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If the charges move around the circuit in the same direction at all times, the current is said to be direct current ( dc ).
If the charges move first one way and then the opposite way, the current is said to be alternating current ( ac ).
Example 1 A Pocket Calculator The current in a 3.0 V battery of a pocket calculator is 0.17 mA. In one hour of operation, (a) how much charge flows in the circuit and (b) how much energy does the battery deliver to the calculator circuit? (a) (b)
Conventional current is the hypothetical flow of positive charges that would have the same effect in the circuit as the movement of negative charges that actually does occur.
20.1.1. In which one of the following situations does a conventional electric current flow due north? a) Protons in a beam are moving due south. b) A water molecule is moving due north. c) Electrons in a beam are moving due south. d) Electrons in a wire connected to a battery are moving from south to north.
20.1.2. The battery capacity of a lithium ion battery in a digital music player is 750 mA-h. The manufacturer claims that the player can operate for eight hours if the battery is initially fully charged. Given this information, determine the number of electrons that flow through the player as you listen to your favorite songs for three hours. a) 6.2 10 18 electrons b) 1.0 10 3 electrons c) 2.4 10 9 electrons d) 6.3 10 21 electrons e) 8.1 10 28 electrons
Chapter 20: Electric Circuits Section 2: Ohm’s Law
The V is proportional to I, where V is the voltage applied across a piece of material and I is the current through the material:
SI Unit of Resistance: volt/ampere (V/A) = ohm ( Ω )
Example 2 A Flashlight The filament in a light bulb is a resistor in the form of a thin piece of wire. The wire becomes hot enough to emit light because of the current in it. The flashlight uses two 1.5-V batteries to provide a current of 0.40 A in the filament. Determine the resistance of the glowing filament.
20.2.1. In a certain circuit containing a battery and a resistor, Ohm’s law is obeyed. An instrument to measure the current in the circuit, an ammeter, is connected in between one of the terminals of the battery and one end of the resistor. The ammeter indicates that the current in the circuit is I . The battery is then removed and replaced with another battery. This time, the ammeter indicates the current is 2 I . Which one of the following statements concerning the resistor is true? a) When the second battery was placed in the circuit, the resistance increased to twice its initial value. b) When the second battery was placed in the circuit, the resistance decreased to one half its initial value. c) When the second battery was placed in the circuit, the resistance increased to four times its initial value. d) When the second battery was placed in the circuit, the resistance increased to one fourth its initial value. e) When the second battery was placed in the circuit, the resistance did not change.
20.2.2. Consider the circuit containing a battery and a resistor shown. For which one of the following combinations of current and voltage does R have the smallest value? a) V = 9 V and I = 0.002 A b) V = 12 V and I = 0.5 A c) V = 1.5 V and I = 0.075 A d) V = 6 V and I = 0.1 A e) V = 4.5 V and I = 0.009 A
20.2.3. A certain circuit contains a battery and a resistor. An instrument to measure the current in the circuit, an ammeter, is connected in between one of the terminals of the battery and one end of the resistor. The graph shows the current in the circuit as the voltage is increased. Which one of the following statements best describes the resistor in this circuit? a) The resistor does not obey Ohm’s law. b) The resistor obeys Ohm’s law for voltages between zero and twenty-five volts. c) The resistor obeys Ohm’s law for voltages between zero and thirty-five volts. d) The resistor obeys Ohm’s law for voltages between zero and forty volts. e) The resistor obeys Ohm’s law for voltages between thirty and forty volts.
Chapter 20: Electric Circuits Section 3: Resistance and Resitivity
Example 3 Longer Extension Cords The instructions for an electric lawn mower suggest that a 20-gauge extension cord can be used for distances up to 35 m, but a thicker 16-gauge cord should be used for longer distances. The cross sectional area of a 20-gauge wire is 5.2x10 -7 Ω ·m, while that of a 16-gauge wire is 13x10 -7 Ω ·m. Determine the resistance of (a) 35 m of 20-gauge copper wire and (b) 75 m of 16-gauge copper wire. (a) (b)
Temperature Effects temperature coefficient of resistivity
20.3.1. For which combination for the length L and radius R of a wire will the resistance have the smallest value? a) L = 0.50 m and R = 0.03 m b) L = 0.25 m and R = 0.08 m c) L = 0.40 m and R = 0.2 m d) L = 0.80 m and R = 0.1 m e) L = 0.10 m and R = 0.05 m
20.3.2. The ends of a wire are connected to the terminals of a battery. For which of the following changes will the resulting current in the circuit have the largest value? a) Replace the wire with one that has a larger resistivity. b) Replace the wire with one that has a larger radius. c) Replace the wire with one that has a longer length.
