Solved: A 240-V electric motor is 90% efficient, meaning that 90% of the energy supplied

Explain the difference between current and current density.

A constant electric field generally produces a constant drift velocity. How is this consistent with Newtons assertion that force results in acceleration, not velocity?

When caught in the open in a lightning storm, a person should crouch low with feet close together rather than lie flat on the ground. Why?

Good conductors of electricity are often good conductors of heat. Why might this be?

Why can current persist forever in a superconductor with no applied voltage?

Does an electric stove burner draw more current when its first turned on or when its fully hot?

A person and a cow are standing in a field when lightning strikes the ground nearby. Why is the cow more likely to be electrocuted?

You put a 1.5-V battery across a piece of material, and a 100-mA current flows. With a 9-V battery, the current increases to 400 mA. Is the material ohmic or not?

The resistance of a metal increases with increasing temperature, while the resistance of a semiconductor decreases. Why the difference?

A 50-W and a 100-W lightbulb are both designed to operate at 120 V. Which has the lower resistance?

Equation 24.8a suggests that no power can be dissipated in a superconductor because R = 0. But Equation 24.8b suggests the power should be infinite. Which is right, and why?

Whats wrong with this news report: A power-line worker was injured when 4000 volts passed through his body?

A wire carries 1.5 A. How many electrons pass through the wire in one second?

A 12-V car battery is rated at 80 ampere-hours, meaning it can supply 80 A of current for 1 hour before it becomes discharged. If you accidentally leave the headlights on until the battery discharges, how much charge moves through the lights?

Biologists measure the total current due to potassium ions moving through the membrane of a rock crab neuron cell as 30 nA. How many ions pass through the membrane each second?

The National Electrical Code specifies a maximum current of 10 A in 16-gauge (1.29-mm-diameter) copper wire. Whats the corresponding current density?

The electric field in an aluminum wire is 85 mV/m. Find the current density in the wire.

What electric field is necessary to drive a 7.5-A current through a 0.95-mm-diameter silver wire?

A cylindrical tube of seawater carries 350 mA of current. If the electric field in the water is 21 V/m, whats the tubes diameter?

A 1.0-cm-diameter rod carries a 50-A current when the electric field in the rod is 1.4 V/m. Whats the resistivity of the rod material?

Use Table 24.1 to determine the conductivity of (a) copper and (b) seawater.

Find the resistance of a heating coil that draws 4.8 A when thevoltage across it is 120 V.

What voltage does it take to drive 300 mA through a 1.2@kresistance?

Whats the current in a 47@k resistor with 110 V across it?

The third rail that carries electric power to a subway train isan iron bar whose rectangular cross section measures 10 cm by15 cm. Find the resistance of a 5.0-km length of this rail.

What current flows when a 45-V potential difference is imposedacross a 1.8@k resistor?

A uniform wire of resistance R is stretched until its length doubles. Assuming its density and resistivity remain constant, whats its new resistance?

A cars starter motor draws 125 A with 11 V across its terminals.Whats its power consumption?

A 4.5-W flashlight bulb draws 750 mA. (a) At what voltage doesit operate? (b) Whats its resistance?

A watch uses energy at the rate of 240 W. What current does itdraw from its 1.5-V battery?

A 35@ electric stove burner consumes 1.5 kW of power. Atwhat voltage does it operate?

An incandescent lightbulb draws 0.50 A, while a compactfluorescent with the same light output draws 125 mA. Both operate on standard 120-V household power. How do their energy- consumption rates compare?

Though rare, electrocution has been reported under wet conditions with voltages as low as 30 V. What resistance would be necessary for this voltage to drive a fatal current of 100 mA?

You touch a defective appliance while standing on the ground, and you feel the tingle of a 2.5-mA current. Whats your resistance, assuming youre touching the hot side of the 120-V household wiring?

You have a typical resistance of 100 k. (a) How much current could a 12-V car battery pass through you? (b) Would you feel this?

An ion channel in a cell membrane carries 2.4 pA when its open, which is only 20% of the time. (a) Whats the average current in the channel? (b) If the channel opens for 1.0 ms, how many singly ionized ions pass through in this time?

A lightbulb filament has diameter 0.050 mm and carries 0.833 A. Find the current density (a) in the filament and (b) in the 12-gauge wire (diameter 2.1 mm) supplying current to the lightbulb.

A gold film in an integrated circuit measures 1.85 m thick by 0.120 mm wide. It carries a current density of 0.482 MA/m2 . Whats the total current?

A copper wire joins an aluminum wire whose diameter is twice that of the copper. The same current flows in both wires. The density of conduction electrons in copper is 1.1*1029 m-3 ; in aluminum its 2.1*1029 m-3 . Compare (a) the drift speeds and (b) the current densities in each wire.

In Fig. 24.17, a 100-mA current flows through a copper wire 0.10 mm in diameter, a salt solution in a 1.0-cm-diameter glass tube, and a vacuum tube where the current is carried by an electron beam 1.0 mm in diameter. The density of conduction electrons in copper is 1.1*1029 m-3 . The current in the solution is carried equally by positive and negative ions with charges {2e; the density of each ion species is 6.1*1023 m-3 . The electron density in the beam is 2.2*1016 m-3 . Find the drift speed in each region.

