Physics Homework Chapter 21

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1. (a) What is the resistance of a lightbulb that uses an average power of 60.0 W when connected to a 60.0-Hz power source having a maximum voltage of 128 V?
_____Ω

(b) What is the resistance of a 150-W lightbulb?
_____Ω

Calculator Problem #1

(Calculate Resistance)

Pav1 =	Watts
ΔVmax =	V
Pav2	Watts
R1	Ω
R2	Ω

2. The figure below shows three lamps connected to a 120-V AC (rms) household supply voltage. Lamps 1 and 2 have 120-W bulbs; lamp 3 has a 40.0-W bulb.

(a) For each bulb, find the rms current.
Irms, lamp 1  =_____A
Irms, lamp 2  =_____A
Irms, lamp 3  =_____A

(b) For each bulb, find the resistance.
Rlamp 1  =_____Ω
Rlamp 2  =_____Ω
Rlamp 3  =_____Ω

3. What is the maximum current delivered to a circuit containing a 1.40 µF capacitor when it is connected across the following outlets?

(a) a North American outlet having ΔVrms = 120 V, f = 60.0 Hz
_____mA

(b) a European outlet having ΔVrms = 240 V and f = 50.0 Hz
_____mA





4. What maximum current is delivered by an AC source with ΔVmax = 56.4 V and f = 79.4 Hz when connected across a 3.70-µF capacitor?
_____mA

Chapter 21 Problem 4

(Calculate Current)

Vmax	V
f	Hz
C	μF
I	mA;

5. In a purely inductive AC circuit as shown in the figure, ΔVmax = 100 V.

(a) The maximum current is 3.80 A at 40.0 Hz. Calculate the inductance L.
_____mH

(b) At what angular frequency ω is the maximum current 1.90 A?
_____rad/s




6. A sinusoidal voltage Δv = (60 V) sin (190t) is applied to a series RLC circuit with L = 90 mH, C = 165 μF, and R = 46 Ω.

(a) What is the impedance of the circuit?
____Ω

(b) What is the maximum current in the circuit?
_____A





7. A resistor (R = 900 Ω), a capacitor (C = 0.25 µF), and an inductor (L = 2.5 H) are connected in series across a 240 Hz AC source for which ΔVmax = 135 V. Calculate the following.
(a) the impedance of the circuit
_____Ω

(b) the maximum current delivered by the source
_____A

(c) the phase angle between the current and voltage
_____°
(d) Is the current leading or lagging behind the voltage?
-The current leads the voltage.
-There is no phase difference between the current and voltage.  
-The current lags behind the voltage.




8. A multimeter in an RL circuit records an rms current of 0.600 A and a 65.0 Hz rms generator voltage of 105 V. A wattmeter shows that the average power delivered to the resistor is 10.0 W. Determine values for the following:

(a) the impedance in the circuit
_____ ohms

(b) the resistance, R
_____ ohms

(c) the inductance, L
_____H



9. A series RLC circuit has a resistance of 10 Ω and an impedance of 70 Ω. If the rms voltage applied to the circuit is 140 V, what average power is delivered to the circuit?
_____W




10.The primary coil of a transformer has N1 = 2.00  102 turns, and its secondary coil has N2 = 4.00  102 turns. If the input voltage across the primary coil is Δv = (180 V) sin ωt, what rms voltage is developed across the secondary coil?
_____V




11. A transformer on a pole near a factory steps the voltage down from 3600 V (rms) to 120 V (rms). The transformer is to deliver 1900 kW to the factory at 90% efficiency. Find values for the following.

(a) the power delivered to the primary
_____kW

(b) the current in the primary
_____A

(c) the current in the secondary
_____A




12. A spaceship is approaching a space station at a speed of 3.45  105 m/s. The space station has a beacon that emits green light with a frequency of 5.97  1014 Hz.

