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REVIEW CIRCUITS
• length, L
• cross-sectional area, A
• material/resistivity, ρ
 Resistance of a wire when the temperature is kept constant is:
 OHM’S LAW: Current through resistor is proportional to potential difference
across the resistor and inversely proportional to resistance
of that resistor.
( )
( )
( )
 Electric power, P, is the rate at which energy is supplied to or used by a device in which electric energy is
converted into another form such as mechanical energy, thermal energy, or light.
Power dissipated in a resistor:
P=IV
P=
Power of the source = ε I
Electric energy is:
(
)
(
)
( )
(
)
(
)
( )
 Electromotive force, , is the voltage generated by battery (how much energy per unit charge is available for
the circuit including internal resistance)
Resistors in Series
• connected in such a way that all components have the same current through them.
Resistors in Parallel
• Electric devices connected in parallel are connected to the same two points of an electric circuit, so all
components have the same potential difference across them.
• The current flowing into the point of splitting is equal to the sum of the currents flowing out at that point:
The greater resistance, the smaller current.
A device that transforms mechanical energy into electrical energy is called a generator.
A device that transforms electrical energy into mechanical energy is called an electric motor.
A transformer is a device that transforms/change voltage.
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REVIEW PROBLEMS:
1. A circuit is wired with a power supply, a resistor and an ammeter (for measuring current). The ammeter reads a
current of 24 mA (milliAmps). Determine the new current if the voltage of the power supply was ...
a. increased by a factor of 3 and the resistance was held constant.
b. held constant and the resistance was increased by a factor of 2.
c. increased by a factor of 3 and the resistance was decreased by a factor of 2.
d. decreased by a factor of 2 and the resistance was increased by a factor of 2.
2. A 541-Watt toaster is connected to a 120-V household outlet. What is the resistance (in ohms) of the toaster?
3. Consider two appliances that operate at the same voltage. Appliance A has a higher power rating then
appliance B.
a. How does the resistance on A compare with that of B. Is it (1) larger, (2) smaller, or (3) the same?
4. A computer system includes a color monitor with a power requirement of 200 W, whereas a countertop
broiler/toaster oven is rated at 1500 W. What is the resistance of each if both are designed to run at 120 V?
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5. Calculate the resistance of an aluminum (ρ = 2.8x10 Ωm) wire that is 2.0 m long and of circular cross section
with a diameter of 1.5 mm.
6. The resistance of a certain wire is 10 ohms. What would the resistance of the same wire be if it were twice as long? If it were
twice as thick?
7. A refrigerator operates on average for 10.0 h a day. If the power rating of the refrigerator is 700 W, how much electrical
energy does the refrigerator use in 1 day?
8. An electrical appliance is rated as 2.5 kW, 240 V.
(a) Determine the current needed for it to operate.
(b) Calculate the energy it would consume in 2.0 hours.
9. What is the equivalent resistance for the resistors in the figure ?
10. Find equivalent resistance for the circuit shown.
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11. A 100 Ω, 120 Ω, and 150 Ω resistor are connected to a 9-V battery in the circuit shown. Which of the three
resistors dissipates the most power?
12. What is the current in the battery of the circuit shown below?
13.
a. Simplify the above circuit so that it consists of one equivalent resistor and the
battery.
b. What is the total current through this circuit?
c. Find the current through each resistor. Find the voltage across each resistor.
d. Find the power of the battery. Find the power dissipated in each resistor.
1. a. Inew = 72 mA
b. Inew = 12 mA c. Inew = 144 mA d. Inew = 6 mA
2. 26.6 Ω
3. smaller
4. 72 W, 9.60 W
5. 32 mΩ
6. 20 2.5 , because twice the diameter gives four times the cross sectional area and one-fourth the resistance
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7. E = Pt = (700 W)(36000 s ) = 25.2 x 10 J
or
E = Pt = (0.7 kW)(10.0 h) = 7 kWhours
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8. (a) I = P/V = 2500W/240V = 10.4 = 1.0 x 10 A (b) energy = Pt = VIt = (240V)(10.4A)(7200s) = 1.8 x 10 J
9. 5.2 Ω
10.
11. 100 Ω
12. Req = 5 +l5 =20 I = V/R = 0.5 A
13. only the first step :
I = V/Req = 0.5 A
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REVIEW MAGNETISM
The direction of a magnetic field line is defined as the direction in which the
north pole of a compass points when it is placed in the magnetic field.
Outside the magnet, the field lines emerge from the magnet at its north
pole and enter the magnet at its south pole.
Inside the magnet, there are no isolated poles on which field lines can start
or stop, so magnetic field lines always travel inside the magnet from the
south pole to the north pole to form closed loops.
Magnetic field is measured in Tesla
1 T(Tesla) =
1. An electric charge experiences a magnetic force when moving in a magnetic field.
Magnetic force acting on a charge q
Magnetic force on a wire carrying current I
in a magnetic Field B: F = qvB sinin a magnetic field B: F = I LB sin
 

q = charge [C]
v = velocity [m/s]
B = magnetic field [Tesla T]
 = angle between v and B
I = current [A]
L = length [m]
B = magnetic field [T]
 = angle between I and B
R-H-R 1: The direction of the magnetic force on a charge/current is given by the right-hand rule 1:
Outstretch fingers in the direction of v (or current I).
Curl fingers as if rotating vector v (I ) into vector B.
