and a \(650-\Omega\) resistor. Using a digital ac voltmeter, the amplitude of the voltage source is measured to be 4.0 V rms, while the voltages across the resistor and across the capacitor are found to be 3.0 V rms and 2.7 V rms, respectively. Determine the frequency of the ac voltage source.Why is the voltage measured across the voltage source not equal to the sum of the voltages measured across the resistor and across the capacitor?

Problem 66P (III) (a) What is the rms current in an LR circuit when a 60.0-Hz 120-V rms ac voltage is applied, where R =2.80 K ? And L =350 mH? (b) What is the phase angle between voltage and current? (c) How much power is dissipated? (d) What are the rms voltage readings across R and L?

Problem 67P (III) (a) What is the rms current in an RC circuit if R =6.60 K?, C =1.80 µ F, and the rms applied voltage is 120 V at 60.0 Hz? (b) What is the phase angle between voltage and current? (c) What are the voltmeter readings across R and C?

(III) Suppose circuit B in Fig. 21–42a consists of a resistance \(R = 520\ \Omega\). The filter capacitor has capacitance \(C = 1.2\ \mu F\). Will this capacitor act to eliminate 60-Hz ac but pass a high-frequency signal of frequency 6.0 kHz? To check this, determine the voltage drop across R for a 130-mV signal of frequency (a) 60 Hz; (b) 6.0 kHz.

Problem 69P (I) A 3500-pF capacitor is connected in series to a 55.0-µH coil of resistance 4.00 ?. What is the resonant frequency of this circuit?

Problem 70P (II) The variable capacitor in the tuner of an AM radio has a capacitance of 2800 pF when the radio is tuned to a station at 580 kHz. (a) What must be the capacitance for a station at 1600 kHz? (b) What is the inductance (assumed constant)?

(II) An LRC circuit has L = 14.8 mH and \(R = 4.10\ \Omega\). (a) What value must C have to produce resonance at 3600 Hz? (b) What will be the maximum current at resonance if the peak external voltage is 150 V?

Problem 72P (III) A resonant circuit using a 260-nF capacitor is to resonate at 18.0 kHz. The air-core inductor is to be a solenoid with closely packed coils made from 12.0 m of insulated wire 1.1 mm in diameter. How many loops will the inductor contain?

Problem 73P (III) A 2200-pF capacitor is charged to 120 V and then quickly connected to an inductor. The frequency of oscillation is observed to be 19 kHz. Determine (a) the inductance, (b) the peak value of the current, and (c) the maximum energy stored in the magnetic field of the inductor.

Suppose you are looking at two wire loops in the plane of the page as shown in Fig. 21–64. When switch S is closed 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? (d) Suppose the right-hand loop also has a switch like the left-hand loop. The switch in the left-hand loop has been closed a long time when the switch in the right-hand loop is closed. What happens in this case? Explain each answer.

A square loop \(24.0 \mathrm{~cm}\) on a side has a resistance of \(6.10 \Omega\). It is initially in a \(0.665-T\) magnetic field, with its plane perpendicular to \(\vec{B}\) but is removed from the field in \(40.0 \mathrm{~ms}\). Calculate the electric energy dissipated in this process. Equation Transcription: Text Transcription: 24.0 ~cm} 6.10 \Omega 0.665-T \vec B 40.0~ms}

A high-intensity desk lamp is rated at 45 W but requires only 12 V. It contains a transformer that converts 120-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?

Problem 77GP A flashlight can be made that is powered by the induced current from a magnet moving through a coil of wire. The coil and magnet are inside a plastic tube that can be shaken causing the magnet to move back and forth through the coil. Assume the magnet has a maximum field strength of 0.05 T. Make reasonable assumptions and specify the size of the coil and the number of turns necessary to light a standard 1-watt, 3-V flashlight bulb.

Conceptual Example 21–9 states that an overloaded motor may burn out due to high currents. Suppose you have a blender with an internal resistance of \(3.0 \Omega\) (a) At \(120 \mathrm{~V}\),, what is the initial current through the blender? (b) The blender is rated at \(2.0 \mathrm{~A}\) for continuous use. What is the back emf of the blender? (c) At what rate is heat dissipated in the blender during normal use? (d) If the blender jams and stops turning, at what rate is heat dissipated in the motor coils? Equation Transcription: Text Transcription: 3.0 120 V 2.0 A

Problem 79GP Power is generated at 24 kV at a generating plant located 56 km from a town that requires 55 MW of power at 12 kV. Two transmission lines from the plant to the town each have a resistance of 0.10 ?/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?

