Solved: What is the required resistance of an immersion

A wire carries a current of 1.6 A. How many electrons per second pass a given point in the wire? Choose the best estimate. (a) 1017 (b) 1018 (c) 1019 (d) 1020 (e) 1021

Wire A has the same length and twice the radius of wire B. Both wires are made of the same material and carry the same current. Which of the following equations is true concerning the drift velocities vA and vB of electrons in the wires? (a) vA _ 2vB (b) vA _ vB (c) vA _ vB/2 (d) vA _ 4vB (e) vA _ vB/4

Wire B has the same resistivity, twice the length, and twice the radius of wire A. If wire A has a resistance R, what is the resistance of wire B? (a) 4R (b) 2R (c) R (d) R/2 (e) R/4

Three wires are made of copper having circular cross sections. Wire 1 has a length L and radius r. Wire 2 has a length L and radius 2r. Wire 3 has a length 2L and radius 3r. Which wire has the smallest resistance? (a) wire 1 (b) wire 2 (c) wire 3 (d) All three wires have the same resistance. (e) Not enough information is given to answer the question.

Which of the following combinations of units has units of energy? (a) C/s (b) kWh (c) kW (d) A h (e) W/s

The current versus voltage behavior of a certain electrical device is shown in Figure MCQ17.6. When the potential difference across the device is 2 V, what is the resistance? (a) 1 _ (b) 34 V (c) 4 3 V (d) undefi ned (e) none of these

The current vs. voltage behavior of a certain electrical device is shown in Figure MCQ17.6. When the potential difference across the device is 3 V, what is the resistance? (a) 0.83 _ (b) 1.2 _ (c) 3.0 _ (d) 1.33 _ (e) 2.3 _

A metal wire has a resistance of 10.00 _ at a temperature of 20.0C. If the same wire has a resistance of 10.55 _ at 90.0C, what is the resistance of this same wire when its temperature is _20C? (a) 0.700 _ (b) 9.69 _ (c) 10.3 _ (d) 13.8 _ (e) 6.59 _

A color television set draws about 2.5 A when connected to a 120 V source. What is the cost (with electrical energy at 8 cents/kWh) of running the set for 8.0 hours? (a) 2.0 cents (b) 4.0 cents (c) 19 cents (d) 40 cents (e) 62 cents

A potential difference of 1.0 V is maintained across a 10.0-_ resistor for a period of 20 s. What total charge passes through the wire in this time interval? (a) 200 C (b) 20 C (c) 2 C (d) 0.005 C (e) 0.05 C

Three resistors, A, B, and C, are connected in parallel and attached to a battery, with the resistance of A being the smallest and the resistance of C the greatest. Which resistor carries the highest current? (a) A (b) B (c) C (d) All wires carry the same current. (e) More information is needed to answer the question.

Three resistors, A, B, and C, are connected in series in a closed loop with a battery, with the resistance of A being the smallest and the resistance of C the greatest. Across which resistor is the voltage drop the greatest? (a) A (b) B (c) C (d) The voltage drops are the same for each. (e) More information is needed to answer the question.

The power delivered to a resistor is 4.0 W when a certain voltage is applied across it. How much power is delivered to the resistor when the voltage is doubled? (a) 2.0 W (b) 4.0 W (c) 8.0 W (d) 16 W (e) 32 W

Car batteries are often rated in ampere-hours. Does this unit designate the amount of current, power, energy, or charge that can be drawn from the battery?

We have seen that an electric fi eld must exist inside a conductor that carries a current. How is that possible in view of the fact that in electrostatics we concluded that the electric fi eld must be zero inside a conductor?

Why dont the free electrons in a metal fall to the bottom of the metal due to gravity? And charges in a conductor are supposed to reside on the surface; why dont the free electrons all go to the surface?

In an analogy between traffi c fl ow and electrical current, what would correspond to the charge Q? What would correspond to the current I ?

Newspaper articles often have statements such as 10 000 volts of electricity surged through the victims body. What is wrong with this statement?

Two lightbulbs are each connected to a voltage of 120 V. One has a power of 25 W, the other 100 W. Which lightbulb has the higher resistance? Which lightbulb carries more current?

When the voltage across a certain conductor is doubled, the current is observed to triple. What can you conclude about the conductor?

There is an old admonition given to experimenters to keep one hand in the pocket when working around high voltages. Why is this warning a good idea?

When is more power delivered to a lightbulb, immediately after it is turned on and the glow of the fi lament is increasing or after it has been on for a few seconds and the glow is steady?

Some homes have light dimmers that are operated by rotating a knob. What is being changed in the electric circuit when the knob is rotated?

