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physics
electricity and magnetism

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

Repeat Exercise 67 assuming, instead, that the capacitors are, instead, connected in parallel. In exercise A capacitor (5.70μF) is connected in a series arrangement with a second capacitor (2.30μF) and a 12-V battery. (a) How much charge is stored on each capacitor? (b) What is the voltage drop
(a) At one-third the original distance from a positive point charge, by what factor is the electric potential changed: (1) 1/3, (2) 3, (3) 1/9, or (4) 9? Why? (b) How far from a +1.0-μC charge is a point with an electric potential value of 10 kV? (c) How much of a change in potential would occur
According to the Bohr model of the hydrogen atom (see Chapter 27), the electron can exist only in circular orbits of certain radii about a proton. (a) Will a larger orbit have (1) a higher, (2) an equal, or (3) a lower electric potential than a smaller orbit? Why? (b) Determine the potential
In Exercise 8, by how much does the potential energy of the atom change if the electron changes location (a) From the lower to the higher orbit, (b) From the higher to the lower orbit, and (c) From the larger orbit to a very large distance?
Filaments in light bulbs usually fail just after the bulbs are turned on rather than when they have already been on for a while. Why?
A wire is connected across a steady voltage source. (a) If that wire is replaced with one of the same material that is twice as long and has twice the cross- sectional area, how will the current in the wire be affected? (b) How will the current be affected if, instead, the new wire has the same
If you cut a long wire in half, what would you have to do to its diameter in order to keep its resistance constant? Explain your reasoning.
From the electric power relationship P = I2R, it would appear that when increasing the value of an appliance’s resistance, its power output would also increase. Yet a 60- W light bulb has less resistance than its lower power 40-W counterpart. Explain.
Explain clearly why, in terms of electric energy generation from nonrenewable fuels, an electric appliance can be, at most, only about efficient.
Why does the battery design shown in Fig. 17.1 require a chemical membrane?
Sketch the following complete circuits, using the symbols shown in Learn by Drawing 17.1: (a) Two ideal 6.0- V batteries in series wired to a capacitor followed by a resistor; (b) Two ideal 12.0- V batteries in parallel, connected as a unit to two resistors in series with one another; (c) A
In the circuit shown in Fig. 17.4a, what is the direction of (a) The electron flow in the resistor, (b) The conventional current in the resistor, (c) The conventional current in the battery?
The drift speed of electrons in a complete circuit, is typically a few millimeters per second. Yet a lamp 3.0 m away from a light switch turns on instantaneously when you flip the switch. Explain this apparent paradox.
To move charges in metallic wires, an internal electric field must exist in the wire. In such a wire, are the electric field and the electric cur-rent in the same or opposite directions? Explain.
If the voltage (V) were plotted (vertically) on the same graph versus current (I) for two ohmic conductors with different resistances, how could you tell which is less resistive?
(a) Three 1.5-V batteries are connected in series. What is the total voltage of the combination? (b) What would be the total voltage if the cells were connected in parallel?
A car’s starter motor draws 50 A from the car’s battery during startup. If the startup time is 1.5 s, how many electrons pass a given location in the circuit during that time?
A net charge of 20 C passes a location in a wire in 1.25 min. How long does it take for a net 30-C charge to pass that location if the current in the wire is doubled?
Car batteries are often rated in “ampere-hours” or A ∙ h. (a) Show that the has units of charge and that 1 A ∙ h = 3600 C. (b) A fully charged, heavy-duty battery is rated at and can deliver a current of 5.0 A steadily until depleted. What is the maximum time this battery can deliver that
Imagine that some protons are moving to the left at the same time that some electrons are moving to the right past the same location. (a) Will the net current be (1) to the right, (2) to the left, (3) zero, or (4) none of the preceding? (b) In 4.5 s, 6.7 C of electrons flow to the right at the
In a proton linear accelerator, a 9.5-mA proton current hits a target. (a) How many protons hit the target each second? (b) How much energy is delivered to the target each second if each proton has a kinetic energy of 20 MeV and loses all its energy in the target? (c) If the target is a 1.00-kg
A battery labeled 12.0 V supplies 1.90 A 6.00-Ω to a resistor (Fig. 17.17). (a) What is the terminal voltage of the battery? (b) What is its internal resistance?
