# Physics: Principles with Applications

## Educators

### Problem 1

(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?

Jayashree B.

### Problem 2

(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 $R$? Explain.

Ceren U.
Texas Tech University

### Problem 3

(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.

Jayashree B.

### Problem 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.

Ceren U.
Texas Tech University

### Problem 5

(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?

Jayashree B.

### Problem 6

(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?

Ceren U.
Texas Tech University

### Problem 7

(II) 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$^\circ$ angle with the field lines.What is the angle $\theta$ in Eq. 21-1 for this situation? ($c$) What is the magnetic flux through the loop at this angle?

Jayashree B.

### Problem 8

(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.

Ceren U.
Texas Tech University

### Problem 9

(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.

Jayashree B.

### Problem 10

(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 $\Omega$?

Ceren U.
Texas Tech University

### Problem 11

(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.

Jayashree B.

### Problem 12

(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?

Ceren U.
Texas Tech University

### Problem 13

(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 $(5.0 \times 10^{-5})$ points north with a dip angle of 38$^\circ$, 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 30.0 m/s on a horizontal road.

Jayashree B.

### Problem 14

(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.

Ceren U.
Texas Tech University

### Problem 15

(II) In order to make the rod of Fig. 21-11a move to the right at speed $\upsilon$ 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.)

Jayashree B.

### Problem 16

(II) In Fig. 21-11, the moving rod has a resistance of 0.25 $\Omega$ and moves on rails 20.0 cm apart. The stationary U-shaped 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 1.50 m/s What is the magnetic field?

Ceren U.
Texas Tech University

### Problem 17

(III) In Fig. 21-11, the rod moves with a speed of 1.6 m/s on rails 30.0 cm apart. The rod has a resistance of 2.5 $\Omega$. The magnetic field is 0.35 T, and the resistance of the U-shaped conductor is 21.0 $\Omega$ at a given instant. Calculate (a) the induced emf, (b) the current in the conductor, and (c) the external force needed to keep the rod's velocity constant at that instant.

Jayashree B.

### Problem 18

(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 $8.65 \times 10^{-3}$ T/s.
Determine ($a$) the current in the loop, and ($b$) the rate at which thermal energy is produced.

Ceren U.
Texas Tech University

### Problem 19

(III) The magnetic field perpendicular to a single 13.2-cm diameter 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 20

(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?

Ceren U.
Texas Tech University

### Problem 21

(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?

Jayashree B.

### Problem 22

(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?

Ceren U.
Texas Tech University

### Problem 23

(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.

Jayashree B.

### Problem 24

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

Ceren U.
Texas Tech University

### Problem 25

(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?

Jayashree B.

### Problem 26

(II) What will be the current in the motor of Example 21-8 if the load causes it to run at half speed?

Ceren U.
Texas Tech University

### Problem 27

(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?

Jayashree B.

### Problem 28

(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?

Ceren U.
Texas Tech University

### Problem 29

(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?

Jayashree B.

### Problem 30

(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?

Ceren U.
Texas Tech University

### Problem 31

(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?

Jayashree B.

### Problem 32

(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?

Ceren U.
Texas Tech University

### Problem 33

(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?

Jayashree B.

### Problem 34

(II) 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.

Ceren U.
Texas Tech University

### Problem 35

(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${-5}$ $\Omega$/m.

Jayashree B.

### Problem 36

(II) For the electric power transmission system shown in Fig. 21-25, what is the ratio $N_S/N_P$ for ($a$) the step-up transformer, ($b$) the step-down transformer next to the home?

Ceren U.
Texas Tech University

### Problem 37

(III) Suppose 2.0 MW is to arrive at a large shopping mall over two 0.100-$\Omega$ 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.

Check back soon!

### Problem 38

(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.

Ceren U.
Texas Tech University

### Problem 39

(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?

Jayashree B.

### Problem 40

(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?

Ceren U.
Texas Tech University

### Problem 41

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

Jayashree B.

### Problem 42

(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?

Ceren U.
Texas Tech University

### Problem 43

(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.

Jayashree B.

### Problem 44

(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?

Ceren U.
Texas Tech University

### Problem 45

(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?

Check back soon!

### Problem 46

(III) A long thin solenoid of length $\ell$ 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.

Ceren U.
Texas Tech University

### Problem 47

(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?

Jayashree B.

### Problem 48

(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?

Ceren U.
Texas Tech University

### Problem 49

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

Jayashree B.

### Problem 50

(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.

Ceren U.
Texas Tech University

### Problem 51

(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 $V_0$ from the circuit?

Jayashree B.