Magnetic force on a positive charge (or I) is in
the direction of the thumb.
Magnetic force on a negative charge points in opposite direction.
2. A moving charge produces a magnetic field.
R-H-R 2: The direction of the magnetic field produced by electric current is given by the right-hand rule 2:
If a wire is grasped in the right hand with the thumb in the direction of current flow, the fingers will curl in the
direction of the magnetic field.
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Magnetic field B around a wire with current I
B=
= the permeability of free space 4×10 T·m/A
I = current [A]
r = distance from the center of the conductor
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Two parallel current carrying wires
attract each other
Two antiparallel current carrying wires
repel each other
Magnetic field of a solenoid with steady current is:
1. uniform from south to north pole inside the solenoid.
(constant in magnitude and direction )
2. not uniform from north to south pole outside of the solenoid.
REVIEW PROBLEMS:
1. The magnetic field of a bar magnet is shown in the figure.
Is the magnet’s north pole at A or B?
2. The direction of the force on a current-carrying wire in an external magnetic field is
a. perpendicular to the current only.
b. perpendicular to the magnetic field only.
c. perpendicular to the current and to the magnetic field.
d. parallel to the current and to the magnetic field.
3. If a proton is released at the equator and falls toward Earth under the influence of gravity, the magnetic force on
the proton will be toward the
a. north.
c. east.
b. south.
d. west.
4. What is the path of an electron moving perpendicular to a uniform magnetic field?
a. a straight line
c. an ellipse
b. a circle
d. a parabola
5. What is the path of an electron moving parallel to a uniform magnetic field?
a. straight line
c. ellipse
b. circle
d. parabola
6. Find the direction of the force on an proton moving
through the magnetic field shown.
7. Find the direction of the force on an electron moving through the magnetic field.
8. A negative charge is moving through a magnetic field. The direction of motion and the direction
of the force acting on it at one moment are shown. Find the direction of the magnetic field.
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9. The direction of the force on a current-carrying wire in an external magnetic field is
a. perpendicular to the current only.
b. perpendicular to the magnetic field only.
c. perpendicular to the current and to the magnetic field.
d. parallel to the current and to the magnetic field.
10. If a proton is released at the equator and falls toward Earth under the influence of gravity, the magnetic force
on the proton will be toward the
a. north.
c. east.
b. south.
d. west.
11. What is the path of an electron moving perpendicular to a uniform magnetic field?
a. a straight line
c. an ellipse
b. a circle
d. a parabola
12. What is the path of an electron moving parallel to a uniform magnetic field?
a. straight line
c. ellipse
b. circle
d. parabola
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13. An electron that moves with a speed of 3.0 x 10 m/s perpendicular to a uniform magnetic field of 0.40 T
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experiences a force of what magnitude? (e = 1.60 x 10 C)
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14. An electron moves north at a velocity of 4.5 x 10 m/s and has a force of 7.2 x 10
magnetic field points upward, what is the magnitude of the magnetic field?
N exerted on it. If the
15. A 2.0 m wire segment carrying a current of 0.60 A oriented perpendicular to a uniform magnetic field of 0.50 T
experiences a force of what magnitude?
16. A 2.0 m wire segment carrying a current of 0.60 A oriented parallel to a uniform magnetic field of 0.50 T
experiences a force of what magnitude?
17. A current-carrying wire 0.50 m long is positioned perpendicular to a uniform magnetic field. If the current is
10.0 A and there is a resultant force of 3.0 N on the wire due to the interaction of the current and field, what is the
magnetic field strength?
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18. A current in a long, straight wire produces a magnetic field. These magnetic field lines
a. go out from the wire to infinity.
c. form circles that pass through the wire.
b. come in from infinity to the wire.
d. form circles that go around the wire.
19. Two long parallel straight wires carry equal currents in opposite directions. At a point midway between the
wires, the magnetic field they produce is:
A) zero
B) non-zero and along a line connecting the wires
C) non-zero and parallel to the wires
D) non-zero and perpendicular to the plane of the two wires
E) none of the above
20. Magnetic field lines inside the solenoid shown are:
A) clockwise circles as one looks down the axis from the top of the page
B) counterclockwise circles as one looks down the axis from the top of the page
C) toward the top of the page
D) toward the bottom of the page
E) in no direction since B = 0
21. A solenoid is in an upright position on a table. A counterclockwise current of electrons causes the solenoid to
have a(n) ____ magnetic pole at its bottom end. If a compass is placed at the top of the solenoid, the north pole of
the compass would be
a.
north; attracted c.
north; repelled
b.
south; attracted d.
south; repelled
22. A solenoid is in an upright position on a table. A clockwise current of electrons causes the solenoid to have a(n)
____ magnetic pole at its bottom end. If a compass is placed at the top of the solenoid, the north pole of the
compass would be
a.
north; attracted c.
north; repelled
b.
south; attracted d.
south; repelled
23. A long straight wire carries current as shown. Two electrons move with velocities that are parallel and
perpendicular to the current. Find the direction of the magnetic force experienced by each electron.
1. A 2. c
3. c 4. b. 5. a.
6. up, toward the top of the page
7. down, toward the bottom of the page
8. to the left
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9. c.
10. c
11. b
12. a
13. 1.9 x 10 N 14. 1.0 mT
18. d 19. D 20. C 21. d. 22. a
23. A. south
B. west
15. 0.60 N 16. 0.0 N
17. 0.60 T