What is the emf of a battery with a 0.15-Ω internal resistance if the battery delivers 1.5 A to an externally connected 5.0-Ω resistor?
Some states allow the use of aluminum wire in houses in place of copper. (a) If you wanted the resistance of your aluminum wire to be the same as that of copper (assuming the same lengths), would the aluminum wire have to have (1) a greater diameter than, (2) a smaller diameter than, or (3) the
What is the voltage across six 1.5-V batteries when they are connected (a) In series, (b) In parallel, (c) Three in parallel with one another and this combination wired in series with the remaining three?
During a research experiment on the conduction of current in the human body, a medical technician attaches one electrode to the wrist and a second to the shoulder of a patient. If 100 mV is applied across the two electrodes and the resulting current is 12.5 mA, what is the overall resistance of the
A 0.60-m-long copper wire has a diameter of 0.10 cm. What is the resistance of the wire?
A material is formed into a long rod with a square cross-section 0.50 cm on each side. When a 100-V voltage is applied across a 20-m length of the rod, a 5.0-A current is carried. (a) What is the resistivity of the material? (b) Is the material a conductor, an insulator, or a semiconductor?
Two copper wires have equal cross-sectional areas and lengths of 2.0 m and 0.50 m, respectively. (a) What is the ratio of the current in the shorter wire to that in the longer one if they are connected to the same power supply? (b) If you wanted the two wires to carry the same current, what would
Two copper wires have equal lengths, but the diameter of one is three times that of the other. (a) The resistance of the thinner wire is (1) 3, (2) 1/3, (3) 9, (4) 1/9 times that of the resistance of the thicker wire. (b) If the thicker wire has a resistance of 1.0-Ω, what is the resistance of
The wire in a heating element of an electric stove burner has a 0.75-m effective length and a 2.0 x 10-6 ∙ m2 cross-sectional area. (a) If the wire is made of iron and operates at 380oC, what is its operating resistance? (b) What is its resistance when the stove is “off”?
(a) What is the percentage variation of the resistivity of copper over the temperature range from room temperature (20oC) to 100oC? (b) Assume that a copper wire’s resistance changes due to only resistivity changes over this temperature range. Further assume that it is connected to the same
A copper wire has a 25-mΩ resistance at 20oC. When the wire is carrying a current, heat produced by the current causes the temperature of the wire to increase by 20oC. (a) What is the change in the wire’s resistance? (b) If its original current was 10.0 mA, what is its final current?
When a resistor is connected to a 12-V source, it draws a 185-mA current. The same resistor connected to a 90-V source draws a 1.25-A current. (a) Is the resistor ohmic? Justify your answer mathematically. (b) What is the rate of Joule heating in this resistor in both cases?
A particular application requires a 20-m length of aluminum wire to have a 0.25-mΩ resistance at 20 oC. (a) What is the wire’s diameter? (b) What would its resistance be if its length was halved and it was then placed in an ice water bath?
Two 6.0-V batteries and one 12-V battery are connected in series. (a) What is the voltage across the whole arrangement? (b) What arrangement of these three batteries would give a total voltage of 12 V?
(a) If the resistance of the wire in Exercise 29 cannot vary by more than from its value at ±5.0%, to what operating temperature range should it be restricted? (b) What would be the operating range if the wire were, instead, made of copper?
As a wire is stretched out so that its length increases, its cross-sectional area decreases, while the total volume of the wire remains constant. (a) Will the resistance after the stretch be (1) greater than, (2) the same as, or (3) less than that before the stretch? (b) A 1.0-m length of copper
Figure 17.18 shows data on the dependence of the current through a resistor on the voltage across that resistor.(a) Is the resistor ohmic? Explain your reasoning.(b) What is the value of its resistance?(c) Use the data to predict what voltage would be needed to produce a 4.0-A current in the
At 20 oC, a silicon rod of uniform cross-section is connected to a battery with a terminal voltage of 6.0 V and a 0.50-A current results. The temperature of the rod is then increased to 25 oC. (a) What is its new resistance? (b) How much current does it carry? (c) If you wanted to cut the
A platinum wire is connected to a battery. (a) If the temperature increases, will the current in the wire (1) increase, (2) remain the same, or (3) decrease? Why? (b) An electrical resistance thermometer is made of platinum wire that has a resistance at 20oC. The wire is connected to a 1.5-V
A digital video disk (DVD) player is rated at 100 W at 120 V. What is its resistance?
