College Physics

Raymond A. Serway, Jerry S. Faughn, Chris Vuille

Chapter 17

Current and Resistance - all with Video Answers

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Chapter Questions

Problem 1

If a current of $80.0 \mathrm{~mA}$ exists in a metal wire, how many electrons flow past a given cross section of the wire in $10.0$ min? In what direction do the electrons travel with respect to the current?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 2

A copper wire has a circular cross section with a radius of $1.25 \mathrm{~mm} .$ (a) If the wire carries a current of $3.70 \mathrm{~A}$, find 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.

Sheh Lit Chang

University of Washington

Problem 3

In the Bohr model of the hydrogen atom, an electron in the lowest energy state moves at a speed of $2.19 \times 10^{6} \mathrm{~m} / \mathrm{s}$ in a circular path having a radius of $5.29 \times 10^{-11} \mathrm{~m}$. What is the effective current associated with this orbiting electron?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 4

A proton beam in an accelerator carries a current of $125 \mu \mathrm{A} .$ If the beam is incident on a target, how many protons strike the target in a period of $23.0 \mathrm{~s}$ ?

Kayla Gephart

Numerade Educator

Problem 5

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

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 6

If $3.25 \times 10^{-3} \mathrm{~kg}$ of gold is deposited on the negative electrode of an electrolytic cell in a period of $2.78 \mathrm{~h}$, what is the current in the cell during that period? Assume the gold ions carry one elementary unit of positive charge.

Ivan Kochetkov

Numerade Educator

Problem 7

A 200-km-long high-voltage transmission line $2.0 \mathrm{~cm}$ in diameter carries a steady current of $1000 \mathrm{~A}$. If the conductor is copper with a free charge density of $8.5 \times$ $10^{28}$ electrons per cubic meter, how many years does it take one electron to travel the full length of the cable?

Supratim Pal

Numerade Educator

Problem 8

An aluminum wire carrying a current of $5.0 \mathrm{~A}$ has a crosssectional area of $4.0 \times 10^{-6} \mathrm{~m}^{2}$. Find the drift speed of the electrons in the wire. The density of aluminum is $2.7 \mathrm{~g} / \mathrm{cm}^{3} .$ (Assume three electrons are supplied by each atom.)

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 9

An iron wire has a cross-sectional area of $5.00 \mathrm{x}$ $10^{-6} \mathrm{~m}^{2} .$ 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 Avogadro's 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 $30.0 \mathrm{~A}$, calculate the drift speed of conduction electrons.

Sheh Lit Chang

University of Washington

Problem 10

An electric heater carries a current of $13.5 \mathrm{~A}$ when operating at a voltage of $1.20 \times 10^{2} \mathrm{~V}$. What is the resistance of the heater?

Mayukh Banik

Numerade Educator

Problem 11

A person notices a mild shock if the current along a path through the thumb and index finger exceeds $80 \mu \mathrm{A}$. Compare the maximum possible voltage without shock across the thumb and index finger with a dry-skin resistance of $4.0 \times 10^{5} \Omega$ and a wet-skin resistance of $2000 \Omega$.

Sheh Lit Chang

University of Washington

Problem 12

Suppose you wish to fabricate a uniform wire out of $1.00 \mathrm{~g}$, of copper. If the wire is to have a resistance $R=0.500 \Omega$, and if all the copper is to be used, what will be (a) the length and (b) the diameter of the wire?

Mayukh Banik

Numerade Educator

Problem 13

Nichrome wire of cross-sectional radius $0.791 \mathrm{~mm}$ is to be used in winding a heating coil. If the coil must carry a current of $9.25 \mathrm{~A}$ when a voltage of $1.20 \times 10^{2} \mathrm{~V}$ is applied across its ends, find (a) the required resistance of the coil and (b) the length of wire you must use to wind the coil.