Chapter 20: Electric Circuits Section 4: Electric Power
When there is current in a circuit as a result of a voltage, the electric power delivered to the circuit is:
SI Unit of Power: watt (W)
Example 5 The Power and Energy Used in a Flashlight In the flashlight, the current is 0.40A and the voltage is 3.0 V. Find (a) the power delivered to the bulb and (b) the energy dissipated in the bulb in 5.5 minutes of operation. (a) (b)
20.4.1. An automatic coffee maker uses a resistive heating element to boil the 2.4 kg of water that was poured into it at 21 C. The current delivered to the coffee pot is 8.5 A when it is plugged into a 120 V electrical outlet. If the specific heat capacity of water is 4186 J/kg C , approximately how long does it take to boil all of the water? a) 5 minutes b) 8 minutes c) 10 minutes d) 13 minutes e) 15 minutes
20.4.2. The insulated wiring in a house can safely carry a maximum current of 18 A. The electrical outlets in the house provide an alternating voltage of 120 V. A space heater when plugged into the outlet operates at an average power of 1500 W. How many space heaters can safely be plugged into a single electrical outlet and turned on for an extended period of time? a) zero b) one c) two d) three e) four
20.4.3. A portable CD player was recently introduced that has a “special power saving technology.” The manufacturer claims that with only two standard AA batteries (together: 3.0 V, 20 kJ energy storage) that the player can be played for about 25 hours. What is the approximate resistance in the CD player’s electrical circuitry? a) 41 b) 0.010 c) 300 d) 1.5 e) 15
20.4.4. A wire is used as a heating element that has a resistance that is fairly independent of its temperature within its operating range. When a current I is applied to the wire, the energy delivered by the heater each minute is E. For what amount of current will the energy delivered by the heater each minute be 4 E ? a) 2 I b) 4 I c) 0.5 I d) 0.25 I e) 8 I
Chapter 20: Electric Circuits Section 5: Alternating Current
In an AC circuit, the charge flow reverses direction periodically.
Example 6 Electrical Power Sent to a Loudspeaker A stereo receiver applies a peak voltage of 34 V to a speaker. The speaker behaves approximately as if it had a resistance of 8.0 Ω . Determine (a) the rms voltage, (b) the rms current, and (c) the average power for this circuit.
Conceptual Example 7 Extension Cords and a Potential Fire Hazard During the winter, many people use portable electric space heaters to keep warm. Sometimes, however, the heater must be located far from a 120-V wall receptacle, so an extension cord must be used. However, manufacturers often warn against using an extension cord. If one must be used, they recommend a certain wire gauge, or smaller. Why the warning, and why are smaller-gauge wires better then larger-gauge wires?
20.5.1. The graph shows the current as a function of time for an electrical device plugged into a outlet with an rms voltage of 120 V. What is the resistance of the device? a) 24 b) 21 c) 17 d) 14 e) 12
20.5.2. Consider the circuits shown in parts A and B in the picture. In part A, a light bulb is plugged into a wall outlet that has an rms voltage of 120 volts. A current I passes through the circuit and the bulb turns on. In part B, a second, identical light bulb is connected in series in the circuit. How does the current in circuit B compare with that in circuit A? a) The current is the same, I , as in part A. b) The current is twice as much, 2 I , as in part A. c) The current in part B is zero amperes. d) The current is one fourth as much, 0.25 I , as in part A. e) The current is one half as much, 0.5 I , as in part A.
Chapter 20: Electric Circuits Section 6: Series Wiring
As we will discuss later, the sum of all voltage in a circuit must equal zero.
Voltage supplied by battery is lost by resistors
Example 8 Resistors in a Series Circuit A 6.00 Ω resistor and a 3.00 Ω resistor are connected in series with a 12.0 V battery. Assuming the battery contributes no resistance to the circuit, find (a) the current, (b) the power dissipated in each resistor, and (c) the total power delivered to the resistors by the battery. (a) (b) (c)
20.6.1. Consider the circuit shown in the drawing. Two identical light bulbs, labeled A and B, are connected in series with a battery and are illuminated equally. There is a switch in the circuit that is initially open. Which one of the following statements concerning the two bulbs is true after the switch is closed? a) Bulbs A and B will be off. b) Bulbs A and B will be equally illuminated. c) Bulb A will be brighter and bulb B will be off. d) Bulb A will be off and bulb B will be brighter. e) Both bulbs will be dimmer than before the switch was closed.