Problem 80GP The primary windings of a transformer which has an 88% efficiency are connected to 110-V ac. The secondary windings are connected across a 2.4-?, 75-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.

Problem 81GP A pair of power transmission lines each have a 0.95-? resistance and carry 740 A over 9.0 km. If the rms input voltage is 42 kV, calculate (a) the voltage at the other end, (b) the power input, (c) power loss in the lines, and (d) the power output.

Problem 89GP Determine the inductance L of the primary of a transformer whose input is 220 V at 60.0 Hz if the current drawn is 6.3 A. Assume no current in the secondary.

Problem 90GP A 130-mH coil whose resistance is 15.8 ? 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?

Problem 91GP 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?

The \(Q\) factor of a resonant ac circuit (Section 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 \(Q=(1 / R) \sqrt{L / C \cdot(b)}\) At a resonant frequency \(f_{0}=1.0 \mathrm{MHz}\),, what must be the values of \(L \text { and } R\) to produce a \(Q\) factor of 650 ? Assume that \(C=0.010 \mu F\) Equation Transcription: Text Transcription: Q Q (a) Q Q=(1 / R) \sqrt L / C \cdot(b) f0=1.0 MHz L and R Q C=0.010 \mu F

The magnetic flux through a coil of wire containing two loops changes at a constant rate from to in 0.34 s. What is the emf induced in the coil?

The north pole of the magnet in Fig.2157 is being inserted into the coil. In which direction is the induced current flowing through resistor R? Explain.

The rectangular loop in Fig. 2158 is being pushed to the right, where the magnetic field points inward. In what direction is the induced current? Explain your reasoning

If the solenoid in Fig. 2159 is being pulled away from the loop shown, in what direction is the induced current in the loop? Explain.

An 18.5-cm-diameter loop of wire is initially oriented perpendicular to a 1.5-T magnetic field. The loop is rotated so that its plane is parallel to the field direction in 0.20 s. What is the average induced emf in the loop?

A fixed 10.8-cm-diameter wire coil is perpendicular to a magnetic field 0.48 T pointing up. In 0.16 s, the field is changed to 0.25 T pointing down. What is the average induced emf in the coil?

A 16-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 42 angle with the field lines. What is the angle in Eq. 211 for this situation? (c) What is the magnetic flux through the loop at this angle?

(a) If the resistance of the resistor in Fig. 2160 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? Explain your answers.

The moving rod in Fig. 2111 is 12.0 cm long and is pulled at a speed of If the magnetic field is 0.800 T, calculate (a) the emf developed, and (b) the electric field felt by electrons in the rod.

A circular loop in the plane of the paper lies in a 0.65-T magnetic field pointing into the paper. The loops diameter changes from 20.0 cm to 6.0 cm in 0.50 s. What is (a) the direction of the induced current, (b) the magnitude of the average induced emf, and (c) the average induced current if the coil resistance is ?

What is the direction of the induced current in the circular loop due to the current shown in each part of Fig. 2161? Explain why

A 600-turn solenoid, 25 cm long, has a diameter of 2.5 cm. A 14-turn coil is wound tightly around the center of the solenoid. If the current in the solenoid increases uniformly from 0 to 5.0 A in 0.60 s, what will be the induced emf in the short coil during this time?

When a car drives through the Earths magnetic field, an emf is induced in its vertical 55-cm-long radio antenna. If the Earths field points north with a dip angle of 38, what is the maximum emf induced in the antenna and which direction(s) will the car be moving to produce this maximum value? The cars speed is on a horizontal road

Part of a single rectangular loop of wire with dimensions shown in Fig. 2162 is situated inside a region of uniform magnetic field of 0.550 T. The total resistance of the loop is Calculate the force required to pull the loop from the field (to the right) at a constant velocity of Neglect gravity

In order to make the rod of Fig. 2111a move to the right at speed you need to apply an external force on the rod to the right. (a) Explain and determine the magnitude of the required force. (b) What external power is needed to move the rod? (Do not confuse this external force on the rod with the upward force on the electrons shown in Fig. 2111b.)

In Fig. 2111, the moving rod has a resistance of and moves on rails 20.0 cm apart. The stationary conductor has negligible resistance. When a force of 0.350 N is applied to the rod, it moves to the right at a constant speed of What is the magnetic field?