A freezer of resistance 10Ω is connected to a 110-V source. What is the power delivered when this freezer is on?
The current in a refrigerator with a resistance of 12 Ω is 13 A (when the refrigerator is on). What is the power delivered to the refrigerator?
Show that the quantity volts squared per ohm (V2/Ω)has SI units of power.
An electric water heater is designed to produce 50 kW of heat when it is connected to a 240-V source. What is its resistance?
Given three batteries with voltages of 1.0 V, 3.0 V, and 12 V, what are the minimum and maximum voltages that could be achieved by connecting them in series?
If the heater in Exercise 39 is efficient, how long would it take to heat 50 gal of water from 20oC to 80oC?
An ohmic resistor in a circuit is designed to operate at 120 V. (a) If you connect the resistor to a 60-V power source, will the resistor dissipate heat at (1) 2, (2) 4, (3) ½, or (4) ¼ times the designed power? Why? (b) If the designed power is 90 W at 120 V, but the resistor is connected to a
An electric toy with a resistance of is operated by a 3.00-V battery. (a) What current does the toy draw? (b) Assuming that the battery delivers a steady current for its lifetime of 4.00 h, how much charge passed through the toy? (c) How much energy was delivered to the toy?
A welding machine draws 18 A of current at 240 V. (a) What is its power rating? (b) What is its resistance? (c) When it is inadvertently connected to a 120 V outlet, the current in it is 10 A. Is the machine’s resistance ohmic? Prove your answer.
On average, an electric water heater operates for 2.0 h each day. (a) If the cost of electricity is $0.15/kWh, what is the cost of operating the heater during a 30-day month? (b) What is the resistance of a typical water heater?
(a) What is the resistance of an immersion-type heating coil if it is to generate 15 kJ of heat per minute when it is connected to a 120-V source? (b) What would the coil’s resistance have to be if instead 10 kJ of heat per minute was desired?
A 200-W computer power supply is on 10 h per day. (a) If the cost of electricity is $0.15/kWh, what is the energy cost (to the nearest dollar) if this computer is used like this for a year (365 days)? (b) If this power supply is replaced by a more efficient 100-W version and it costs $ 75, how
A 120-V air conditioner unit draws 15 A of current. If it operates for 20 min, (a) How much energy in kilowatt-hours does it use in that time? (b) If the cost of electricity is $0.15/kWh, what is the cost (to the nearest penny) of operating the unit for 20 min? (c) If the air conditioner
Two resistors, 100 Ω and 25kΩ, are rated for a maximum power output of 1.5 W and 0.25 W, respectively. (a) What is the maximum voltage that can be safely applied to each resistor? (b) What is the maximum current that each resistor can have?
A wire 5.0 m long and 3.0 mm in diameter has a resistance of 100 Ω. A 15-V potential difference is applied across the wire. Find (a) The current in the wire, (b) The resistivity of its material, and (c) The rate at which heat is being produced in the wire.
You are given four A batteries that are rated at 1.5 V each. The batteries are grouped in pairs. In arrangement A, the two batteries in each pair are in series, and then the pairs are connected in parallel. In arrangement B, the two batteries in each pair are in parallel, and then the pairs are
When connected to a voltage source, a coil of tungsten wire initially dissipates 500 W of power. In a short time, the temperature of the coil increases by 150oC because of joule heating. (a) Will the dissipated power (1) increase, (2) remain the same, or (3) decrease? Why? (b) What is the
A 20-Ω resistor is connected to four 1.5-V batteries. What is the joule heat loss per minute in the resistor if the batteries are connected (a) In series and (b) In parallel?
