Mastering Physics Solutions Chapter 21 Electric Current and Direct-Current Circuits
Chapter 21 Electric Current and Direct-Current Circuits Q.1CQ
What is the direction of the electric current produced by an electron that falls toward the ground?
Solution:
By convention, the direction of electric current is always in the opposite direction to the motion of negative charge. If the electron falls toward the ground. then the direction of current is in the upward direction
Chapter 21 Electric Current and Direct-Current Circuits Q.1P
How many coulombs of charge are in one ampere-hour?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.2CQ
Your body is composed of electric charges Does it follow, then, that you produce an electric current when you walk?
Solution:
No An electric current ¡s proc1ucei when a net charge mores Your body is electrically neutral, so no current is produced when you walk
Chapter 21 Electric Current and Direct-Current Circuits Q.2P
A flashlight bulb carries a current of 0.18 A for 78 s. How much charge flows through the bulb in this time? How many electrons?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.3CQ
Suppose you charge a comb by rubbing it through your hair Do you produce a current when you walk across the room carrying the comb?
Solution:
No.
By rubbing the comb through your hair you have transferred charge from your hair to the comb but the net charge of you and the comb together is still zero Therefore no current is produced when you walk across the room carrying the comb
Chapter 21 Electric Current and Direct-Current Circuits Q.3P
The picture tube in a particular television draws a current of 15 A. How many electrons strike the viewing screen every second?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.4CQ
Suppose you charge a comb by rubbing t through the fur on your dog’s back Do you produce a current when you walk across the room carrying the comb?
Solution:
Yes
There is a net charge separated and deposited on the comb surface and by moving the comb one place to another you have created an electric current
Chapter 21 Electric Current and Direct-Current Circuits Q.4P
IP A car battery does 260 J of work on the charge passing through it as it starts an engine,
(a) If the emf of the battery is 12 V, how much charge passes through the battery during the start?
(b) If the emf is doubled to 24 V, does the amoun,t of charge passing through the battery increase or decrease? By what factor?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.5CQ
An electron moving through a wire has an average drift speed that is very small Does this mean that its instantaneous velocity is also very small?
Solution:
No.
An electron may have a fairly large instant velocity at any given time But because its direction of motion keeps changing due to its collisions with atoms in the wire its average velocity in particular direction is almost very very small.
Chapter 21 Electric Current and Direct-Current Circuits Q.5P
Highly sensitive ammeters can measure currents as small as 10.0 fA. How many electrons per second flow through a wire with a 10.0-fA current?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.6CQ
Arc car headlights connected in series or parallel? Give an everyday observation that supports your answer
Solution:
Car head lights are wired in parallel as we can tell by the fact that some care has only one working head light.
Chapter 21 Electric Current and Direct-Current Circuits Q.6P
A television set connected to a 120-V outlet consumes 78 W of power, (a) How much current flows through the television? (b) How long does it take for 10 million electrons to pass through the TV?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.7CQ
Give an example of how four resistors of resistance R can be combined to produce an equivalent resistance of R.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.7P
BIO Pacemaker Batteries Pacemakers designed for longterm use commonly employ a lithium-iodine battery capable of
supplying 0.42 A · h of charge,
(a) How many coulombs of charge can such a battery supply?
(b) If the average current produced by the pacemaker is 5.6 μ A, what is the expected lifetime of the device?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.8CQ
Is it possible to connect a group of resistors of value R in such a way that the equivalent resistance is less than R? If so, give a specific example.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.8P
CE A conducting wire is quadrupled in length and tripled in diameter,
(a) Does its resistance increase, decrease, or stay the same? Explain,
(b) By what factor does its resistance change?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.9CQ
What physical quantity do resistors connected in series have in common?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.9P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.10CQ
What physical quantity do resistors connected in parallel have in common?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.10P
Current-versus-voltage plots for two materials, A and B, are shown in Figure 21-26.
(a) Is the resistance of material A greater than, less than, or equal to the resistance of material B at the voltage V1?
(b) Choose the best explanation from among the following:
I. Curve B is higher in value than curve A.
II. A larger slope means a larger value of I/V, and hcnce a smaller value of R.
III. Curve B has the larger slope at the voltage V1 and hence the larger resistance.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.11CQ
Explain how electrical devices can begin operating almost immediately after you throw a switch. even though individual electrons in the wire may take hours to reach the device
Solution:
Each electron in the wire affects its neighbors by means of electric field exerting a force on them causing them to move
Thus when electrons begin to move out of a battery their motion sets up a propagating influence that moves through the wire at nearly the speed of light causing electrons everywhere in the wire to begin moving.
