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College Physics 2017

Raymond A. Serway, Chris Vuille, John hughes

Chapter 17

Current and resistance

Educators


Problem 1

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

Salamat A.
Numerade Educator

Problem 2

A copper wire has a circular cross section with a radius of 1.25 $\mathrm{mm}$ . (a) If the wire carrics a current of 3.70 $\mathrm{A}$ , find the drift speed of clectrons in the wire. (Take the density of mobile charge carriers in copper to be $n=1.10 \times 10^{29} \mathrm{clec}-$ electrons/m'.) (b) For the same wire size and current, find the drift speed of electrons if the wire is made of aluminum with $n=2.11 \times 10^{29}$ electrons/m.

Mayukh B.
Numerade Educator

Problem 3

In the Bohr model of the hydrogen atom, an electron in the lowest energy state moves at a speed equal to $2.19 \times 10^{6} \mathrm{m} / \mathrm{s}$ 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?

Salamat A.
Numerade Educator

Problem 4

A typical lightning bolt may last for 0.200 s and transfer $1.00 \times$ $10^{20}$ electrons. Calculate the average current in the lightning bolt.

Mayukh B.
Numerade Educator

Problem 5

A certain laboratory experiment requires an aluminum wire of length of 32.0 $\mathrm{m}$ and a resistance of 2.50$\Omega$ at $20.0^{\circ} \mathrm{C}$ . What diameter wire must be used?

Salamat A.
Numerade Educator

Problem 6

If $3.25 \times 10^{-3} \mathrm{kg}$ of gold is deposited on the negative electrode of an clectrolytic 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.

Mayukh B.
Numerade Educator

Problem 7

$\mathrm{A} 2.0 \times 10^{2}-\mathrm{km}$ -long high-voltage transmission line 2.0 $\mathrm{cm}$ in diameter carries a steady current of $1.0 \times 10^{3} \mathrm{A}$ . If the conductor is copper with a free charge density of $8.5 \times 10^{29}$ electrons/m", how many years does it take one electron to
travel the full length of the cable?

Salamat A.
Numerade Educator

Problem 8

An aluminum wire having a cross-sectional area of $4.00 \times 10^{-6} \mathrm{m}^{2}$ carrics a current of 5.00 $\mathrm{A}$ . The density of aluminum is 2.70 $\mathrm{g} / \mathrm{cm}^{3}$ . Assume cach aluminum atom supplies one conduction electron per atom. Find the drift speed
of the electrons in the wire.

Mayukh B.
Numerade Educator

Problem 9

An iron wire has a cross-sectional area of $5.00 \times 10^{-6 \mathrm{i}} \mathrm{m}^{2}$ . sCarry out steps (a) through (c) to compute the drift speed of the conduction clectrons 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.

Salamat A.
Numerade Educator

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 B.
Numerade Educator

Problem 11

A voltmeter connected across the terminals of a tungstenfilament light bulb measures 115 $\mathrm{V}$ when an ammeter in line with the bulb registers a current of 0.522 $\mathrm{A}$ . (a) Find the resistance of the light bulb. (b) Find the resistivity of tungsten at the bulb's operating temperature if the filament has an uncoiled length of 0.600 $\mathrm{m}$ and a radius of $2.30 \times 10^{-5} \mathrm{m} .$

Salamat A.
Numerade Educator

Problem 12

Germanium is a semiconducting metal with a resistivity of 0.460$\Omega \cdot \mathrm{m}$ . (a) Determine the current per unit area through a $5.00-\mathrm{V}$ germanium junction with a length of 2.00 $\mathrm{mm}$ . (b) Find the current through the junction if its cross-sectional area is $2.00 \times 10^{-5} \mathrm{m}^{2}$

Mayukh B.
Numerade Educator

Problem 13

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 2.0 $\mathrm{k} \Omega$ .

Salamat A.
Numerade Educator

Problem 14

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 B.
Numerade Educator

Problem 15

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 A.
Numerade Educator

Problem 16

A wire of diameter 0.800 $\mathrm{mm}$ and length 25.0 $\mathrm{m}$ has a measured resistance of 1.60$\Omega$ . What is the resistivity of the wire?

Mayukh B.
Numerade Educator

Problem 17

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 A.
Numerade Educator

Problem 18

The current supplied by a battery in a portable device is typically 0.15 A. Find the number of electrons passing through the device in one hour.

Mayukh B.
Numerade Educator

Problem 19

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 A.
Numerade Educator

Problem 20

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 B.
Numerade Educator

Problem 21

The resistivity of copper is $1.70 \times 10^{-8} \Omega \cdot \mathrm{m} .$ (a) Find the resistance of a copper wire with a radius of 1.29 $\mathrm{mm}$ and a length of 1.00 $\mathrm{m} .$ (b) Calculate the volume of copper in the wire. (c) Suppose that volume of copper is formed into a new wire with a length of 2.00 $\mathrm{m}$ . Find the new resistance of the wire.