In Fig. 2111, the rod moves with a speed of on rails 30.0 cm apart. The rod has a resistance of The magnetic field is 0.35 T, and the resistance of the conductor is at a given instant. Calculate (a) the induced emf, (b) the current in the conductor, and (c) the external force needed to keep the rods velocity constant at that instant

A 22.0-cm-diameter coil consists of 30 turns of circular copper wire 2.6 mm in diameter. A uniform magnetic field, perpendicular to the plane of the coil, changes at a rate of Determine (a) the current in the loop, and (b) the rate at which thermal energy is produced

The magnetic field perpendicular to a single 13.2-cmdiameter circular loop of copper wire decreases uniformly from 0.670 T to zero. If the wire is 2.25 mm in diameter, how much charge moves past a point in the coil during this operation?

The generator of a car idling at 1100 rpm produces 12.7 V. What will the output be at a rotation speed of 2500 rpm, assuming nothing else changes?

A 550-loop circular armature coil with a diameter of 8.0 cm rotates at 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?

A generator rotates at 85 Hz in a magnetic field of 0.030 T. It has 950 turns and produces an rms voltage of 150 V and an rms current of 70.0 A. (a) What is the peak current produced? (b) What is the area of each turn of the coil?

A simple generator has a square armature 6.0 cm on a side. The armature has 85 turns of 0.59-mm-diameter copper wire and rotates in a 0.65-T magnetic field. The generator is used to power a lightbulb rated at 12.0 V and 25.0 W. At what rate should the generator rotate to provide 12.0 V to the bulb? Consider the resistance of the wire on the armature.

A motor has an armature resistance of If it draws 8.20 A when running at full speed and connected to a 120-V line, how large is the back emf?

The back emf in a motor is 72 V when operating at 1800 rpm. What would be the back emf at 2300 rpm if the magnetic field is unchanged?

What will be the current in the motor of Example 218 if the load causes it to run at half speed?

A transformer is designed to change 117 V into 13,500 V, and there are 148 turns in the primary coil. How many turns are in the secondary coil?

A transformer has 360 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?

Neon signs require 12 kV for their operation. To operate from a 240-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 in reverse?

A model-train transformer plugs into 120-V ac and draws 0.35 A while supplying 6.8 A to the train. (a) What voltage is present across the tracks? (b) Is the transformer step-up or step-down?

The output voltage of a 95-W transformer is 12 V, and the input current is 25 A. (a) Is this a step-up or a step-down transformer? (b) By what factor is the voltage multiplied?

A transformer has 330 primary turns and 1240 secondary turns. The input voltage is 120 V and the output current is 15.0 A. What are the output voltage and input current?

(II) A transformer has 330 primary turns and 1240 secondary turns. The input voltage is 120 V and the output current is 15.0 A. What are the output voltage and input current?

For the transmission of electric power from power plant to home, as depicted in Fig. 2125, where the electric power sent by the plant is 100 kW, about how far away could the house be from the power plant before power loss is 50%? Assume the wires have a resistance per unit length of

For the transmission of electric power from power plant to home, as depicted in Fig. 2125, where the electric power sent by the plant is 100 kW, about how far away could the house be from the power plant before power loss is 50%? Assume the wires have a resistance per unit length of

For the electric power transmission system shown in Fig. 2125, what is the ratio for (a) the step-up transformer, (b) the step-down transformer next to the home?

Suppose 2.0 MW is to arrive at a large shopping mall over two lines. Estimate how much power is saved if the voltage is stepped up from 120 V to 1200 V and then down again, rather than simply transmitting at 120 V. Assume the transformers are each 99% efficient.

Design a dc transmission line that can transmit 925 MW of electricity 185 km with only a 2.5% loss. The wires are to be made of aluminum and the voltage is 660 kV.

If the current in a 160-mH coil changes steadily from 25.0 A to 10.0 A in 350 ms, what is the magnitude of the induced emf?

(I) What is the inductance of a coil if the coil produces an emf of 2.50 V when the current in it changes from -28 mA to +31.0 mA in 14.0 ms?

Determine the inductance L of a 0.60-m-long air-filled solenoid 2.9 cm in diameter containing 8500 loops.

How many turns of wire would be required to make a 130-mH inductor out of a 30.0-cm-long air-filled solenoid with a diameter of 5.8 cm?

An air-filled cylindrical inductor has 2600 turns, and it is 2.5 cm in diameter and 28.2 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.