In this way electrical device can begin operating almost immediately after we throw a switch even though individual electrons in the wire may take hours to reach the device
Chapter 21 Electric Current and Direct-Current Circuits Q.11P
Two cylindrical wires are made of the same material and have the same length. If wire B is to have nine times the resistance of wire A, what must be the ratio of their radii, rB/rA?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.12CQ
Explain the difference between resistivity and resistance.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.12P
A silver wire is 5.9 m long and 0.49 mm in diameter. What is its resistance?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.13CQ
Explain why birds can roost on high-voltage wire without being electrocuted
Solution:
A number of factors come into play hera
—t First the bottom of a bird’s foot is tough and definitely not a good conductor of electricity.
—, Secondly the potential difference is required for the flow of current thru the bird’s body. contact with a high voltage wire isn’t enough to cause a problem. there need a contact with a lower voltage Source
But the bird is in contact with essentially the same high voltage in two different places (Where its two feet touch the wire) which doesn’t lead to a potential difference The only potential difference the bird experience is due to the very small voltage drop along the segment of wire between the bird’s two feet
Chapter 21 Electric Current and Direct-Current Circuits Q.13P
When a potential difference of 18 V is applied to a given wire, it conducts 0.35 A of current. What is the resistance of the wire?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.14CQ
List two electrical applications that would benefit from room-temperature superconductors. List two applications for which room-temperature superconductivity would not be beneficial.
Solution:
Magnetic resonance imaging (MRI) machines would definitely benefit from room temperature super conductivity
As it is. they must cool their magnets to law temperature Similarly.
Electric power transmission would benefit if the resistance of the wires could be eliminated On the other hand, a toaster or an electric oven requires resistance to do its job: super conductivity would not help
Chapter 21 Electric Current and Direct-Current Circuits Q.14P
The tungsten filament of a lightbulb has a resistance of 0.07 Ω. If the filament is 27 cm long, what is its diameter?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.15CQ
Oil what basic conservation laws are Kirchhoffs rules based?
Solution:
The junction rule is based on conservation of electric charge the loop rule is based on the conservation energy
Chapter 21 Electric Current and Direct-Current Circuits Q.15P
What is the resistance of 6.0 mi of copper wire with a diameter of 0.55 mm?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.16CQ
What physical quantity do capacitors connected in series have in common?
Solution:
Consider some capacitors connected in series with a battery The plate of the capacitor which is connected to the positive end of the battery will acquire positive charge and this will cause
same amount of negative charge to develop at the other negative plate of the capacitor The negative charge will then cause the capacitor next to it to develop same amount of charge- In this way all the capacitors in the series connection will get same amount of charga Hence, in a series connection, the physical quantity that the capacitors have in common is the electric charge
Chapter 21 Electric Current and Direct-Current Circuits Q.16P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.17CQ
What physical quantity do capacitors connected in parallel have in common?
Solution:
When the capacitors are connected in parallel then the potential difference is the common quantity on all the capacitors.
Chapter 21 Electric Current and Direct-Current Circuits Q.17P
IP A bird lands on a bare copper wire carrying a current of 32 A. The wire is 8 gauge, which means that its cross-sectional area is 0.13 cm2,
(a) Find the difference in potential between the bird’s feet, assuming they are separated by a distance of 6.0 cm.
(b) Will your answer to part (a) increase or decrease if the separation between the bird’s feet increases? Explain.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.18CQ
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.18P
A current of 0.96 A flows through a copper wire 0.44 mm in diameter when it is connected to a potential difference of 15 V. How long is the wire?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.19P
IP BIO Current Through a Cell Membrane A typical cell membrane is 8.0 nm thick and has an electrical resistivity of 1.3 × 107 Ω · m.
(a) If the potential difference between the inner and outer surfaces of a cell membrane is 75 mV, how much current flows through a square area of membrane 1.0 μ m on a side?
(b) Suppose the thickness of the membrane is doubled,
but the resistivity and potential difference remain the same. Does the current increase or decrease? By what factor?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.20P
When a potential difference of 12 V is applied to a wire 6.9 m long and 0.33 mm in diameter, the result is an electric current of 2.1 A. What is the resistivity of the wire?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.21P
IP
(a) What is the resistance per meter of an aluminum wire with a cross-sectional area of 2.4 × 10-7 m2.