(a) What is the frequency of the beacon observed on the spaceship? (Carry five digits in these calculations. Use c = 2.9979  108 m/s for the speed of light. State your answer to five significant figures.)
_____Hz

(b) What is the change in frequency?
_____Hz

Chapter 21 Problem 12

(Calculate Observed Frequency)

v	m/s
fs	Hz
c	m/s
fo	Hz
Δf	Hz

Physics Homework Chapter 20

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1.A uniform magnetic field of magnitude 1.00 T is directed perpendicular to the plane of a rectangular loop having dimensions 8.5 cm by 14 cm. Find the magnetic flux through the loop.
_____mWb


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2. Find the flux of Earth's magnetic field of magnitude 5.00  10-5 T through a square loop of area 20.0 cm2 for the following:

(a) when the field is perpendicular to the plane of the loop
_____T · m2

(b) when the field makes a 60.0° angle with the normal to the plane of the loop
_____T · m2

(c) when the field makes a 90.0° angle with the normal to the plane
_____T · m2


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3. A long, straight wire carrying a current of 1.00 A is placed along the axis of a cylinder of radius 0.500 m and a length of 5.00 m. Determine the total magnetic flux through the cylinder.
____T·m2


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4. A 410 turn solenoid of length 34.0 cm and radius 3.20 cm carries a current of 5.10 A. Find the following.

(a) the magnetic field strength inside the coil at its midpoint
_____mT

(b) the magnetic flux through a circular cross-sectional area of the solenoid at its midpoint
_____T · m2


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5.A cube of edge length  = 8.0 cm is positioned as shown in the figure below. There is a uniform magnetic field throughout the region with components Bx = +3.0 T, By = +2.0 T, and Bz = +5.0 T.

(a) Calculate the flux through the shaded face of the cube.
_____T · m2

(b) What is the net flux emerging from the volume enclosed by the cube (i.e., the net flux through all six faces)?
_____T · m2


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6.Three loops of wire move near a long straight wire carrying a current as in the following figure.

(a) What is the direction of the induced current, if any, in loop A?
clockwise
counterclockwise  
No current is induced.


(b) What is the direction of the induced current, if any, in loop B?
clockwise
counterclockwise  
No current is induced.


(c) What is the direction of the induced current, if any, in loop C?
clockwise
counterclockwise  
No current is induced.


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7.A circular loop of wire of radius 12.4 cm is placed in a magnetic field directed perpendicular to the plane of the loop, as shown in the figure below. If the field decreases at the rate of 0.530 T/s in some time interval, what is the magnitude of the emf induced in the loop during this interval?
_____mV


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8.A square, single-turn wire loop  = 1.00 cm on a side is placed inside a solenoid that has a circular cross section of radius r = 3.00 cm, as shown in the end view of the figure below. The solenoid is 21.0 cm long and wound with 90 turns of wire.

(a) If the current in the solenoid is 4.00 A, what is the magnetic flux through the square loop?
_____T · m2

(b) If the current in the solenoid is reduced to zero in 4.00 s, what is the magnitude of the average induced emf in the square loop?
_____V


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9. Consider the arrangement shown in the figure below. Assume R = 6.00 Ω and  = 1.20 m, and a uniform 2.90-T magnetic field is directed into the page. At what speed should the bar be moved to produce a current of 0.500 A in the resistor?
_____m/s


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10. A square coil of wire of side 2.00 cm is placed in a uniform magnetic field of magnitude 1.50 T directed into the page as in the figure shown below. The coil has 32.0 turns and a resistance of 0.780 Ω. If the coil is rotated through an angle of 90.0° about the horizontal axis shown in 0.335 s, find the following.

(a) the magnitude of the average emf induced in the coil during this rotation
_____mV

(b) the average current induced in the coil during this rotation
_____mA


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11.A motor has coils with a resistance of 26  and operates from a voltage of 236 V. When the motor is operating at its maximum speed, the back emf is 150 V.
(a) Find the current in the coils when the motor is first turned on.
_____A

(b) Find the current in the coils when the motor has reached maximum speed.
_____A

(c) If the current in the motor were 5.0 A at some instant, what is the back emf at that time?
_____V


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12. A technician wraps wire around a tube of length 38 cm having a diameter of 7.8 cm. When the windings are evenly spread over the full length of the tube, the result is a solenoid containing 560 turns of wire.
(a) Find the self-inductance of this solenoid.
_____mH

(b) If the current in this solenoid increases at the rate of 3 A/s, what is the self-induced emf in the solenoid?
_____mV


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13. An electromagnet can be modeled as an inductor in series with a resistor. Consider a large electromagnet of inductance L = 12.5 H and resistance R = 6.00 Ω connected to a 18.0-V battery and switch as in the figure shown below. After the switch is closed, find the following.