What could happen to the drift velocity of the electrons in a wire and to the current in the wire if the electrons could move through it freely without resistance?

Use the atomic theory of matter to explain why the resistance of a material should increase as its temperature increases.

If a current of 80.0 mA exists in a metal wire, how many electrons fl ow past a given cross section of the wire in 10.0 min? In what direction do the electrons travel with respect to the current?

A copper wire has a circular cross section with a radius of 1.25 mm. (a) If the wire carries a current of 3.70 A, fi nd the drift speed of the electrons in the wire. (See Example 17.2 for relevant data on copper.) (b) All other things being equal, what happens to the drift speed in wires made of metal having a larger number of conduction electrons per atom than copper? Explain.

In the Bohr model of the hydrogen atom, an electron in the lowest energy state moves at a speed of 2.19 _ 106 m/s in a circular path having a radius of 5.29 _ 10_11 m. What is the effective current associated with this orbiting electron?

A proton beam in an accelerator carries a current of 125 mA. If the beam is incident on a target, how many protons strike the target in a period of 23.0 s?

If the current carried by a conductor is doubled, what happens to (a) the charge carrier density? (b) The electron drift velocity?

If 3.25 _ 10_3 kg of gold is deposited on the negative electrode of an electrolytic cell in a period of 2.78 h, what is the current in the cell during that period? Assume the gold ions carry one elementary unit of positive charge.

A 200-km-long high-voltage transmission line 2.0 cm in diameter carries a steady current of 1 000 A. If the conductor is copper with a free charge density of 8.5 _ 1028 electrons per cubic meter, how many years does it take one electron to travel the full length of the cable?

An aluminum wire carrying a current of 5.0 A has a crosssectional area of 4.0 _ 10_6 m2. Find the drift speed of the electrons in the wire. The density of aluminum is 2.7 g/cm3. (Assume three electrons are supplied by each atom.)

An iron wire has a cross-sectional area of 5.00 _ 10_6 m2. Carry out steps (a) through (e) to compute the drift speed of the conduction electrons in the wire. (a) How many kilograms are there in 1 mole of iron? (b) Starting with the density of iron and the result of part (a), compute the molar density of iron (the number of moles of iron per cubic meter). (c) Calculate the number density of iron atoms using Avogadros number. (d) Obtain the number density of conduction electrons given that there are two conduction electrons per iron atom. (e) If the wire carries a current of 30.0 A, calculate the drift speed of conduction electrons.

An electric heater carries a current of 13.5 A when operating at a voltage of 1.20 _ 102 V. What is the resistance of the heater?

A person notices a mild shock if the current along a path through the thumb and index fi nger exceeds 80 mA. Compare the maximum possible voltage without shock across the thumb and index fi nger with a dry-skin resistance of 4.0 _ 105 _ and a wet-skin resistance of 2 000 _.

Suppose you wish to fabricate a uniform wire out of 1.00 g of copper. If the wire is to have a resistance R _ 0.500 _, and if all the copper is to be used, what will be (a) the length and (b) the diameter of the wire?

Nichrome wire of cross-sectional radius 0.791 mm is to be used in winding a heating coil. If the coil must carry a current of 9.25 A when a voltage of 1.20 _ 102 V is applied across its ends, fi nd (a) the required resistance of the coil and (b) the length of wire you must use to wind the coil.

Eighteen-gauge wire has a diameter of 1.024 mm. Calculate the resistance of 15 m of 18-gauge copper wire at 20C.

A potential difference of 12 V is found to produce a current of 0.40 A in a 3.2-m length of wire with a uniform radius of 0.40 cm. What is (a) the resistance of the wire? (b) The resistivity of the wire?

Aluminum and copper wires of equal length are found to have the same resistance. What is the ratio of their radii?

A wire 50.0 m long and 2.00 mm in diameter is connected to a source with a potential difference of 9.11 V, and the current is found to be 36.0 A. Assume a temperature of 20C and, using Table 17.1, identify the metal out of which the wire is made.

A rectangular block of copper has sides of length 10 cm, 20 cm, and 40 cm. If the block is connected to a 6.0-V source across two of its opposite faces, what are (a) the maximum current and (b) the minimum current the block can carry?

A wire of initial length L0 and radius r0 has a measured resistance of 1.0 _. The wire is drawn under tensile stress to a new uniform radius of r _ 0.25r0. What is the new resistance of the wire?