Chapter 20: Electric Circuits Section 7: Parallel Wiring
As we will discuss later, the total current flowing into any point must equal the total current flowing out.
Simplifying Circuits R 1 = 5 Ω R 2 = 3 Ω R Total OR 0 5
Example 10 Main and Remote Stereo Speakers Most receivers allow the user to connect to “remote” speakers in addition to the main speakers. At the instant represented in the picture, the voltage across the speakers is 6.00 V. Determine (a) the equivalent resistance of the two speakers, (b) the total current supplied by the receiver, (c) the current in each speaker, and (d) the power dissipated in each speaker.
Conceptual Example 11 A Three-Way Light Bulb and Parallel Wiring Within the bulb there are two separate filaments. When one burns out, the bulb can produce only one level of illumination, but not the highest. Are the filaments connected in series or parallel? How can two filaments be used to produce three different illumination levels?
20.7.1. Consider the three resistors and the battery in the circuit shown. Which resistors, if any, are connected in parallel? a) R 1 and R 2 b) R 1 and R 3 c) R 2 and R 3 d) R 1 and R 2 and R 3 e) No resistors are connected in parallel.
20.7.2. Consider the circuits shown in parts A and B in the picture. In part A, a light bulb is plugged into a wall outlet that has an rms voltage of 120 volts. A current I passes through the circuit and the bulb turns on. In part B, a second, identical light bulb is connected in parallel in the circuit. How does the total current in circuit B compare with that in circuit A? a) The current is the same, I , as in part A. b) The current is twice as much, 2 I , as in part A. c) The current in part B is zero amperes. d) The current is one fourth as much, 0.25 I , as in part A. e) The current is one half as much, 0.5 I , as in part A.
20.7.3. Two light bulbs, one “50 W” bulb and one “100 W” bulb, are connected in parallel with a standard 120 volt ac electrical outlet. The brightness of a light bulb is directly related to the power it dissipates. Therefore, the 100 W bulb appears brighter. How does the brightness of the two bulbs compare when these same bulbs are connected in series with the same outlet? a) Both bulbs will be equally bright. b) The “100 W” bulb will be brighter. c) The “50 W” bulb will be brighter.
Chapter 20: Electric Circuits Section 8: Series and Parallel Wiring
20.8.1. Consider the three identical light bulbs shown in the circuit. Bulbs B and C are wired in series with each other and are wired in parallel with bulb A. When the bulbs are connected to the battery as shown, how does the brightness of each bulb compare to the others? a) Bulbs B and C are equally bright, but bulb A is less bright. b) Bulbs B and C are equally bright, but less bright than bulb A. c) All three bulbs are equally bright. d) Bulbs A and B are equally bright, but bulb C is less bright. e) Only bulb A is illuminated.
20.8.2. A circuit is formed using a battery, three identical resistors, and connecting wires as shown. How does the current passing through R 3 compare with that passing through R 1 ? a) I 3 < I 1 b) I 3 = I 1 c) I 3 > I 1 d) This cannot be determined without knowing the amount of current passing through R 2 .
20.8.3. What is the approximate equivalent resistance of the five resistors shown in the circuit? a) 21 b) 7 c) 11 d) 14 e) 19
R R R Resistance = 3 R What is the resistance between x and y? x y
R R R Resistance = R What is the resistance between x and y? x y a
R R R Resistance = R What is the resistance between x and y? x y b
R R R What is the resistance between x and y? x y a b
Redraw the circuit R x R R y a b R R R x y a b
R R R What is the resistance between x and y? x y a b
Chapter 20: Electric Circuits Section 9: Internal Resistance
Batteries and generators add some resistance to a circuit. This resistance is called internal resistance.
The actual voltage between the terminals of a battery is known as the terminal voltage.