In a study of proteins mediating cell membrane transport, biologists measure current versus time through the cell membranes of oocytes (nearly mature egg cells) taken from the African clawed frog, Xenopus. The measured current versus time is given approximately by I = 60t + 200t 2 + 4.0t 3 with t in seconds and I in nA. Find the total charge that flows through the cell membrane in the interval from t = 0 to t = 5.0 s

Theres a 2.5-V potential difference between opposite ends of a 6.0-m-long iron wire 1.0 mm in diameter. Assuming a uniform electric field in the wire, find (a) the current density and (b) the total current.

The maximum safe current in 12-gauge (2.1-mm-diameter) copper wire is 20 A. Find (a) the current density and (b) the electric field under these conditions.

Silver and iron wires of the same length and diameter carry the same current. How do the voltages across the two compare?

You have a cylindrical piece of material 2.4 cm long and 2.0 mm in diameter. When you attach a 9-V battery to its ends, a 2.6-mA current flows. Which material from Table 24.1 do you have?

How must the diameters of copper and aluminum wire be related if theyre to have the same resistance per unit length?

Youre writing the instruction manual for a power saw, and you have to specify the maximum permissible length for an extension cord made from 18-gauge copper wire (diameter 1.0 mm). The saw draws 7.0 A and needs a minimum of 115 V across its motor when the outlet supplies 120 V. What do you specify for the maximum length extension cord, given that they come in 25-foot increments?

An implanted pacemaker supplies the heart with 72 pulses per minute, each pulse providing 6.0 V for 0.65 ms. The resistance of the heart muscle between the pacemakers electrodes is 550 . Find (a) the current that flows during a pulse, (b) the energy delivered in one pulse, and (c) the average power supplied by the pacemaker.

A solid rectangular iron bar measures 0.50 cm by 1.0 cm by 20 cm. Find the resistance between each of the three pairs of opposing faces, assuming the faces in question are equipotentials.

Each pulse produced by the Taser described in the Application on page 449 typically delivers 100 C of charge to the victim. Use this value, along with other quantities given in the Application, to find (a) the instantaneous current during a pulse, (b) the average current, and (c) the effective resistance of the victim between the points where the probes make contact.

The Nissan Leaf is an all-electric car powered by a 107-hp electric motor and a lithium-ion battery that stores 24 kWh and produces 394 V at its terminals when fully charged. The Leafs battery can charge at the rate of 3.3 kW from a standard 120-V power outlet, at 6.6 kW from a 240-V outlet, and at 44 kW using a special 480-V charger. The Leafs fuel economy is 3.38 miles per kWh, the equivalent of 114 miles per gallon in a gasolinepowered car. Find (a) the range of the Leaf, assuming the battery can be fully depleted, (b) the charging time for each mode, and (c) the current delivered by the fully charged battery when the motor is operating at full power.

An electric heater is tested by immersing it in 0.500 kg of water and measuring the time t it takes to raise the water temperature by 10.0C. The experiment is repeated for different currents I through the heater, and the results are tabulated below. Determine two quantities, based on heating time and current, which, when plotted, will give a straight line. Make your plot, determine a best-fit line, and use it to find the heaters resistance. Hint: You may need to consult Chapter 16.

Magnetic effects involving Jupiters moon Io result in an effective voltage of about 400 kV, which drives current of some 5 MA between Io and Jupiters polar regions. At Jupiter the current produces auroras analogous to those on Earth, as well as powerful bursts of radio waves that help radio astronomers analyze the Jovian current system. Estimate the total power associated with this current system, and compare with the 2-TW rate at which humankind consumes electrical energy.

At a particular point in a material with resistivity r the current density has magnitude J. Show that the power per unit volume dissipated at this point is J2 r

A thermally insulated container of seawater carries a uniform current density of 75 mA/cm2 . How long does it take for its temperature to increase from 15C to 20C? Use the result of the preceding problem and any other information you might look up.

Youre heading out for spring break, but your car wont start. Your friend says you might have corrosion at the battery terminalsa frequent cause of hard starting because of increased resistance. Having read Example 24.4, you know that the resistance between battery and starter should be around 1 m. While your friend cranks the starter, you measure 4.2 V between the battery terminal and the wire carrying current to the starter motor. If the motor draws 125 A, is the resistance in its normal range?

Two cylindrical resistors are made from the same material and have the same length. When connected across the same battery, one dissipates twice as much power as the other. How do their diameters compare?

Youre working on a new high-speed rail system. It uses 6000-horsepower electric locomotives, getting power from a single overhead wire with resistance 15 m/km, at 25 kV potential relative to the track. Current returns through the track, whose resistance is negligible. Energy-efficiency standards call for no more than 3% power loss in the wire. How far from the power plant can the train go and still meet this standard?

A 100%-efficient electric motor is lifting a 15-N weight at 25 cm/s. How much current does it draw from a 6.0-V battery?