The human body can exhibit a wide range of resistances to current depending on the path of the current, contact area, and sweatiness of the skin. Suppose the resistance across the chest from the left hand to the right hand is 1.0 _ 106 _. (a) How much voltage is required to cause possible heart fi brillation in a man, which corresponds to 500 mA of direct current? (b) Why should rubber-soled shoes and rubber gloves be worn when working around electricity?

Starting from Ohms law, show that E _ Jr, where E is the magnitude of the electric fi eld (assumed constant) and J _ I/A is called the current density. The result is in fact true in general.

If a certain silver wire has a resistance of 6.00 _ at 20.0C, what resistance will it have at 34.0C?

While taking photographs in Death Valley on a day when the temperature is 58.0C, Bill Hiker fi nds that a certain voltage applied to a copper wire produces a current of 1.000 A. Bill then travels to Antarctica and applies the same voltage to the same wire. What current does he register there if the temperature is _88.0C? Assume no change occurs in the wires shape and size.

A length of aluminum wire has a resistance of 30.0 _ at 20.0C. When the wire is warmed in an oven and reaches thermal equilibrium, the resistance of the wire increases to 46.2 _ (a) Neglecting thermal expansion, fi nd the temperature of the oven. (b) Qualitatively, how would thermal expansion be expected to affect the answer?

A certain lightbulb has a tungsten fi lament having a resistance of 15 _ at 20C and 160 _ when hot. Assume Equation 17.7 can be used over the large temperature range here. Find the temperature of the fi lament when it is hot.

At what temperature will aluminum have a resistivity that is three times the resistivity of copper at room temperature?

At 20C, the carbon resistor in an electric circuit connected to a 5.0-V battery has a resistance of 2.0 _ 102 _. What is the current in the circuit when the temperature of the carbon rises to 80C?

A wire 3.00 m long and 0.450 mm2 in cross-sectional area has a resistance of 41.0 _ at 20C. If its resistance increases to 41.4 _ at 29.0C, what is the temperature coeffi cient of resistivity?

(a) A 34.5-m length of copper wire at 20.0C has a radius of 0.25 mm. If a potential difference of 9.0 V is applied across the length of the wire, determine the current in the wire. (b) If the wire is heated to 30.0C while the 9.0-V potential difference is maintained, what is the resulting current in the wire?

A toaster rated at 1 050 W operates on a 120-V household circuit and a 4.00-m length of Nichrome wire as its heating element. The operating temperature of this element is 320C. What is the cross-sectional area of the wire?

In one form of plethysmograph (a device for measuring volume), a rubber capillary tube with an inside diameter of 1.00 mm is fi lled with mercury at 20C. The resistance of the mercury is measured with the aid of electrodes sealed into the ends of the tube. If 100.00 cm of the tube is wound in a spiral around a patients upper arm, the blood fl ow during a heartbeat causes the arm to expand, stretching the tube to a length of 100.04 cm. From this observation, and assuming cylindrical symmetry, you can fi nd the change in volume of the arm, which gives an indication of blood fl ow. (a) Calculate the resistance of the mercury. (b) Calculate the fractional change in resistance during the heartbeat. (Hint: The fraction by which the cross-sectional area of the mercury thread decreases is the fraction by which the length increases, since the volume of mercury is constant.) Take rHg _ 9.4 _ 10_7 _ m.

A platinum resistance thermometer has resistances of 200.0 _ when placed in a 0C ice bath and 253.8 _ when immersed in a crucible containing melting potassium. What is the melting point of potassium? (Hint: First determine the resistance of the platinum resistance thermometer at room temperature, 20C.)

Suppose your waffl e iron is rated at 1.00 kW when connected to a 1.20 _ 102 V source. (a) What current does the waffl e iron carry? (b) What is its resistance?

If electrical energy costs 12 cents, or $0.12, per kilowatthour, how much does it cost to (a) burn a 100-W lightbulb for 24 h? (b) Operate an electric oven for 5.0 h if it carries a current of 20.0 A at 220 V?

A certain compact disc player draws a current of 350 mA at 6.0 V. How much power is required to operate the player?

A high-voltage transmission line with a resistance of 0.31 _/km carries a current of 1 000 A. The line is at a potential of 700 kV at the power station and carries the current to a city located 160 km from the station. (a) What is the power loss due to resistance in the line? (b) What fraction of the transmitted power does this loss represent?

The heating element of a coffeemaker operates at 120 V and carries a current of 2.00 A. Assuming the water absorbs all the energy converted by the resistor, calculate how long it takes to heat 0.500 kg of water from room temperature (23.0C) to the boiling point.