A 5.5-kW water heater operates at 240 V. (a) Should the heater circuit have a 20-A or a 30-A circuit breaker? (A circuit breaker is a safety device that opens the circuit at its rated current.) (b) Assuming efficiency, how long will the heater take to heat the water in a 55-gal tank from 20oC to
A student uses an immersion heater to heat 0.30 kg of water from 20oC to 80oC for tea. (a) If the heater is efficient and takes 2.5 min to heat the water. What is its resistance? (b) How much current is in the heater? (Assume 120-V household voltage.)
An ohmic appliance is rated at 100 W when it is connected to a 120-V source. If the power company cuts the voltage by to conserve energy, what is (a) The current in the appliance and (b) The power consumed by the appliance after the voltage drop?
A lightbulb’s output is 60 W when it operates at 120 V. If the voltage is cut in half and the power dropped to 20 W during a brownout, what is the ratio of the bulb’s resistance at full power to its resistance during the brownout?
To empty a flooded basement, a water pump must do work (lift the water) at a rate of 2.00 kW. If the pump is wired to a 240-V source and is 84% efficient, (a) How much current does it draw and (b) What is its resistance?
(a) Find the individual monthly (30-day) electric energy costs (to the nearest dollar) for each of the following household appliances if the utility rate is $0.12/kWh: central air conditioning that runs 30% of the time; a blender that is used 0.50 h/month; a dishwasher that is used 8.0 h/month; a
A piece of carbon and a piece of copper have the same resistance at room temperature. (a) If the temperature of each piece is increased by 10.0oC, will the copper piece have (1) a higher resistance than, (2) the same resistance as, or (3) a lower resistance than the carbon piece? Why? (b)
Two pieces of aluminum and copper wire are identical in length and diameter. At some temperature, one of the wires will have the same resistance that the other has at 20oC. (a) What is that temperature? (b) If the two wires are connected in series, compute the ratio of the total resistance
How long does it take for a charge of 3.50 C to pass through the cross-sectional area of a wire that is carrying a current of 0.57 A?
A battery delivers 2.54 A to a resistor rated at 4.52Ω. When it is connected to a 2.21-Ω resistor, it delivers 4.98 A. Determine the battery’s (a) Internal resistance (assumed constant), (b) Emf, and (c) Terminal voltage (in both cases).
An external resistor is connected to a battery with a variable emf but constant internal resistance of 0.200 Ω. At an emf of 3.00 V, the resistor draws a current of 0.500 A, and at 6.00 V, the resistor draws a current of 1.50 A. (a) Is the external resistor ohmic? Prove your answer. (b)
An electric eel delivers a current of 0.75 A to a small pencil-thin prey 15 cm long. If the eel’s “bio-battery” was charged to 500 V, and it was constant for 20 ms before dropping to zero, estimate (a) The resistance of the fish, (b) The energy delivered to the fish, and (c) The average
Most modern TVs have an “instant warm-up” feature. Even though the set appears to be off, it is “off” only in that there is no picture and audio. To provide a “quick on” feature, the TV’s electronics are kept ready. This takes about 10 W of electric power, constantly. Under these
A computer CD-ROM drive that operates on 120 V is rated at 40 W when it is operating. (a) How much current does the drive draw? (b) What is the drive’s resistance? (c) How much energy (in kWh) does this drive use per month assuming it operates 15 min per day? (d) Estimate the electric energy
The tungsten filament of an incandescent lamp has a resistance of 200 Ω at room temperature. (a) What would the resistance be at an operating temperature of 1600oC? (b) Assuming it is plugged into a 120-V outlet, what is its power output when just starting up? (c) By how much does its power
A common sight in our modern world is high-voltage lines carrying electric energy over long distances from power plants to populated areas. The delivery voltage of these lines is typically 500 kV, whereas by the time the energy reaches our households it is down to 120 V (see Chapter 20 for how this
In a country setting it is common to see a hawk sitting on a single high-voltage electric power line searching for a roadkill meal (Fig. 17.19). To understand why this bird isn€™t electrocuted, let€™s do a ballpark estimate of the voltage between her feet. Assume dc conditions
A cylindrical resistor is made of carbon and is 10.0 cm long with a diameter of 1.00 cm. Assuming the resistor is kept at room temperature, (a) What is its resistance? (b) If it is then connected to a 12.0-V battery, how many electrons pass through one end of The resistor in 1 min? (c) In that 1
A high voltage power supply (10.0 kV) is encased in a metal box and rests on a metal table, which is grounded. Between the power supply’s box and the table is a square sheet of rubber, 2.54 cm thick and 30.0 cm on a side. (a) What is the resistance of the rubber mat? (b) Suppose the output of
(a) How long would it take for a net charge of 2.5 C to pass a location in a wire if it is to carry a steady current of 5.0 mA? (b) If the wire is actually connected directly to the two electrodes of a battery and the battery does 25 J of work on the charge during this time, what is the terminal
A small toy car draws a 0.50-mA current from a 3.0-V NiCd (nickel– cadmium) battery. In 10 min of operation, (a) How much charge flows through the toy car, and (b) How much energy is lost by the battery?