(b) Would your answer to part (a) increase, decrease, or stay the same if the diameter of the wire were increased? Explain,
(c) Repeat part (a) for a wire with a cross-sectional area of 3.6 × 10−7 m2.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.22P
BIO Resistance and Current in the Human Finger The interior of the human body has an electrical resistivity of 0.15 Ω · m.
(a) Estimate the resistance for current flowing the length of your index finger. (For this calculation, ignore the much higher resistivity of your skin.)
(b) Your muscles will contract when they carry a current greater than 15 mA. What voltage is required to produce this current through your finger?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.23P
CE Light A has four times the power rating of light B when operated at the same voltage,
(a) Is the resistance of light A greater than, less than, or equal to the resistance of light B? Explain,
(b) What is the ratio of the resistance of light A to the resistance of light B?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.24P
CE Light A has four times the power rating of light B when operated at the same voltage.
(a) Is the resistance of light A greater than, less than, or equal to the resistance of light B? Explain.
(b) What is the ratio of the resistance of light A to the resistance of light B?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.25P
CE Two lightbulbs operate on the same potential difference. Bulb Ahas four times the power output of bulb B.
(a) Which bulb has the greater current passing through it? Explain,
(b) What is the ratio of the current in bulb A to the current in bulb B?
Solution:
Given that,
Two light bulbs operate on the same potential difference. Bulb ‘A’ has 4 times the power output of bulb B.
(a) In terms of potential difference ‘V’ and current ‘I’, the power output of the bulbs can be written as
P = I V
It is given that ‘V’ is the same for both bulbs.
It follows, then, that the current in bulb ‘A’ is greater than the current in bulb ‘B’
(b) Since power is proportional to current, the current in bulb ‘A’ is four times greater than the current in bulb B.
Chapter 21 Electric Current and Direct-Current Circuits Q.26P
CE Two lightbulbs operate on the same current. Bulb A has four times the power output of bulb B.
(a) Is the potential difference across bulb A greater than or less than the potential difference across bulb B? Explain,
(b) What is the ratio of the potential difference across bulb A to that across bulb B?
Solution:
Given that,
Two light bulbs operate on the same current; Bulb ‘A’ has four times the power output of bulb ‘B’.
(a) In terms of potential difference ‘V’ and current ‘I’, the power output of the bulbs can be written as
P = I V
It is given that current ‘I’ is same for both bulbs.
It follows, that the potential difference in bulb ‘A’ is greater than the potential difference in bulb ‘B’.
(b) Since power is proportional to potential difference, the potential difference in bulb ‘A’ is four times greater than the potential difference in bulb ‘B’.
Chapter 21 Electric Current and Direct-Current Circuits Q.27P
A 75-V generator supplies 3.8 kW of power. How much current does the generator produce?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.28P
A portable CD player operates with a current of 22 mA at a potential difference of 4.1 V. What is the power usage of the player?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.29P
Find the power dissipated in a 25-Ω electric heater connected to a 120-V outlet.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.30P
The current in a 120-V reading lamp is 2.6 A. If the cost of electrical energy is $0.075 per kilowatt-hour, how much does it cost to operate the light for
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.31P
It costs 2.6 cents to charge a car battery at a voltage of 12 V and a current of 15 A for 120 minutes. What is the cost of electrical energy per kilowatt-hour at this location?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.32P
IP A 75-W lightbulb operates on a potential difference of 95 V. Find
(a) the current in the bulb and
(b) the resistance of the bulb,
(c) If this bulb is replaced with one whose resistance is half the value found in part
(b), is its power rating greater than or less than 75 W? By what factor?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.33P
Rating Car Batteries Car batteries are rated by the following two numbers:
(1) cranking amps = current the battery can produce for 30.0 seconds while maintaining a terminal voltage of at least 7.2 V and
(2) reserve capacity = number of minutes the battery can produce a 25-A current while maintaining a terminal voltage of at least 10.5 V. One particular battery is advertised as having 905 cranking amps and a 155-minute reserve capacity. Which of these two ratings represents the greater amount of energy delivered by the battery?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.34P
CE Predict/Explain A dozen identical lightbulbs are connected to a given emf.
(a) Will the lights be brighter if they are connected in series or in parallel?