(a) the maximum current carried by the electromagnet
_____A

(b) the time constant of the circuit
_____s

(c) the time it takes the current to reach 95.0% of its maximum value
_____s


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14. An RL circuit with L = 4.00 H and an RC circuit with C = 9.00 µF have the same time constant.

(a) If the two circuits have the same resistance, R, what is the value of R?
_____

(b) What is this common time constant?
_____ms


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15. A battery is connected in series with a 0.31-Ω resistor and an inductor, as shown in the figure below. The switch is closed at t = 0. The time constant of the circuit is 0.10 s, and the maximum current in the circuit is 7.9 A.

(a) Find the emf of the battery.
_____V

(b) Find the inductance of the circuit.
_____mH

(c) Find the current in the circuit after one time constant has elapsed.
_____A

(d) Find the voltage across the resistor after one time constant has elapsed.
_____V

(e) Find the voltage across the inductor after one time constant has elapsed.
_____V


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16.The Sun delivers an average power of 583.9 W/m2 to the top of Mars's atmosphere. Find the magnitudes of      Bmax and Emax for the electromagnetic waves at the top of the atmosphere.
Bmax =  
_____T

Emax =  
_____V/m


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Physics Homework Chapter 19

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CALCULATOR 19-1


1. Consider the following figure.

(a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields in the figure, as shown.
Field      Force Direction
(a)   _____
(b)   _____
(c)   _____
(d)   _____
(e)   _____
(f)   _____


(b) Repeat part (a), assuming the moving particle is an electron.
Field      Force Direction
(a)   _____
(b)   _____
(c)   _____
(d)   _____
(e)   _____
(f)    _____


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2. Find the direction of the magnetic field acting on the positively charged particle moving in the various situations shown in the figure below if the direction of the magnetic force acting on it is as indicated.
Figure (a)    

Figure (b)    

Figure (c)


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3. An electron is accelerated through 2600 V from rest and then enters a region where there is a uniform 1.90 T magnetic field. What are the maximum and minimum magnitudes of the magnetic force acting on this electron?

(a) maximum
_____N

(b) minimum.
_____N


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4. A proton moving at 5.60 X 10^6 m/s through a magnetic field of magnitude 1.80 T experiences a magnetic force of magnitude 7.40 X 10^-13 N. What is the angle between the proton's velocity and the field? (Enter both possible answers from smallest to largest. Enter only positive values between 0 and 360.)
smaller value    
_____°
larger value    
_____°

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5. A current I = 17 A is directed along the positive x-axis and perpendicular to a magnetic field. A magnetic force per unit length of 0.16 N/m acts on the conductor in the negative y-direction. Calculate the magnitude and direction of the magnetic field in the region through which the current passes.
_____T


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6. A wire carries a current of 5.0 A in a direction that makes an angle of 35.0° with the direction of a magnetic field of strength 0.300 T. Find the magnetic force on a 7.00 m length of the wire.
_____N


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7. A wire is formed into a circle having a diameter of 10.7 cm and is placed in a uniform magnetic field of 2.78 mT. The wire carries a current of 5.00 A. Find the maximum torque on the wire.
_____µN · m


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8. A current of 29.0 mA is maintained in a single circular loop with a circumference of 2.40 m. A magnetic field of 0.450 T is directed parallel to the plane of the loop. What is the magnitude of the torque exerted by the magnetic field on the loop?
_____ N · m

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9. A rectangular loop consists of 102 closely wrapped turns and has dimensions 0.400 m by 0.300 m. The loop is hinged along the y-axis, and the plane of the coil makes an angle of 30.0° with the x-axis (see figure below).

What is the magnitude of the torque exerted on the loop by a uniform magnetic field of 0.760 T directed along the x-axis when the current in the windings has a value of 1.20 A in the direction shown?
_____N · m


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10. An electron moves in a circular path perpendicular to a magnetic field of magnitude 0.240 T. If the kinetic energy of the electron is 3.20 X 10^-19 J, find the speed of the electron and the radius of the circular path.

(a) the speed of the electron
_____m/s

(b) the radius of the circular path
_____µm


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11. A proton travels with a speed of 4.90 X 10^6 m/s at an angle of 62° with the direction of a magnetic field of magnitude 0.150 T in the positive x-direction.