Salamat Ali

Numerade Educator

Problem 14

Eighteen-gauge wire has a diameter of $1.024 \mathrm{~mm}$. Calculate the resistance of $15 \mathrm{~m}$ of 18 -gauge copper wire at $20^{\circ} \mathrm{C} .$

Sheh Lit Chang

University of Washington

Problem 15

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

Salamat Ali

Numerade Educator

Problem 16

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

Kayla Gephart

Numerade Educator

Problem 17

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

Salamat Ali

Numerade Educator

Problem 18

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

Mayukh Banik

Numerade Educator

Problem 19

A wire of initial length $L_{0}$ and radius $r_{0}$ has a measured resistance of $1.0 \Omega$. The wire is drawn under tensile stress to a new uniform radius of $r=0.25 r_{0}$. What is the new resistance of the wire?

Ivan Kochetkov

Numerade Educator

Problem 20

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 $1.0 \times 10^{6} \Omega$. (a) How much voltage is required to cause possible heart fibrillation in a man, which corresponds to $500 \mathrm{~mA}$ of direct current? (b) Why should rubber-soled shoes and rubber gloves be worn when working around electricity?

Sheh Lit Chang

University of Washington

Problem 21

Starting from Ohm's law, show that $E=J \rho$, where $E$ is the magnitude of the electric field (assumed constant) and $J=I / A$ is called the current density. The result is in fact true in general.

Salamat Ali

Numerade Educator

Problem 22

If a certain silver wire has a resistance of $6.00 \Omega$ at $20.0^{\circ} \mathrm{C}$, what resistance will it have at $34.0^{\circ} \mathrm{C}$ ?

Kayla Gephart

Numerade Educator

Problem 23

While taking photographs in Death Valley on a day when the temperature is $58.0^{\circ} \mathrm{C}$, Bill Hiker finds that a certain voltage applied to a copper wire produces a current of $1.000 \mathrm{~A}$. Bill then travels to Antarctica and applies the same voltage to the same wire. What current does he register there if the temperature is $-88.0^{\circ} \mathrm{C}$ ? Assume no change occurs in the wire's shape and size.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 24

A length of aluminum wire has a resistance of $30.0 \Omega$ at $20.0^{\circ} \mathrm{C}$. When the wire is warmed in an oven and reaches thermal equilibrium, the resistance of the wire increases to $46.2 \Omega$ (a) Neglecting thermal expansion, find the temperature of the oven. (b) Qualitatively, how would thermal expansion be expected to affect the answer?

Sheh Lit Chang

University of Washington

Problem 25

A certain lightbulb has a tungsten filament having a resistance of $15 \Omega$ at $20^{\circ} \mathrm{C}$ and $160 \Omega$ when hot. Assume Equation $17.7$ can be used over the large temperature range here. Find the temperature of the filament when it is hot.

Sheh Lit Chang

University of Washington

Problem 26

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

Mayukh Banik

Numerade Educator

Problem 27

At $20^{\circ} \mathrm{C}$, the carbon resistor in an electric circuit connected to a $5.0-V$ battery has a resistance of $2.0 \times 10^{2} \Omega$. What is the current in the circuit when the temperature of the carbon rises to $80^{\circ} \mathrm{C}$ ?

Salamat Ali

Numerade Educator

Problem 28

A wire $3.00 \mathrm{~m}$ long and $0.450 \mathrm{~mm}^{2}$ in cross-sectional area has a resistance of $41.0 \Omega$ at $20^{\circ} \mathrm{C}$. If its resistance increases to $41.4 \Omega$ at $29.0^{\circ} \mathrm{C}$, what is the temperature coefficient of resistivity?

Sheh Lit Chang

University of Washington

Problem 29

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

Salamat Ali

Numerade Educator

Problem 30

A toaster rated at $1050 \mathrm{~W}$ operates on a $120-\mathrm{V}$ household circuit and a $4.00-\mathrm{m}$ length of Nichrome wire as its heating element. The operating temperature of this element is $320^{\circ} \mathrm{C}$. What is the cross-sectional area of the wire?