A power plant produces 1000 MW to supply a city 40 km away. Current flows from the power plant on a single wire with resistance 50 m/km, through the city, and returns via the ground, which has negligible resistance. At the power plant the voltage between wire and ground is 115 kV. Find (a) the current in the wire and (b) the fraction of the power lost in transmission.

Youre estimating costs for a new power line with your companys financial group. Engineering specifies a resistance per unit length of 50 m/km. The costs of copper and aluminum wire are $4.65/kg and $2.30/kg and their densities are 8.9 g/cm3 and 2.7 g/cm3 , respectively. Which material is more economical?

A 240-V electric motor is 90% efficient, meaning that 90% of the energy supplied to it ends up as mechanical work. If the motor lifts a 200-N weight at 3.1 m/s, how much current does it draw?

A metal bar has rectangular cross section 5.0 cm by 10 cm, as shown in Fig. 24.18. The bar has a nonuniform conductivity, and as a result the current density increases linearly from zero at the bottom to 0.10 A/cm2 at the top. Find the total current in the bar.

An immersion-type heating coil is connected to a 120-V outlet and immersed in a 250-mL cup of water initially at 10C. The water comes to a boil in 85 s. Assuming no heat loss, and neglecting the heaters mass, find (a) the power and (b) the heaters resistance.

The resistivity of copper as a function of temperature is given approximately by r = r0 31 + a1T - T024, where r0 is Table 24.1s entry for 20C, T0 = 20C, and a = 4.3*10-3 C-1 . Find the temperature at which coppers resistivity is twice its roomtemperature value

Each atom in aluminum contributes about 3.5 conduction electrons. Find the drift speed in a 2.1-mm-diameter aluminum wire carrying 20 A.

A circular pan of radius b has a plastic bottom and metallic sidewall of height h. Its filled with a solution of resistivity r. A metal disk of radius a and height h is at the center, as shown in Fig. 24.19. The side and disk are essentially perfect conductors. Show that the resistance measured from side to disk is R = r ln 1b/a2/2ph.

Figure 24.20 shows a truncated cone of material with resistivity r. Assume the equipotentials are planes parallel to the two faces, and integrate over slices of thickness dx like the one shown to find an expression for the total resistance between the faces.

The current density in a particle beam with circular cross section of radius a points along the beam axis with a magnitude that decreases linearly from J0 at the center 1r = 02 to half that value at the edge 1r = a2. Find an expression for the total current in the beam.

A cylindrical resistor is 5.0 mm in diameter and 1.5 cm long. Its made of a composite material whose resistivity varies from one end to the other according to the equation r = r011 + x/L2ex/L , for 0 x L, where r0 = 2.41 * 10-3 # m. Find its resistance

You work for an automobile manufacturer developing a new plug-in hybrid car. The cars mass is 1200 kg, and it uses a 360-V battery driving an electric motor that can handle a maximum current of 180 A. Youre to specify the greatest slope the car can climb, maintaining 60 km/h, without its gasoline engine coming on to assist.

A brownout occurs when an electric utility cant supply enough power to meet demand. Rather than cut off some customers completely, the utility reduces the voltage across its system. Brownouts are most likely on hot summer days, when heavy air-conditioning loads drive up demand for electricity. In a particular brownout, the utility reduces the voltage by 10%. During the brownout, the current in conductors whose resistance is nearly independent of temperature a. decreases by approximately 10%. b. decreases by approximately 20%. c. decreases by approximately 5%. d. You cant tell without knowing the resistance.

A brownout occurs when an electric utility cant supply enough power to meet demand. Rather than cut off some customers completely, the utility reduces the voltage across its system. Brownouts are most likely on hot summer days, when heavy air-conditioning loads drive up demand for electricity. In a particular brownout, the utility reduces the voltage by 10%. Which of the following occurs in the conductors of the preceding problem during the brownout? a. Both the electric field and electron drift speed decrease. b. The electric field decreases but the electron drift speed doesnt. c. The current is carried by fewer electrons. d. The electrons undergo more frequent collisions

A brownout occurs when an electric utility cant supply enough power to meet demand. Rather than cut off some customers completely, the utility reduces the voltage across its system. Brownouts are most likely on hot summer days, when heavy air-conditioning loads drive up demand for electricity. In a particular brownout, the utility reduces the voltage by 10%. During the brownout, the power dissipated in conductors whose resistance is nearly independent of temperature a. decreases by approximately 10%. b. decreases by approximately 20%. c. decreases by approximately 5%. d. You cant tell without knowing the resistance.

A brownout occurs when an electric utility cant supply enough power to meet demand. Rather than cut off some customers completely, the utility reduces the voltage across its system. Brownouts are most likely on hot summer days, when heavy air-conditioning loads drive up demand for electricity. In a particular brownout, the utility reduces the voltage by 10%. Metallic conductors like lightbulb filaments and electric stove burners have resistance that increases with increasing temperature. During the brownout, the current in such devices a. decreases by 10%. b. decreases by more than 10%. c. decreases by less than 10%. d. You cant tell without knowing more about how the resistance varies.