(II) A coil has \(2.25-\Omega\) resistance and 112-mH inductance. If the current is 3.00 A and is increasing at a rate of 3.80 A/s, what is the potential difference across the coil at this moment?

A physics professor wants to demonstrate the large size of the henry unit. On the outside of a 12-cm-diameter plastic hollow tube, she wants to wind an air-filled solenoid with self-inductance of 1.0 H using copper wire with a 0.81-mm diameter. The solenoid is to be tightly wound with each turn touching its neighbor (the wire has a thin insulating layer on its surface so the neighboring turns are not in electrical contact). How long will the plastic tube need to be and how many kilometers of copper wire will be required? What will be the resistance of this solenoid?

A long thin solenoid of length and cross-sectional area A contains closely packed turns of wire. Wrapped tightly around it is an insulated coil of turns, Fig. 2163. Assume all the flux from coil 1 (the solenoid) passes through coil 2, and calculate the mutual inductance.

The magnetic field inside an air-filled solenoid 36 cm long and 2.0 cm in diameter is 0.72 T. Approximately how much energy is stored in this field?

At the current through a 45.0-mH inductor is 50.0 mA and is increasing at the rate of What is the initial energy stored in the inductor, and how long does it take for the energy to increase by a factor of 5.0 from the initial value?

Assuming the Earths magnetic field averages about near Earths surface, estimate the total energy stored in this field in the first 10 km above Earths surface.

It takes 2.56 ms for the current in an LR circuit to increase from zero to 0.75 its maximum value. Determine (a) the time constant of the circuit, (b) the resistance of the circuit if L = 31.0 mH.

How many time constants does it take for the potential difference across the resistor in an LR circuit like that in Fig. 2137 to drop to 2.5% of its original value, after the switch is moved to the upper position, removing from the circuit?

Determine at (when the battery is connected) for the LR circuit of Fig. 2137 and show that if I continued to increase at this rate, it would reach its maximum value in one time constant

After how many time constants does the current in Fig. 2137 reach within (a) 10%, (b) 1.0%, and (c) 0.1% of its maximum value?

What is the reactance of a capacitor at a frequency of (a) 60.0 Hz, (b) 1.00 MHz?

At what frequency will a 32.0-mH inductor have a reactance of 660 ?

At what frequency will a capacitor have a reactance of 6.10 k?

Calculate the reactance of, and rms current in, a 260-mH radio coil connected to a 240-V (rms) 10.0-kHz ac line. Ignore resistance.

An inductance coil operates at 240 V and 60.0 Hz. It draws 12.2 A. What is the coils inductance?

What is the reactance of a well-insulated capacitor connected to a 2.0-kV (rms) 720-Hz line? (b) What will be the peak value of the current?

For a 120-V rms 60-Hz voltage, an rms current of 70 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?

A resistor is in series with a 55-mH inductor and an ac source. Calculate the impedance of the circuit if the source frequency is (a) 50 Hz, and 3.0 * 104 Hz

A resistor and a capacitor are connected in series to an ac source. Calculate the impedance of the circuit if the source frequency is (a) 60 Hz, and (b) 60,000 Hz

Determine the resistance of a coil if its impedance is 225 and its reactance is 115 .

Determine the total impedance, phase angle, and rms current in an LRC circuit connected to a 10.0-kHz, 725-V (rms) source if and C = 6250 pF

An ac voltage source is connected in series with a capacitor and a resistor. Using a digital ac voltmeter, the amplitude of the voltage source is measured to be 4.0 V rms, while the voltages across the resistor and across the capacitor are found to be 3.0 V rms and 2.7 V rms, respectively. Determine the frequency of the ac voltage source. Why is the voltage measured across the voltage source not equal to the sum of the voltages measured across the resistor and across the capacitor?

(a) What is the rms current in an LR circuit when a 60.0-Hz 120-V rms ac voltage is applied, where and (b) What is the phase angle between voltage and current? (c) How much power is dissipated? (d) What are the rms voltage readings across R and L?

(a) What is the rms current in an RC circuit if and the rms applied voltage is 120 V at 60.0 Hz? (b) What is the phase angle between voltage and current? (c) What are the voltmeter readings across R and C?

Suppose circuit B in Fig. 2142a consists of a resistance The filter capacitor has capacitance Will this capacitor act to eliminate 60-Hz ac but pass a high-frequency signal of frequency 6.0 kHz? To check this, determine the voltage drop across R for a 130-mV signal of frequency (a) 60 Hz; (b) 6.0 kHz.