Vishal Gupta

Numerade Educator

Problem 31

In one form of plethysmograph (a device for measuring volume), a rubber capillary tube with an inside diameter of $1.00 \mathrm{~mm}$ is filled with mercury at $20^{\circ} \mathrm{C}$. The resistance of the mercury is measured with the aid of electrodes sealed into the ends of the tube. If $100.00 \mathrm{~cm}$ of the tube is wound in a spiral around a patient's upper arm, the blood flow during a heartbeat causes the arm to expand, stretching the tube to a length of $100.04 \mathrm{~cm}$. From this observation, and assuming cylindrical symmetry, you can find the change in volume of the arm, which gives an indication of blood flow. (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 $\rho_{\mathrm{Hg}}=$ $9.4 \times 10^{-7} \Omega \cdot \mathrm{m}$

Eduard Sanchez

Numerade Educator

Problem 32

A platinum resistance thermometer has resistances of $200.0 \Omega$ when placed in a $0^{\circ} \mathrm{C}$ ice bath and $253.8 \Omega$ 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, $20^{\circ} \mathrm{C.}$.)

Sheh Lit Chang

University of Washington

Problem 33

Suppose your waffle iron is rated at $1.00 \mathrm{~kW}$ when connected to a $1.20 \times 10^{2} \mathrm{~V}$ source.
(a) What current does the waffle iron carry? (b) What is its resistance?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 34

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 $5.0 \mathrm{~h}$ if it carries a current of $20.0 \mathrm{~A}$ at $220 \mathrm{~V} ?$

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 35

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

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 36

A high-voltage transmission line with a resistance of $0.31 \Omega / \mathrm{km}$ carries a current of $1000 \mathrm{~A}$. The line is at a potential of $700 \mathrm{kV}$ at the power station and carries the current to a city located $160 \mathrm{~km}$ 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?

Sheh Lit Chang

University of Washington

Problem 37

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

Ivan Kochetkov

Numerade Educator

Problem 38

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

Sheh Lit Chang

University of Washington

Problem 39

What is the required resistance of an immersion heater that will increase the temperature of $1.50 \mathrm{~kg}$ of water from $10.0^{\circ} \mathrm{C}$ to $50.0^{\circ} \mathrm{C}$ in $10.0 \mathrm{~min}$ while operating at. $120 \mathrm{~V} ?$

Ivan Kochetkov

Numerade Educator

Problem 40

A certain toaster has a heating element made of Nichrome resistance wire. When the toaster is first connected to a $120-\mathrm{V}$ source of potential difference (and the wire is at a temperature of $20.0^{\circ} \mathrm{C}$ ), the initial current is $1.80 \mathrm{~A}$ but the current begins to decrease as the resistive element warms up. When the toaster reaches its final 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 final temperature of the heating element?

Mayukh Banik

Numerade Educator

Problem 41

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

Salamat Ali

Numerade Educator

Problem 42

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

Mayukh Banik

Numerade Educator

Problem 43

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

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 44

The cost of electricity varies widely throughout the United States; $\$ 0.120 / \mathrm{kWh}$ is a typical value. At this unit price, calculate the cost of (a) leaving a $40.0-\mathrm{W}$ porch light on for 2 weeks while you are on vacation, (b) making a piece of dark toast in $3.00$ min with a $970-\mathrm{W}$ toaster, and (c) drying a load of clothes in $40.0$ min in a $5200-\mathrm{W}$ dryer.

Sheh Lit Chang

University of Washington

Problem 45

An 11-W energy-efficient fluorescent lamp is designed to produce the same illumination as a conventional $40-\mathrm{W}$ lamp. How much does the energy-efficient lamp save during 100 hours of use? Assume a cost of $\$ 0.080 / \mathrm{kWh}$ for electrical energy.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 46

An office worker uses an immersion heater to warm $250 \mathrm{~g}$ of water in a light, covered, insulated cup from $20^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ in $4.00$ minutes. The heater is a Nichrome resistance wire connected to a $120-\mathrm{V}$ power supply. Assume the wire is at $100^{\circ} \mathrm{C}$ throughout the $4.00$ -min time interval. Specify a diameter and a length the wire can have. Can it be made from less than $0.5 \mathrm{~cm}^{3}$ of Nichrome?