### Problem 52

(III) Determine $\Delta I/ \Delta t$ at $t = 0$ (when the battery is connected) for the $LR$ circuit of Fig. 21-37 and show that if $I$ continued to increase at this rate, it would reach its maximum value in one time constant.

Ceren U.
Texas Tech University

### Problem 53

(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?

Jayashree B.

### Problem 54

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

Ceren U.
Texas Tech University

### Problem 55

(I) At what frequency will a 32.0-mH inductor have a reactance of 660 $\Omega$?

Jayashree B.

### Problem 56

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

Ceren U.
Texas Tech University

### Problem 57

(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.

Jayashree B.

### Problem 58

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

Ceren U.
Texas Tech University

### Problem 59

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

Jayashree B.

### Problem 60

(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?

Ceren U.
Texas Tech University

### Problem 61

(II) A 36-k$\Omega$ 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 (b) 3.0 $\times$ 10$^4$ Hz.

Jayashree B.

### Problem 62

(II) A 3.5-k$\Omega$ resistor and a 3.0-$\mu$F 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.

Ceren U.
Texas Tech University

### Problem 63

(II) Determine the resistance of a coil if its impedance is 235 $\Omega$ and its reactance is 115 $\Omega$.

Jayashree B.

### Problem 64

(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$\Omega$, and $C =$ 6250 pF.

Ceren U.
Texas Tech University

### Problem 65

(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?

Jayashree B.

### Problem 66

(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$\Omega$ 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 $L$?

Ceren U.
Texas Tech University

### Problem 67

(III) ($a$) What is the rms current in an RC circuit if $R =$ 6.60 k$\Omega, C =$ 1.80 $\mu$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 $C$?

Check back soon!

### Problem 68

(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.

Ceren U.
Texas Tech University

### Problem 69

(I) A 3500-pF capacitor is connected in series to a 5.0-$\mu$H coil of resistance 4.00 $\Omega$. What is the resonant frequency of this circuit?

Jayashree B.

### Problem 70

(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)?

Ceren U.
Texas Tech University

### Problem 71

(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?

Jayashree B.

### Problem 72

(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?

Ceren U.
Texas Tech University

### Problem 73

(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.

Jayashree B.

### Problem 74

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.

Ceren U.
Texas Tech University

### Problem 75

A square loop 24.0 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 $\overrightarrow{B}$, but is removed from the field in 40.0 ms. Calculate the electric energy dissipated in this process.

Jayashree B.

### Problem 76

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?

Ceren U.
Texas Tech University

### Problem 77

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.

Jayashree B.

### Problem 78

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?

Ceren U.
Texas Tech University

### Problem 79

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?

Jayashree B.

### Problem 80

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-$\Omega$, 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.

Ceren U.
Texas Tech University

### Problem 81

A pair of power transmission lines each have a 0.95-$\Omega$ 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.

Jayashree B.

### Problem 82

Two resistanceless rails rest 32 cm apart on a 6.0$^\circ$ ramp. They are joined at the bottom by a 0.60-$\Omega$ resistor. At the top a copper bar of mass 0.040 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?

Ceren U.
Texas Tech University

### Problem 83

Show that the power loss in transmission lines, $P_L,$ is given by $P_L = (P_T)_2 R_L/V^2$ where $P_T$ is the power transmitted to the user, $V$ is the delivered voltage, and $R_L$ is the resistance
of the power lines.

Jayashree B.

### Problem 84

A coil with 190 turns, a radius of 5.0 cm, and a resistance of 12$\Omega$ surrounds a solenoid with 230 turns/cm and a radius of 4.5 cm (Fig. 21-65). 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.

Ceren U.
Texas Tech University

### Problem 85

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?

Jayashree B.

### Problem 86

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 T/s) must the magnetic field change if the emf is to be 120 V?

Ceren U.
Texas Tech University

### Problem 87

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

Jayashree B.

### Problem 88

Typical large values for electric and magnetic fields attained in laboratories are about 1.0 $\times$ 10$^4$ V/m 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?

Ceren U.
Texas Tech University

### Problem 89

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.

Jayashree B.

### Problem 90

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

Ceren U.
Texas Tech University

### Problem 91

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?

Jayashree B.

### Problem 92

The $\textbf{Q factor}$ of a resonant ac circuit (Section 21-15) can be defined as the ratio of the voltage across the capacitor (or inductor) to the voltage across the resistor, at resonance. The larger the $Q$ factor, the sharper the resonance curve will be and the sharper the tuning. ($a$) Show that the $Q$ factor is given by the equation $Q = (1/R) \sqrt{L/C}$. ($b$) At a resonant frequency $f_0 =$ 1.0 MHz, what must be the values of L and R to produce a Q factor of 650? Assume that $C =$ 0.010 $\mu$F.

Ceren U.
Texas Tech University