The power supplied to a typical black-and-white television set is 90 W when the set is connected to 120 V. (a) How much electrical energy does this set consume in 1 hour? (b) A color television set draws about 2.5 A when connected to 120 V. How much time is required for it to consume the same energy as the black-and-white model consumes in 1 hour?

What is the required resistance of an immersion heater that will increase the temperature of 1.50 kg of water from 10.0C to 50.0C in 10.0 min while operating at 120 V?

A certain toaster has a heating element made of Nichrome resistance wire. When the toaster is fi rst connected to a 120-V source of potential difference (and the wire is at a temperature of 20.0C), the initial current is 1.80 A but the current begins to decrease as the resistive element warms up. When the toaster reaches its fi nal operating temperature, the current has dropped to 1.53 A. (a) Find the power the toaster converts when it is at its operating temperature. (b) What is the fi nal temperature of the heating element?

A copper cable is designed to carry a current of 300 A with a power loss of 2.00 W/m. What is the required radius of this cable?

Batteries are rated in terms of ampere-hours (A h). For example, a battery that can deliver a current of 3.0 A for 5.0 h is rated at 15 A h. (a) What is the total energy, in kilowatt-hours, stored in a 12 V battery rated at 55 A h? (b) At $0.12 per kilowatt-hour, what is the value of the electricity that can be produced by this battery?

The potential difference across a resting neuron is about 75 mV and carries a current of about 0.20 mA. How much power does the neuron release?

The cost of electricity varies widely throughout the United States; $0.120/kWh is a typical value. At this unit price, calculate the cost of (a) leaving a 40.0-W porch light on for 2 weeks while you are on vacation, (b) making a piece of dark toast in 3.00 min with a 970-W toaster, and (c) drying a load of clothes in 40.0 min in a 5 200-W dryer.

An 11-W energy-effi cient fl uorescent lamp is designed to produce the same illumination as a conventional 40-W lamp. How much does the energy-effi cient lamp save during 100 hours of use? Assume a cost of $0.080/kWh for electrical energy.

An offi ce worker uses an immersion heater to warm 250 g of water in a light, covered, insulated cup from 20C to 100C in 4.00 minutes. The heater is a Nichrome resistance wire connected to a 120-V power supply. Assume the wire is at 100C throughout the 4.00-min time interval. Specify a diameter and a length the wire can have. Can it be made from less than 0.5 cm3 of Nichrome?

The heating coil of a hot-water heater has a resistance of 20 _ and operates at 210 V. If electrical energy costs $0.080/kWh, what does it cost to raise the 200 kg of water in the tank from 15C to 80C? (See Chapter 11.)

A tungsten wire in a vacuum has length 15.0 cm and radius 1.00 mm. A potential difference is applied across it. (a) What is the resistance of the wire at 293 K? (b) Suppose the wire reaches an equilibrium temperature such that it emits 75.0 W in the form of radiation. Neglecting absorption of any radiation from its environment, what is the temperature of the wire? (Note: e _ 0.320 for tungsten.) (c) What is the resistance of the wire at the temperature found in part (b)? Assume the temperature changes linearly over this temperature range. (d) What voltage drop is required across the wire? (e) Why are tungsten lightbulbs energetically ineffi cient as light sources? ADDITIONAL PROBLEMS

If a battery is rated at 60.0 A h, how much total charge can it deliver before it goes dead?

A car owner forgets to turn off the headlights of his car while it is parked in his garage. If the 12-V battery in his car is rated at 90 A h and each headlight requires 36 W of power, how long will it take the battery to completely discharge?

An electronic device requires a power of 15 W when connected to a 9.0-V battery. How much power is delivered to the device if it is connected to a 6.0-V battery? (Neglect the resistances of the batteries and assume the resistance of the device does not change.)

Determine the temperature at which the resistance of an aluminum wire will be twice its value at 20C. (Assume its coeffi cient of resistivity remains constant.)

A particular wire has a resistivity of 3.0 _ 10_8 _ m and a cross-sectional area of 4.0 _ 10_6 m2. A length of this wire is to be used as a resistor that will develop 48 W of power when connected across a 20-V battery. What length of wire is required?

Birds resting on high-voltage power lines are a common sight. The copper wire on which a bird stands is 2.2 cm in diameter and carries a current of 50 A. If the birds feet are 4.0 cm apart, calculate the potential difference across its body.