A 3500-pF capacitor is connected in series to a coil of resistance What is the resonant frequency of this circuit?

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

An LRC circuit has and (a) What value must C have to produce resonance at 3600 Hz? (b) What will be the maximum current at resonance if the peak external voltage is 150 V?

A resonant circuit using a 260-nF capacitor is to resonate at 18.0 kHz. The air-core inductor is to be a solenoid with closely packed coils made from 12.0 m of insulated wire 1.1 mm in diameter. How many loops will the inductor contain?

A 2200-pF capacitor is charged to 120 V and then quickly connected to an inductor. The frequency of oscillation is observed to be 19 kHz. Determine (a) the inductance, (b) the peak value of the current, and (c) the maximum energy stored in the magnetic field of the inductor.

Suppose you are looking at two wire loops in the plane of the page as shown in Fig. 2164. When switch S is closed 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? (d) Suppose the right-hand loop also has a switch like the left-hand loop. The switch in the left-hand loop has been closed a long time when the switch in the right-hand loop is closed. What happens in this case? Explain each answer.

A square loop 24.0 cm on a side has a resistance of It is initially in a 0.665-T magnetic field, with its plane perpendicular to but is removed from the field in 40.0 ms. Calculate the electric energy dissipated in this process

A high-intensity desk lamp is rated at 45 W but requires only 12 V. It contains a transformer that converts 120-V household voltage. (a) Is the transformer step-up or stepdown? (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?

A flashlight can be made that is powered by the induced current from a magnet moving through a coil of wire. The coil and magnet are inside a plastic tube that can be shaken causing the magnet to move back and forth through the coil. Assume the magnet has a maximum field strength of 0.05 T. Make reasonable assumptions and specify the size of the coil and the number of turns necessary to light a standard 1-watt, 3-V flashlight bulb

Conceptual Example 219 states that an overloaded motor may burn out due to high currents. Suppose you have a blender with an internal resistance of (a) At 120 V, what is the initial current through the blender? (b) The blender is rated at 2.0 A for continuous use. What is the back emf of the blender? (c) At what rate is heat dissipated in the blender during normal use? (d) If the blender jams and stops turning, at what rate is heat dissipated in the motor coils?

Power is generated at 24 kV at a generating plant located 56 km from a town that requires 55 MW of power at 12 kV. Two transmission lines from the plant to the town each have a resistance of 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?

The primary windings of a transformer which has an 88% efficiency are connected to 110-V ac. The secondary windings are connected across a 75-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.

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

Two resistanceless rails rest 32 cm apart on a 6.0 ramp. They are joined at the bottom by a resistor. At the top a copper bar of mass 0.040 kg (ignore its resistance) is laid across the rails. Assuming a vertical 0.45-T magnetic field, what is the terminal (steady) velocity of the bar as it slides frictionlessly down the rails?

. Show that the power loss in transmission lines, is given by where is the power transmitted to the user, V is the delivered voltage, and is the resistance of the power lines.

A coil with 190 turns, a radius of 5.0 cm, and a resistance of surrounds a solenoid with and a radius of 4.5 cm (Fig. 2165). The current in the solenoid changes at a constant rate from 0 to 2.0 A in 0.10 s. Calculate the magnitude and direction of the induced current in the outer coil.

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 mA in the first \(120\ \mu s\). The device has resistance \(120\ \Omega\) and is designed to operate at 55 mA. How would you protect this device?

A 35-turn 12.5-cm-diameter coil is placed between the pole pieces of an electromagnet. When the electromagnet is turned on, the flux through the coil changes, inducing an emf. At what rate (in ) must the magnetic field change if the emf is to be 120 V?

Calculate the peak output voltage of a simple generator whose square armature windings are 6.60 cm on a side; the armature contains 125 loops and rotates in a field of 0.200 T at a rate of 120 rev/s.

Typical large values for electric and magnetic fields attained in laboratories are about and 2.0 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-T magnetic field?

Determine the inductance L of the primary of a transformer whose input is 220 V at 60.0 Hz if the current drawn is 6.3 A. Assume no current in the secondary

A 130-mH coil whose resistance is 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?

. 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?

The Q factor of a resonant ac circuit (Section 2115) 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 (b) At a resonant frequency what must be the values of L and R to produce a Q factor of 650? Assume that C = 0.010 mF.