Salamat A.
Numerade Educator

Problem 22

The human body can exhibit a wide range of resistances to current depending on the path of the current, contact area, and sweat liness 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 mA of direct current? (b) Why should rubber-soled shoes and rubber gloves be worn when working around electricity?

Mayukh B.
Numerade Educator

Problem 23

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 A.
Numerade Educator

Problem 24

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

Mayukh B.
Numerade Educator

Problem 25

Digital thermometers often make use of thermistors, a type of resistor with resistance that varies with temperature more than standard resistors. Find the temperature coefficient of resistivity for a linear thermistor with resistances of 75.0$\Omega$ at $0.00^{\circ} \mathrm{C}$ and 275$\Omega$ at $525^{\circ} \mathrm{C}$ .

Salamat A.
Numerade Educator

Problem 26

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 cxpansion, find the temperature of the oven. (b) Qualitatively, how would thermal cxpansion be expected to affect the answer?

Mayukh B.
Numerade Educator

Problem 27

Gold is the most ductile of all metals. For example, onc gram of gold can be drawn into a wire 2.40 $\mathrm{km}$ long. The density of gold is $19.3 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$ , and its resistivity is $2.44 \times 10^{-8} \Omega \cdot \mathrm{m} .$ What is the resistance of such a wire at $20.0^{\circ} \mathrm{C}$ ?

Salamat A.
Numerade Educator

Problem 28

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

Mayukh B.
Numerade Educator

Problem 29

At $20.0^{\circ} \mathrm{C},$ the carbon resistor in an electric circuit connected to a 5.0 $\mathrm{-V}$ 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 $80.0^{\circ} \mathrm{C}$ ?

Salamat A.
Numerade Educator

Problem 30

A wire 3.00 $\mathrm{m}$ long and 0.450 $\mathrm{mm}^{2}$ in cross-sectional area has a resistance of 41.0 $\mathrm{s}$ at $20.0^{\circ} \mathrm{C}$ . If its resistance increases to 41.4 s at $29.0^{\circ} \mathrm{C},$ what is the temperature cocfficient of resistivity?

Mayukh B.
Numerade Educator

Problem 31

(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 A.
Numerade Educator

Problem 32

An engineer needs a resistor with a zero overall temperature coefficient of resistance at $20.0^{\circ} \mathrm{C}$ . She designs a pair of circular cylinders, one of carbon and one of Nichrome as shown in
Figure $\mathrm{P} 17.32$ . The device must have an overall resistance of $R_{1}+R_{2}=10.0 \Omega$ independent of temperature and a uniform radius of $r=1.50 \mathrm{mm}$ . Ignore thermal expansion of the cylinders and assume both are always at the same temperature. (a) Can she meet the design goal with this method? (b) If so, state what you can determine about the lengths $L_{1}$ and $L_{2}$ of
each segment. If not, explain.

Mayukh B.
Numerade Educator

Problem 33

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 heart beat 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. Take $\rho_{\mathrm{Hg}}=9.4 \times 10^{-7} \Omega \cdot \mathrm{m} .$ Hint: Because the cylindrical volume is constant, $V=A_{i} L_{i}=A_{j} I_{\gamma}$ and $A_{f}=A_{i}\left(L_{i} / L_{\cdot}\right)$

Salamat A.
Numerade Educator

Problem 34

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 determinc the resistance of the platinum resistance thermometer at room temperature, $20.0^{\circ} \mathrm{C}$ .

Mayukh B.
Numerade Educator

Problem 35

A 5.00 -V power supply provides a maximum current of 10.0 $\mathrm{A}$ . (a) Calculate the maximum power delivered by the power supply. (b) How many $2.00-\mathrm{W}$ cell phone chargers could be
powered by the power supply? Include fractional numbers in your answer.

Salamat A.
Numerade Educator

Problem 36

If electrical energy costs $\$ 0.12$ per kilowatt-hour, how much does it cost to (a) burn a $100-$ W light bulb for 24 $\mathrm{h}$ ? (b) Operate an electric oven for 5.0 $\mathrm{h}$ if it carries a current of 20.0 $\mathrm{A}$ at 220 $\mathrm{V}$ ?

Mayukh B.
Numerade Educator

Problem 37

Residential building codes typically require the use of 12 -gauge copper wire (diameter 0.205 $\mathrm{cm} )$ for wiring receptacles. Such circuits carry currents as large as 20.0 $\mathrm{A}$ . If a wire of smaller diameter (with a higher gauge number) carried that much current, the wire could rise to a high temperature and cause a fire. (a) Calculate the rate at which internal energy is produced in 1.00 $\mathrm{m}$ of 12-gauge copper wire carrying 20.0 $\mathrm{A}$ . (b) Repeat the calculation for a 12 -gauge aluminum wire. (c) Explain whether a 12 -gauge aluminum wire would be as safe as a copper wire.