(a) What is the magnitude of the magnetic force on the proton?
_____N

(b) What is the proton's acceleration?
_____m/s^2


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12. In each of parts (a), (b), and (c) of the figure below, find the direction of the current in the wire that would produce a magnetic field directed as shown.
part (a)    
part (b)    
part (c)


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13. Two long, parallel wires separated by 5.00 cm carry currents in opposite directions. The current in one wire is 1.30 A, and the current in the other is 3.40 A.
(a) Find the magnitude of the force per unit length that one wire exerts on the other.
_____N/m

(b) Is the force attractive or repulsive?
__attractive
__repulsive  


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14. A long solenoid that has 1,190 turns uniformly distributed over a length of 0.395 m produces a magnetic field of magnitude 1.00 X 10^-4 T at its center. What current is required in the windings for that to occur?
_____mA


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15. A certain superconducting magnet in the form of a solenoid of length 0.40 m can generate a magnetic field of 12.0 T in its core when its coils carry a current of 120 A. The windings, made of a niobium-titanium alloy, must be cooled to 4.2 K. Find the number of turns in the solenoid.
_____turns


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Physics Homework Chapter 18

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1. A battery having an emf of 11.00 V delivers 112 mA when connected to a 67.0  load. Determine the internal resistance of the battery.
_____Ω



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2. What is the equivalent resistance of the combination of identical resistors between points a and b in the figure below?
____R

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3. Three 10.0 Ω resistors are connected in series with a 9.0 V battery. Find the following.

(a) the equivalent resistance of the circuit
_____Ω

(b) the current in each resistor
_____A

(c) Repeat for the case in which all three resistors are connected in parallel across the battery.
equivalent resistance
_____Ω

current in each resistor
_____A



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4. Consider the circuit shown in the figure below. (R = 19.0 Ω.)

(a) Find the current in the R = 19.0 Ω resistor.
_____A

(b) Find the potential difference between points a and b.
_____V

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5. (a) Find the current in a 6.00 Ω resistor connected to a battery that has an internal resistance of 0.40 Ω if the voltage across the battery (the terminal voltage) is 21.00 V.
_____A

(b) What is the emf of the battery?
_____V



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6. The figure below shows a circuit diagram. (R₁ = 1460 , R₂

 = 570 , ΔV = 30.0 V)
(a) Determine the current. 
_____mA

(b) Determine the potential of wire A relative to ground. 
_____V

(c) Determine the voltage drop across the 1460  resistor.
_____V

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7. Consider the combination of resistors shown in the figure below.

(a) Find the equivalent resistance between point a and b.
_____Ω

(b) If a voltage of 41.9 V is applied between points a and b, find the current in each resistor.
12 Ω        _____A
6 Ω          _____A
5 Ω          _____A
4 Ω          _____A
8 Ω          _____A

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8. The ammeter shown in the figure below reads 1.50 A. Find I₁
, I₂, and ε. (Assume R = 7.50 Ω.)I₁  =     _____A
I
2  =     _____Aε=        _____V

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9. In the circuit of the figure below, the current I₁
 is 3.4 A and the values of ε and R are unknown. What are the currents I₂ and I₃?I₂
 =   _____AI₃
 =   _____A

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10. An uncharged capacitor and a resistor are connected in series to a source of emf. If ε = 7.00 V, C = 25.0 µF, and R = 100 Ω, find the following:
(a) the time constant of the circuit
_____s

(b) the maximum charge on the capacitor
_____µC

(c) the charge on the capacitor after one time constant
_____µC


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11. Consider a series RC circuit for which R = 4.0 MΩ, C = 8.0 µF, and ε = 25 V. Find the charge on the capacitor 10 s after the switch is closed.
_____µC

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12. A charged capacitor is connected to a resistor and a switch as in the figure below. The circuit has a time constant of 1.00 s. Soon after the switch is closed, the charge on the capacitor is 80.0% of its initial charge.

(a) Find the time interval required for the capacitor to reach this charge.
_____s

(b) If R = 220 kΩ, what is the value of C?
C =   _____µF

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13. What minimum number of 100 W lightbulbs must be connected in parallel to a single 180 V household circuit to trip a 40.0 A circuit breaker? 
_____lightbulbs


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