An experiment is conducted to measure the electrical resistivity of Nichrome in the form of wires with different lengths and cross-sectional areas. For one set of measurements, a student uses 30-gauge wire, which has a crosssectional area of 7.30 _ 10_8 m2. The student measures the potential difference across the wire and the current in the wire with a voltmeter and an ammeter, respectively. For each of the measurements given in the following table taken on wires of three different lengths, calculate the resistance of the wires and the corresponding value of the resistivity. L (m) _V (V) I (A) R (_) R (_ m) 0.540 5.22 0.500 1.028 5.82 0.276 1.543 5.94 0.187 What is the average value of the resistivity, and how does this value compare with the value given in Table 17.1?

A carbon wire and a Nichrome wire are connected one after the other. If the combination has a total resistance of 10.0 k_ at 20C, what is the resistance of each wire at 20C so that the resistance of the combination does not change with temperature?

You are cooking breakfast for yourself and a friend using a 1 200-W waffl e iron and a 500-W coffeepot. Usually, you operate these appliances from a 110-V outlet for 0.500 h each day. (a) At 12 cents per kWh, how much do you spend to cook breakfast during a 30.0-day period? (b) You fi nd yourself addicted to waffl es and would like to upgrade to a 2 400-W waffl e iron that will enable you to cook twice as many waffl es during a half-hour period, but you know that the circuit breaker in your kitchen is a 20-A breaker. Can you do the upgrade?

The current in a conductor varies in time as shown in Figure P17.58. (a) How many coulombs of charge pass through a cross section of the conductor in the interval from t _ 0 to t _ 5.0 s? (b) What constant current would transport the same total charge during the 5.0-s interval as does the actual current?

An electric car is designed to run off a bank of 12.0-V batteries with a total energy storage of 2.00 _ 107 J. (a) If the electric motor draws 8.00 kW, what is the current delivered to the motor? (b) If the electric motor draws 8.00 kW as the car moves at a steady speed of 20.0 m/s, how far will the car travel before it is out of juice?

(a) A 115-g mass of aluminum is formed into a right circular cylinder, shaped so that its diameter equals its height. Calculate the resistance between the top and bottom faces of the cylinder at 20C. (b) Calculate the resistance between opposite faces if the same mass of aluminum is formed into a cube.

A length of metal wire has a radius of 5.00 _ 10_3 m and a resistance of 0.100 _. When the potential difference across the wire is 15.0 V, the electron drift speed is found to be 3.17 _ 10_4 m/s. On the basis of these data, calculate the density of free electrons in the wire.

In a certain stereo system, each speaker has a resistance of 4.00 _. The system is rated at 60.0 W in each channel. Each speaker circuit includes a fuse rated at a maximum current of 4.00 A. Is this system adequately protected against overload?

A resistor is constructed by forming a material of resistivity 3.5 _ 105 _ _ m into the shape of a hollow cylinder of length 4.0 cm and inner and outer radii 0.50 cm and 1.2 cm, respectively. In use, a potential difference is applied between the ends of the cylinder, producing a current parallel to the length of the cylinder. Find the resistance of the cylinder.

A 50.0-g sample of a conducting material is all that is available. The resistivity of the material is measured to be 11 _ 10_8 _ _ m, and the density is 7.86 g/cm3. The material is to be shaped into a solid cylindrical wire that has a total resistance of 1.5 _. (a) What length of wire is required? (b) What must be the diameter of the wire?

An x-ray tube used for cancer therapy operates at 4.0 MV, with a beam current of 25 mA striking the metal target. Nearly all the power in the beam is transferred to a stream of water fl owing through holes drilled in the target. What rate of fl ow, in kilograms per second, is needed if the rise in temperature (_T) of the water is not to exceed 50C?

When a straight wire is heated, its resistance changes according to the equation R _ R0[1 _ (T _ T0)] (Eq. 17.7), where is the temperature coeffi cient of resistivity. (a) Show that a more precise result, which includes the length and area of a wire change when it is heated, is R 5 R0 31 1 a1T 2 T02 4 31 1 ar 1T 2 T0 2 4 31 1 2ar 1T 2 T02 4 where is the coeffi cient of linear expansion. (See Chapter 10.) (b) Compare the two results for a 2.00-m-long copper wire of radius 0.100 mm, starting at 20.0C and heated to 100.0C.

A man wishes to vacuum his car with a canister vacuum cleaner marked 535 W at 120 V. The car is parked far from the building, so he uses an extension cord 15.0 m long to plug the cleaner into a 120-V source. Assume the cleaner has constant resistance. (a) If the resistance of each of the two conductors of the extension cord is 0.900 _, what is the actual power delivered to the cleaner? (b) If, instead, the power is to be at least 525 W, what must be the diameter of each of two identical copper conductors in the cord the young man buys? (c) Repeat part (b) if the power is to be at least 532 W. (Suggestion: A symbolic solution can simplify the calculations.)