Example 12 The Terminal Voltage of a Battery The car battery has an emf of 12.0 V and an internal resistance of 0.0100 Ω . What is the terminal voltage when the current drawn from the battery is (a) 10.0 A and (b) 100.0 A? (a) (b)
20.9.1. In physics lab, two students measured the potential difference between the terminals of a battery and the current in a circuit connected to the battery. The students then made a graph of the two parameters as shown. They then drew a best fit line through the data. From their results, determine the approximate internal resistance of the battery. a) 0.002 b) 0.08 c) 0.1 d) 0.3 e) 0.6
Chapter 20: Electric Circuits Section 10: Kirchoff’s Rules
Draw the current in each branch of the circuit. Choose any direction. If your choice is incorrect, the value obtained for the current will turn out to be a negative number.
Mark each resistor with a + at one end and a – at the other end in a way that is consistent with your choice for current direction in step 1. Outside a battery, conventional current is always directed from a higher potential (the end marked +) to a lower potential (the end marked -).
Apply the junction rule and the loop rule to the circuit, obtaining in the process as many independent equations as there are unknown variables.
Solve these equations simultaneously for the unknown variables.
20.10.1. What is the current through the 4- resistor in this circuit? a) 0.67 A b) 0.75 A c) 1.0 A d) 1.3 A e) 1.5 A
20.10.2. What is the current through the 1- resistor in this circuit? a) 2.8 A b) 3.0 A c) 3.4 A d) 4.3 A e) 4.8 A
20.10.3. Which one of the following equations is not correct relative to the other four equations determined by applying Kirchoff’s Rules to the circuit shown? a) I 2 = I 1 + I 4 b) I 2 = I 3 + I 5 c) 6 V (8 ) I 1 (5 ) I 2 (4 ) I 3 = 0 d) 6 V (6 ) I 4 (5 ) I 2 (2 ) I 5 = 0 e) 6 V (8 ) I 1 (6 ) I 4 6 V (2 ) I 5 (4 ) I 3 = 0
Chapter 20: Electric Circuits Section 11: The Measurement of Current and Voltage
A dc galvanometer. The coil of wire and pointer rotate when there is a current in the wire.
An ammeter must be inserted into a circuit so that the current passes directly through it.
If a galvanometer with a full-scale limit of 0.100 mA is to be used to measure the current of 60.0 mA, a shunt resistance must be used so that the excess current of 59.9 mA can detour around the galvanometer coil.
To measure the voltage between two points in a circuit, a voltmeter is connected between the points.
Chapter 20: Electric Circuits Section 12: Capacitors in series and in parallel
Since there is only one path, charge is the same in all capacitors regardless of capacitance
Voltage drop of each capacitor directly add
20.12.1. A parallel plate capacitor is connected to a battery and becomes fully charged. A voltmeter is used to measure the potential difference across the plates of the capacitor. Then, an uncharged thin metal plate is inserted into the gap between the parallel plates without touching either plate. What affect, if any, does the insertion of the plate have on the potential difference across the plates? a) The potential difference will not change. b) The potential difference will increase to twice its initial value. c) The potential difference will decrease to one half its initial value. d) The potential difference will increase to a value that cannot be determined without having more information. e) The potential difference will decrease to a value that cannot be determined without having more information.
20.12.2. Three parallel plate capacitors, each having a capacitance of 1.0 µF are connected in series. The potential difference across the combination is 100 V. What is the charge on any one of the capacitors? a) 30 C b) 300 C c) 3000 C d) 100 C e) 1000 C
Chapter 20: Electric Circuits Section 13: RC Circuits
20.13.1. In physics lab, Rebecca measured the voltage across an unknown capacitor in an RC circuit, every ten seconds after a switch in the circuit that allows the capacitor to discharge is closed. The capacitor was initially fully charged. Using the graph, estimate the time constant. a) 7.5 s b) 15 s c) 30 s d) 45 s e) 60 s
20.13.2. An RC circuit contains a battery, a switch, a resistor, and a capacitor – all connected in series. Initially, the switch is open and the capacitor is uncharged. Which one of the following statements correctly describes the current in the circuit during the time the capacitor is charging? a) The current is increasing with increasing time. b) The current is constant with increasing time. c) The current is decreasing with increasing time. d) The current increases for the first half of the time until the capacitor is fully discharged, and then decreases during the second half of the time. e) The current can either increase or decrease with increasing time depending on the value of the time constant.
Chapter 20: Electric Circuits Section 14: Safety and the Physiological Effects of Current
20.14 Safety and the Physiological Effects of Current To reduce the danger inherent in using circuits, proper electrical grounding is necessary.