(b) Choose the best explanation from among the following:
I. When connected in parallel each bulb experiences the maximum emf and dissipates the maximum power.
II. Resistors in series have a larger equivalent resistance and dissipate more power.
III. Resistors in parallel have a smaller equivalent resistance and dissipate less power.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.35P
CE Predict/Explain A fuse is a device to protect a circuit from the effects of a large current. The fuse is a small strip of metal that burns through when the current in it exceeds a certain value, thus producing an open circuit,
(a) Should a fuse be connected in series or in parallel with the circuit it is intended to protect?
(b) Choose the best explanation from among the following:
I. Either connection is acceptable; the main tiling is to have a fuse in the circuit.
II. The fuse should be connected in parallel, otherwise it will interrupt the current in the circuit.
III. With the fuse connected in series, the current in the circuit drops to zero as soon as the fuse bruns through.
Solution:
(a) Fuse should be always connected in series.
If the fuse is connected in series, when the fuse is blown out it makes an open circuit and the appliances are protected from high current.
(b) If the fuse is connected in series and when the fuse is blown it becomes an open circuit and the current in the circuit becomes zero.
Hence best explanation is III
Chapter 21 Electric Current and Direct-Current Circuits Q.36P
CE A circuit consists of three resistors, R123, connected in series to a battery. Rank these resistors in order of increasing
(a) current through them and
(b) potential difference across them. Indicate ties where appropriate.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.37P
CE Predict/Explain Two resistors are connected in parallel,
(a) If a third resistor is now connected in parallel with the original two, does the equivalent resistance of the circuit increase, decrease, or remain the same?
(b) Choose the best explanation from among the following:
I. Adding a resistor generally tends to increase the resistance, but putting it in parallel tends to decrease the resistance; therefore the effects offset and the resistance stays the same.
II. Adding more resistance to the circuit will increase the equivalent resistance.
III. The third resistor gives yet another path for current to flow in the circuit, which means that the equivalent resistance is less.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.38P
Solution:
The equivalent resistance (R) of the resistors which are connected in series is equal to the sum of the resistance of the individual resistors.
Chapter 21 Electric Current and Direct-Current Circuits Q.39P
What is the minimum number of 65-Ω resistors that must be connected in parallel to produce an equivalent resistance of 11 Ω or less?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.40P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.41P
Your toaster has a power cord with a resistance of 0.020 Ω connected in series with a 9.6-Ω nichrome heating element. If the potential difference between the terminals of the toaster is 120 V, how much power is dissipated in
(a) the power cord and
(b) the heating element?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.42P
A hobbyist building a radio needs a 150-Ω resistor in her circuit, but has only a 220-Ω, a 79-Ω, and a 92-Ω resistor available. How can she connect these resistors to produce the desired resistance?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.43P
A circuit consists of a 12.0-V battery connected to three resistors (42 Ω, 17 Ω, and 110 Ω) in series. Find
(a) the current that flows through the battery and
(b) the potential difference across each resistor.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.44P
IP Three resistors, 11 Ω, 53 Ω, and R, are connected in series with a 24.0-V battery. The total current flowing through the battery is 0.16 A.
(a) Find the value of resistance R.
(b) Find the potential difference across each resistor,
(c) If the voltage of the battery had been greater than 24.0 V, would your answer to part (a) have been larger or smaller? Explain.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.45P
A circuit consists of a battery connected to three resistors (65 Ω, 25 Ω, and 170 Ω) in parallel. The total current through the resistors is 1.8 A. Find
(a) the emf of the battery and
(b) the current through each resistor.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.46P
IP Three resistors, 22 Ω, 67 Ω, and R, are connected in parallel with a 12.0-V battery. The total current flowing through the battery is 0.88 A.
(a) Find the value of resistance R.
(b) Find the current through each resistor,
(c) If the total current in the battery had been greater than 0.88 A, would your answer to part (a) have been larger or smaller? Explain.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.47P
An 89-Ω resistor has a current of 0.72 A and is connected in series with a 130-Ω resistor. What is the emf of the battery to wliich the resistors are connected?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.48P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.49P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.50P
How many 65-W lightbulbs can be connected m parallel across a potential difference of 85 V before the total current in the circuit exceeds 2.1 A?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.51P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.52P
IP A 12-V battery is connected to terminals A and B in Figure 21-30.
(a) Given that R = 85 Ω, find the current in each resistor.
(b) Suppose the value of R is increased. For each resistor in turn, state whether the current flowing through it increases or decreases. Explain.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.53P
IP The terminals A and B in Figure 21-31 are connected to a 9.0-V battery,
(a) Find the current flowing through each resistor,
(b) Is the potential difference across the 6.3-Ω resistor greater than, less than, or the same as the potential difference across the 1.5-Ω resistor? Explain.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.54P
IP Suppose the battery in Figure 21-32 has an internal resistance r = 0.25 Ω
(a) How much current flows through the battery?