Use Kirchhoff’s loop theorem to explain why a 60-W lightbulb produces more light than one rated at 100 W when they are connected in series to a 120-V source.
Use both of Kirchhoff’s theorems to explain why a 60-W lightbulb produces less light than one rated at 100 W when they are connected in parallel to a 120-V source.
Is the time it takes to charge a capacitor in an RC circuit to of its maximum value longer or shorter than one time constant? Is the time it takes to discharge a capacitor to of its initial charge longer or shorter than one time constant? Explain your answers.
Use Kirchhoff’s loop theorem to explain why the current in an RC circuit that is discharging a capacitor decreases as time goes on. Use the loop theorem to explain why the current in a charging RC circuit also decreases with time.
(a) What would happen if an ammeter were connected in parallel with a current-carrying circuit element? (b) What would happen if a voltmeter were connected in series with a current-carrying circuit element?
Explain clearly, using Kirchhoff’s laws, why the resistance of an ideal voltmeter is infinite.
If designed properly, a good ammeter should have a very small resistance. Why? Explain clearly, using Kirchhoff’s laws.
Are the joule heating rates for resistors in series generally the same? If not, under what circumstance(s) could they be the same?
Draw the circuit diagrams indicating the correct placement for the ammeter in the following situations. (Use a circle with an “A” in it to represent the ammeter.) (a) Three resistors are wired in parallel and you want to measure the total current through all of them with just one measurement.
Draw the circuit diagrams indicating the correct placement for the voltmeter in the following situations. (Use a circle with an “V” in it to represent the voltmeter.) (a) Three resistors are wired in parallel and you want to measure the total voltage across all of them with just one
Are the joule heating rates in resistors in parallel generally the same? If not, under what circumstance(s) could they be the same?
If a large resistor and a small resistor are connected in series, will the value of the effective resistance be closer to that of the large resistance or that of the small one? What if they are connected in parallel?
Light bulbs are labeled with their power output. For example, when a lightbulb is labeled 60 W, it is assumed that the bulb is connected to a 120- V source. Suppose you have two bulbs. A60- W bulb is followed by a 40- W bulb in series to a 120- V source. Which one glows brighter? Why? What happens
Three identical resistors are connected to a battery. Two are wired in parallel, and that combination is followed in series by the third resistor. Which resistor has (a) The largest current, (b) The largest voltage, and (c) The largest power output?
Three resistors have values of 5.0 Ω, 2.0 Ω, and 1.0 Ω. The first one is followed in series by the last two wired in parallel. When this arrangement is connected to a battery, which resistor has (a) The largest current, (b) The largest voltage, and (c) The largest power output?
Three resistors that have values of 10 Ω, 20 Ω, and 30 Ω are to be connected. (a) How should you connect them to get the maximum equivalent resistance, and what is this maximum value? (b) How should you connect them to get the minimum equivalent resistance, and what is this minimum value?
What is the equivalent resistance of the resistors in Fig. 18.28?
What is the equivalent resistance between points A and B in Fig. 18.29?
Find the current in and voltage across the resistor shown in Fig. 18.30. 10-Ã†

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