Vidhi Bhatt

Numerade Educator

Problem 47

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

Sheh Lit Chang

University of Washington

Problem 48

A tungsten wire in a vacuum has length $15.0 \mathrm{~cm}$ and radius $1.00 \mathrm{~mm}$. A potential difference is applied across it. (a) What is the resistance of the wire at $293 \mathrm{~K}$ ? (b) Suppose the wire reaches an equilibrium temperature such that it emits $75.0 \mathrm{~W}$ 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 inefficient as light sources?

Eduard Sanchez

Numerade Educator

Problem 49

If a battery is rated at $60.0 \mathrm{~A} \cdot \mathrm{h}$, how much total charge can it deliver before it goes "dead"?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 50

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

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 51

An electronic device requires a power of $15 \mathrm{~W}$ 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.)

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 52

Determine the temperature at which the resistance of an aluminum wire will be twice its value at $20^{\circ} \mathrm{C}$. (Assume its coefficient of resistivity remains constant.)

Kayla Gephart

Numerade Educator

Problem 53

A particular wire has a resistivity of $3.0 \times 10^{-8} \Omega \cdot \mathrm{m}$ and a cross-sectional area of $4.0 \times 10^{-6} \mathrm{~m}^{2}$. A length of this wire is to be used as a resistor that will develop $48 \mathrm{~W}$ of power when connected across a 20-V battery. What length of wire is required?

Salamat Ali

Numerade Educator

Problem 54

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

Sheh Lit Chang

University of Washington

Problem 55

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 $7.30 \times 10^{-8} \mathrm{~m}^{2}$. 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.
$$
\begin{array}{lclll}
L(\mathbf{m}) & \Delta V(\mathbf{V}) & I(\mathbf{A}) & R(\Omega) & \rho(\Omega \cdot \mathbf{m}) \\
\hline 0.540 & 5.22 & 0.500 & & \\
1.028 & 5.82 & 0.276 & & \\
1.543 & 5.94 & 0.187 & & \\
\hline
\end{array}
$$
What is the average value of the resistivity, and how does this value compare with the value given in Table $17.1 ?$

Eduard Sanchez

Numerade Educator

Problem 56

A carbon wire and a Nichrome wire are connected one after the other. If the combination has a total resistance of $10.0 \mathrm{k} \Omega$ at $20^{\circ} \mathrm{C}$, what is the resistance of each wire at $20^{\circ} \mathrm{C}$ so that the resistance of the combination does not change with temperature?

Sheh Lit Chang

University of Washington

Problem 57

You are cooking breakfast for yourself and a friend using a $1200-\mathrm{W}$ waffle iron and a $500-\mathrm{W}$ coffeepot. Usually, you operate these appliances from a $110-\mathrm{V}$ outlet for $0.500 \mathrm{~h}$ each day. (a) At 12 cents per kWh, how much do you spend to cook breakfast during a $30.0$ -day period? (b) You find yourself addicted to waffles and would like to upgrade to a $2400-\mathrm{W}$ waffle iron that will enable you to cook twice as many waffles during a half-hour period, but you know that the circuit breaker in your kitchen is a $20-\mathrm{A}$ breaker. Can you do the upgrade?

Salamat Ali

Numerade Educator

Problem 58

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 $t=5.0 \mathrm{~s}$ ? (b) What constant current would transport the same total charge during the $5.0$ -s interval as does the actual current?

Mayukh Banik

Numerade Educator

Problem 59

An electric car is designed to run off a bank of $12.0-\bar{V}$ batteries with a total energy storage of $2.00 \times 10^{7} \mathrm{~J}$. (a) If the electric motor draws $8.00 \mathrm{~kW}$, what is the current delivered to the motor? (b) If the electric motor draws $8.00 \mathrm{~kW}$ as the car moves at a steady speed of $20.0 \mathrm{~m} / \mathrm{s}$ how far will the car travel before it is "out of juice"?