(b) What is the potential difference between the terminals of the battery? (c) If the 3.2-Ω resistor is increased in value, will the current in the battery increase or decrease? Explain.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.55P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.56P
The current in the 13.8-Ω resistor in Figure 21- 0.795 A. Find the current in the other resistors in the circuit
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.57P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.58P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.59P
IP Suppose the polarity of the 11.5-V battery in Figure 21-35 is reversed,
(a) Do you expect this to increase or decrease the amount of current flowing in the circuit? Explain,
(b) Calculate the magnitude and direction (clockwise or counterclockwise) of the current in this case.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.60P
IP It is given that point A in Figure 21-35 is grounded (V = 0).
(a) Is the potential at point B greater than or less than zero? Explain,
(b) Is the potential at point C greater than or less than zero? Explain,
(c) Calculate the potential at point D.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.61P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.62P
Suppose point A is grounded (V = 0) in Figure 21-36. Find the potential at points B and C.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.63P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.64P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.65P
CE Two capacitors, C1 = C and C2 = 2C, are connected to a battery,
(a) Which capacitor stores more energy when they are connected to the battery in series? Explain,
(b) Which capacitor stores more energy when they are connected in parallel? Explain.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.66P
CE Predict/Explain Two capacitors are connected in series,
(a) If a third capacitor is now connected in series with the original two, does the equivalent capacitance increase, decrease, or remain the same?
(b) Choose the best explanation from among the following:
I. Adding a capacitor generally tends to increase the capacitance, but putting it in series tends to decrease the capacitance; therefore, the net result is no change.
II. Adding a capacitor in series will increase the total amount of charge stored, and hence increase the equivalent capacitance.
III. Adding a capacitor in series decreases the equivalent capacitance since each capacitor now has less voltage across it, and hence stores less charge.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.67P
CE Predict/Explain Two capacitors are connected in parallel,
(a) If a third capacitor is now connected in parallel with the original two, does the equivalent capacitance increase, decrease, or remain the same?
(b) Choose the best explanation from among the following:
I. Adding a capacitor tends to increase the capacitance, but putting it in parallel tends to decrease the capacitance; therefore, the net result is no change.
II. Adding a capacitor in parallel will increase the total amount of charge stored, and hence increase the equivalent capacitance.
III. Adding a capacitor in parallel decreases the equivalent capacitance since each capacitor now has less voltage across it, and hence stores less charge.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.68P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.69P
A 12-V battery is connected to three capacitors in series. The capacitors have the following capacitances: 4.5 μ F, 12 μ F, and 32 μ F. Find the voltage across the 32- μ F capacitor.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.70P
CE You conduct a series of experiments in which you connect the capacitors C1 and C2 > C1 to a battery in various ways. The experiments are as follows:
A, C1 alone connected to the battery;
B, C2 alone connected to the battery;
C, C1 and C2 connected to the battery in series;
D, C1 and C2 connected to the battery in parallel. Rank these four experiments in order of increasing equivalent capacitance. Indicate ties where appropriate.
Solution:
The ranking is C<A<B<D
This follows because two capacitors in series have equivalent capacitances less than the smallest of the capacitor and two capacitor connected in parallel have an equivalent capacitance greater than the largest of the capacitors.
Chapter 21 Electric Current and Direct-Current Circuits Q.71P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.72P
Terminals A and B in Figure 21-39 are connected to a 9.0-V battery. Find the energy stored in each capacitor.
Solution:
Therefore, energy stored incapacitor is approximately.
Chapter 21 Electric Current and Direct-Current Circuits Q.73P
IP Two capacitors, one 7.5 μ F and the other 15 μ F, are connected in parallel across a 15-V battery,
(a) Find the equivalent capacitance of the two capacitors,
(b) Which capacitor stores more charge? Explain,
(c) Find the charge stored on each capacitor.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.74P
IP Two capacitors, one 7.5 μ F and the other 15 μ F, are connected in series across a 15-V battery,
(a) Find the equivalent capacitance of the two capacitors,
(b) Which capacitor stores more charge? Explain,
(c) Find the charge stored on each capacitor.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.75P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.76P
Two capacitors, C1 and C2, are connected in series and charged by a battery. Show that the energy stored in C1 plus the energy stored in C2 is equal to the energy stored in the equivalent capacitor, Ceq, when it is connected to the same battery.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.77P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.78P
The switch on an RC circuit is closed at t = 0. Given that ε = 9.0 V, R = 150 Ω, and C = 23 μ F, how much charge is on the capacitor at time t = 4.2 ms?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.79P
ε The capacitor in an RC circuit (R = 120 Ω, C = 45 μ F) is initially uncharged. Find
(a) the charge on the capacitor and
(b) the current in the circuit one time constant (τ = RC) after the circuit is connected to a 9.0-V battery.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.80P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.81P
Consider an RC circuit with ε = 12.0 V, R = 175 Ω, and C = 55.7 μ F. Find
(a) the time constant for the circuit,
(b) the maximum charge on the capacitor, and
(c) the initial current in the circuit.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.82P
The resistor in an RC circuit has a resistance of 145 Ω.
(a) What capacitance must be used in this circuit if the time constant is to be 3.5 ms?
(b) Using the capacitance determined in part (a), calculate the current in the circuit 7.0 ms after the switch is closed. Assume that the capacitor is uncharged initially and that the emf of the battery is 9.0 V.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.83P
A flash unit for a camera has a capacitance of 1500 μ F. What resistance is needed in this RC circuit if the flash is to charge to 90% of its full charge in 21 s?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.84P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.85P
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.86P
The capacitor in an RC circuit is initially uncharged. In terms of R and C, determine
(a) the time required for the charge on the capacitor to rise to 50% of its final value and
(b) the time required for the initial current to drop to 10% of its initial value.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.87GP
CE A given car battery is rated as 250 amp-hours. Is this rating a measure of energy, power, charge, voltage, or current? Explain.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.88GP
CE Predict/Explain The resistivity of tungsten increases with temperature,
(a) When a light containing a tungsten filament heats up, does its power consumption increase, decrease, or stay the same?
(b) Choose the best explanation from among the following:
I. The voltage is unchanged, and therefore an increase in resistance implies a reduced power, as we can see from P = V2/R.
II. Increasing the resistance increases the power, as is clear from P = I2R.
III. The power consumption is independent of resistance, as we can see from P = IV.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.89GP
CE A cylindrical wire is to be doubled in length, but it is desired that its resistance remain the same,
(a) Must its radius be increased or decreased? Explain,
(b) By what factor must the radius be changed?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.90GP
CE Predict/Explain An electric space heater has a power rating of 500 W when connected to a given voltage V.
(a) If two of these heaters are connected in series to the same voltage, is the power consiuned by the two heaters greater than, less than, or equal to 1000 W? (b) Choose the best explanation from among the following:
I. Each heater consumes 500 W; therefore two of them will consume 500 W + 500 W = 1000 W.
II. The voltage is the same, but the resistance is doubled by connecting the heaters in scries. Therefore, the power consumed (P = V2/R) is less than 1000 W.
III. Connecting two heaters in series doubles the resistance. Since power depends on the resistance squared, it follows that the power consumed is greater than 1000 W.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.91GP
CE Two resistors, R1 = R and R2 = 2R, are connected to a battery.
(a) Which resistor dissipates more power when they are connected to the battery in series? Explain,
(b) Which resistor dissipates more power when they aie connected in parallel? Explain.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.92GP
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.93GP
CE Predict/Explain
(a) Referring to Problem 92 arid the circuit in Figure 21-45, does the current supplied by the battery increase, decrease, or remain the same when the switch is closed?
(a) Choose the best explanation from among the following:
I. The current decreases because only two resistors can draw current from the battery when the switch is closed.
II. Closing the switch makes no difference to the current since the second resistor is still connected to the battery as before.
III. Closing the switch shorts out the second resistor, decreases the total resistance of the circuit, and increases the current.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.94GP
CE Predict/Explain
(a) Referring to Problem 92 and the circuit in Figure 21-45, does the total power dissipated in the circuit increase, decrease, or remain the same when the switch is closed?
(b) Choose the best explanation from among the following:
I. Closing the switch shorts out one of the resistors, which means that the power dissipated decreases.
II. The equivalent resistance of the circuit is reduced by closing the switch, but the voltage remains the same. Therefore, from P = V2/R we see that the power dissipated increases.
III. The power dissipated remains the same because power, P = IV, is independent of resistance.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.95GP
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.96GP
CE Predict/Explain
(a) When the switch is closed in the circuit shown in Figure 21-46, does the current supplied by the battery increase, decrease, or stay the same?