Shahab Ullah

Numerade Educator

Problem 60

(a) A $115-\mathrm{g}$ 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 $20^{\circ} \mathrm{C}$. (b) Calculate the resistance between opposite faces if the same mass of aluminum is formed into a cube.

Narayan Hari

Numerade Educator

Problem 61

A length of metal wire has a radius of $5.00 \times 10^{-3} \mathrm{~m}$ and a resistance of $0.100 \Omega .$ When the potential difference across the wire is $15.0 \mathrm{~V}$, the electron drift speed is found to be $3.17 \times 10^{-4} \mathrm{~m} / \mathrm{s}$. On the basis of these data, calculate the density of free electrons in the wire.

Salamat Ali

Numerade Educator

Problem 62

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

Mayukh Banik

Numerade Educator

Problem 63

A resistor is constructed by forming a material of resistivity $3.5 \times 10^{5} \Omega \cdot \mathrm{m}$ into the shape of a hollow cylinder of length $4.0 \mathrm{~cm}$ and inner and outer radii $0.50 \mathrm{~cm}$ and $1.2 \mathrm{~cm}$, 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.

Salamat Ali

Numerade Educator

Problem 64

A $50.0-\mathrm{g}$ sample of a conducting material is all that is available. The resistivity of the material is measured to be $11 \times 10^{-8} \Omega \cdot \mathrm{m}$, and the density is $7.86 \mathrm{~g} / \mathrm{cm}^{3}$. The material is to be shaped into a solid cylindrical wire that has a total resistance of $1.5 \Omega .$ (a) What length of wire is required? (b) What must be the diameter of the wire?

Mayukh Banik

Numerade Educator

Problem 65

An x-ray tube used for cancer therapy operates at $4.0 \mathrm{MV}$, with a beam current of $25 \mathrm{~mA}$ striking the metal target. Nearly all the power in the beam is transferred to a stream of water flowing through holes drilled in the target. What rate of flow, in kilograms per second, is needed if the rise in temperature $(\Delta T)$ of the water is not to exceed $50^{\circ} \mathrm{C}$ ?

Sheh Lit Chang

University of Washington

Problem 66

When a straight wire is heated, its resistance changes according to the equation
$$
R=R_{0}\left[1+\alpha\left(T-T_{0}\right)\right]
$$
(Eq. 17.7), where $\alpha$ is the temperature coefficient of resistivity. (a) Show that a more precise result, which includes the length and area of a wire change when it is heated, is
$$
R=\frac{R_{0}\left[1+\alpha\left(T-T_{0}\right)\right]\left[1+\alpha^{\prime}\left(T-T_{0}\right)\right]}{\left[1+2 \alpha^{\prime}\left(T-T_{0}\right)\right]}
$$
where $\alpha^{\prime}$ is the coefficient of linear expansion. (See Chap$\begin{array}{ll}\text { Ler } 10 .) & \text { (b) Compare the two results for a } 2.00-\mathrm{m} \text { -long }\end{array}$ copper wire of radius $0.100 \mathrm{~mm}$, starting at $20.0^{\circ} \mathrm{C}$ and heated to $100.0^{\circ} \mathrm{C}$.

Eduard Sanchez

Numerade Educator

Problem 67

A man wishes to vacuum his car with a canister vacuum cleaner marked $535 \mathrm{~W}$ at $120 \mathrm{~V}$. The car is parked far from the building, so he uses an extension cord $15.0 \mathrm{~m}$ long to plug the cleaner into a $120-\mathrm{V}$ source. Assume the cleaner has constant resistance. (a) If the resistance of each of the two conductors of the extension cord is $0.900 \Omega$, what is the actual power delivered to the cleaner? (b) If, instead, the power is to be at least $525 \mathrm{~W}$, 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 $532 \mathrm{~W}$. (Suggestion: A symbolic solution can simplify the calculations.)

Sophie S

Numerade Educator