(b) Choose the best explanation from among the following:
I. The current increases because three resistors are drawing current from the battery when the switch is closed, rather than just two.
II. Closing the switch makes no difference to the current because the voltage is the same as before.
III. Closing the switch decreases the current because an additional resistor is added to the circuit.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.97GP
CE Predict/Explain
(a) When the switch is closed in the circuit shown in Figure 21-46, does the total power dissipated in the circuit increase, decrease, or stay the same?
(b) Choose the best explanation from among the following:
I. Closing the switch adds one more resistor to the circuit This makes it harder for the battery to supply current which decreases the power dissipated.
II. The equivalent resistance of the circuit is reduced by closing the switch, but the voltage remains the same. Therefore from P = V2/R we see that the power dissipated increases
III. The power dissipated remains the same because power P = IV, is independent of resistance.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.98GP
Suppose that points A and B in Figure 21-30 are connected to a 12-V battery. Find the power dissipated in each of the resistors assuming that R = 65 Ω.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.99GP
You are given resistors of 413 Ω, 521 Ω, and 146 Ω. Describe how these resistors must be connected to produce an equivalent resistance of 255 Ω.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.100GP
You arc given capacitors of 18 μF, 7.2 μF, and 9.0 μF. Describe how these capacitors must be connected to produce an equivalent capacitance of 22 μF.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.101GP
Suppose your car carries a chargc of 85 μC. What current does it produce as it travels from Dallas to Fort Worth (35 mi) in 0.75 h?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.102GP
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.103GP
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.104GP
It is desired to construct a 5.0-Ω resistor from a 1.2-m length of tungsten wire. What diameter is needed for this wire?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.105GP
Electrical Safety Codes For safety reasons, electrical codes have been established that limit the amount of current a wire of a given size can carry. For example, an 18-gauge (cross- sectional area = 1.17 mm2), rubber-insulated extension cord with copper wires can carry a maximum current of 5.0 A. Find the voltage drop in a 12-ft, 18-gauge extension cord carrying a current of 5.0 A. (Note: In an extension cord, the current must flow through two lengths—down and back.)
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.106GP
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.107GP
A portable CD player uses a current of 7.5 mA at a potential difference of 3.5 V.
(a) How much energy does the player use in 35 s?
(b) Suppose the player has a mass of 0.65 kg. For what length of time could the player operate on the energy required to lift it through a height of 1.0 m?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.108GP
An electrical heating coil is immersed in 4.6 kg of water at 22 °C. The coil, which has a resistance of 250 Ω, warms the water to 32 °C in 15 min. What is the potential difference at
which the coil operates?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.109GP
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.110GP
A silver wire and a copper wire have the same volume and the same resistance. Find the ratio of their radii, r silver/r copper·
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.111GP
Two resistors are connected in series to a battery with an emf of 12 V. The voltage across the first resistor is 2.7 V and the current through the second resistor is 0.15 A. Find the resistance of the two resistors.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.112GP
BIOPacemaker Pulses A pacemaker sends a pulse to a patient’s heart every time the capacitor in the pacemaker charges to a voltage of 0.25 V. It is desired that the patient receive 75 pulses per minute. Given that the capacitance of the pacemaker is 110 μF and that the battery has a voltage of 9.0 V, what value should the resistance have?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.113GP
A long, thin wire has a resistance R. The wire is now cut into three segments of equal length, which are connected in parallel. In terms of R, what is the equivalent resistance of the three wire segments?
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.114GP
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.115GP
IP Suppose we connect a 12.0-V battery to terminals A and B in Figure 21-29.
(a) Is the current in the 45-Ω resistor greater than, less than, or the same as the current in the 35-Ω resistor? Explain,
(b) Calculate the current flowing through each of the three resistors in this circuit.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.116GP
IP Suppose the battery in Figure 21-50 has an internal resistance of 0.73 Ω.
(a) What is the potential difference across the terminals of the battery when the switch is open?
(b) When the switch is closed, does the potential difference of the battery increase or decrease? Explain,
(c) Find the potential difference across the battery after the switch has been closed a long time.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.117GP
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.118GP
IP 15.0-V battery is connected to terminals A and B in Figure 21-41.
(a) Given that C = 15.0 μF, find the charge on each of the capacitors,
(b) Find the total energy stored in this system,
(c) If the 7.22-μF capacitor is increased in value, will the total energy stored in the circuit increase or decrease? Explain.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.119GP
IP The switch in the RC circuit shown in Figure 21-44 is closed at t = 0.
(a) How much power is dissipated in each resistor just after t = 0 and in the limit t → ∞?
(b) What is the charge on the capacitor at the time t = 0.35 ms?
(c) How much energy is stored in the capacitor in the limit t → ∞??
(d) If the voltage of the battery is doubled, by what factor does your answer to part (c) change? Explain.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.120GP
Two resistors, R1 and R2, are connected in parallel and connected to a battery. Show that the power dissipated in R1 plus the power dissipated in R2 is equal to the power dissipated in the equivalent resistor, Req, when it is connected to the same battery.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.121GP
A battery has an emf ε and an internal resistance r. When the battery is connected to a 25-Ω resistor, the current through the battery is 0.65 A. When the battery is connected to a 55-Ω resistor, the current is 0.45 A. Find the battery’s emf and internal resistance.
Solution:
Calculate battery’s emf and internal resistance by applying Kirchhoff’s loop rule to the circuit.
Kirchhoff’s loop rule states that as one moves around a closed loop in a circuit, the algebraic sum of the potential difference must be zero.
Chapter 21 Electric Current and Direct-Current Circuits Q.122GP
When two resistors, R1 and R2, are connected in series across a 6.0-V battery, the potential difference across R1 is 4.0 V. When R1 and R2 are connccted in parallel to the same battery, the current through R2 is 0.45 A. Find the values of R1 and R2.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.123GP
Suppose the voltmeter measures a potential difference of 3.70 V across the resistor. What is the current that flows through the person’s body?
A. 3.70 × 10-6A
B. 5.00 × 10-5A
C. 0.0740 A
D. 3.70 A
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.124PP
What is the resistance of the person and footwear when the voltmeter reads 3.70 V?
A. 1.25 × 107Ω
B. 1.35 × 107 Ω
C. 4.63 × 107 Ω
D. 1.71 × 108 Ω
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.125PP
The resistance of a given person and footwear is 4.00 × 107Ω What is the reading on the voltmeter when this person is tested?
A. 0.976 V
B. 1.22 V
C. 1.25 V
D. 50.0 V
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.126PP
The resistance of a given person and footwear is 4.00 × 107Ω What is the reading on the voltmeter when this person is tested?
A. 0.976 V
B. 1.22 V
C. 1.25 V
D. 50.0 V
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.127PP
Suppose that during one test a person’s shoes become wet when water spills onto the floor. When this happens, do you expect the reading on the voltmeter to increase, decrease, or stay the same?
Solution:
Given if the shoes become wet the resistance of the person foot wear will be decreased and the current flow will be increased. This results increase in the voltmeter reading.
Chapter 21 Electric Current and Direct-Current Circuits Q.128IP
Referring to Example 21-7 Suppose the three resistors in this circuit have the values R1 = 100.0 Ω, R2 = 200.0 Ω, and R3 = 300.0 Ω, and that the emf of the battery is 12.0 V. (The resistor numbers are given in the Interactive Figure.)
(a) Find the potential difference across each resistor,
(b) Find the current that flows through each resistor.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.129IP
Referring to Example 21-7 Suppose R1 = R2 = 225 Ω and R3 = R. The emf of the battery is 12.0 V. (The resistor numbers are given in the Interactive Figure.)
(a) Find the value of R such that the current supplied by the battery is 0.0750 A. (b) Find the value of R that gives a potential difference of 2.65 V across resistor 2.
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.130IP
IP Referring to Example 21-9 Suppose the resistance of the 126-Ω resistor is reduced by a factor of 2. The other resistor is 275 Ω, the capacitor is 182 μF, and the battery has an emf of 3.00 V.
(a) Does the filial value of the charge on the capacitor increase, decrease, or stay the same? Explain,
(b) Does the time for the capacitor to charge to 80.0% of its final value increase, decrease, or stay the same? Explain, (c) Find the time referred to in part (b).
Solution:
Chapter 21 Electric Current and Direct-Current Circuits Q.131IP
IP Referring to Example 21-9 Suppose the capacitance of the 182-μF capacitor is reduced by a factor of 2. The two resistors are 126 Ω and 275 Ω, and the battery has an emf of 3.00 V.
(a) Find the final value of the charge on the capacitor,
(b) Does the time for the capacitor to charge to 80.0% of its final value increase, decrease, or stay the same? Explain,
(c) Find the time referred to in part (b).
Solution:
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