Salamat A.
Numerade Educator

Problem 38

A portable coffee heater supplics a potential difference of 12.0 $\mathrm{V}$ across a Nichrome heating element with a resistance of 2.00$\Omega .$ (a) Calculate the power consumed by the heater. (b) How many minutes would it take to heat 1.00 $\mathrm{kg}$ of coffee from $20.0^{\circ} \mathrm{C}$ to $50.0^{\circ} \mathrm{C}$ with this heater? Coffee has a specific heat of 4184 $\mathrm{J} /\left(\mathrm{kg} \cdot^{\circ} \mathrm{C}\right) .$ Neglect any energy losses to the environment.

Mayukh B.
Numerade Educator

Problem 39

The heating element of a coffecmaker 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.

Salamat A.
Numerade Educator

Problem 40

A typical cell phone consumes an average of about 1.00 $\mathrm{W}$ of electrical power and operates on 3.80 $\mathrm{V}$ . (a) What average current does the phone draw from its battery? (b) Calculate the
energy stored in a fully charged battery if the phone requires charging after 5.00 hours of use.

Mayukh B.
Numerade Educator

Problem 41

Light bulb $\mathrm{A}$ is marked $-25.0 \mathrm{W} 120 . \mathrm{V},$ "and lightbulb $\mathrm{B}$ is marked " $100 . \mathrm{W} 120 . \mathrm{V}$ ." These labels mean that each light bulb has its respective power delivered to it when it is connected to a constant $120 .$ -V source. (a) Find the resistance of each light bulb. (b) During what time interval does 1.00 $\mathrm{C}$ pass into light bulb $\mathrm{A}^{2}(\mathrm{c})$ Is this charge different upon its exit versus its entry into the light bulb? Explain. (d) In what time interval does 1.00 $\mathrm{J}$ pass into light bulb $\mathrm{A}$ ? (e) By what mechanisms does this energy enter and exit the light bulb? Explain. (f) Find the cost of running light bulb A continuously for 30.0 days, assuming the electric company sells its product at $\$ 0.110$ per kWh.

Salamat A.
Numerade Educator

Problem 42

A certain toaster has a heating element made of Nichrome resistance wire. When the toaster is first connected to a $120 .$ . -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 $\mathrm{A}$ . (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 B.
Numerade Educator

Problem 43

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 A.
Numerade Educator

Problem 44

Batteries are rated in terms of ampere-hours (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 B.
Numerade Educator

Problem 45

The potential difference across a resting neuron in the human body is about 75.0 $\mathrm{mV}$ and carries a current of about 0.200 $\mathrm{mA}$ . How much power does the neuron release?

Salamat A.
Numerade Educator

Problem 46

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 -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 $\mathrm{min}$ in a 200 - W dryer.

Mayukh B.
Numerade Educator

Problem 47

An electric utility company supplies a customer's house from the main power lines $(120 . \mathrm{V})$ with two copper wires, each of which is 50.0 $\mathrm{m}$ long and has a resistance of 0.108$\Omega$ per $300 . \mathrm{m} .$ (a) Find the potential difference at the customer's house for a load current of $110 . \mathrm{A}$ . For this load current, find (b) the power delivered to the customer.

Salamat A.
Numerade Educator

Problem 48

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. (a) Calculate the average power required to warm the water to $100 .^{\circ} \mathrm{C}$ in 4.00 $\mathrm{min.}$ (b) Calculate the required resistance in the heating element at $100 .^{\circ} \mathrm{C}$ . (c) Calculate the resistance of the heating element at $20 .^{\circ} \mathrm{C}$ (d) Derive a relationship between the diameter of the wire, the resistivity at $20 .^{\circ} \mathrm{C}, \rho_{0},$ the resistance at $20 .^{\circ} \mathrm{C}, R_{0},$ and the length $L$ . (e) If $L=3.00 \mathrm{m},$ what is the diameter of the wire?

Mayukh B.
Numerade Educator

Problem 49

Two wires $A$ and $B$ made of the same material and having the same lengths are connected across the same voltage source. If the power supplicd to wire $A$ is three times the power supplied to wire $B$ , what is the ratio of their diameters?

Salamat A.
Numerade Educator

Problem 50

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 cquilibrium temperature such that it cmits 75.0 $\mathrm{W}$ in the form of radiation. Neglecting absorption of any radiation from its environment, what is the tempera-
ture 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?

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Problem 51

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

Salamat A.
Numerade Educator

Problem 52

A car owner forgets to turn off the headlights of his car while it is parked in his garage. If the $12.0-\mathrm{V}$ battery in his car is rated at 90.0 $\mathrm{A} \cdot \mathrm{h}$ and each headlight requires 36.0 $\mathrm{W}$ of power, how long will it take the battery to completely discharge?

Mayukh B.
Numerade Educator

Problem 53

Consider an aluminum wire of diameter 0.600 $\mathrm{mm}$ and length 15.0 $\mathrm{m} .$ The resistivity of aluminum at $20.0^{\circ} \mathrm{C}$ is $2.82 \times 10^{28} \Omega \cdot \mathrm{m} .$ (a) Find the resistance of this wire at $20.0^{\circ} \mathrm{C}$ (b) If a $9.00-\mathrm{V}$
battery is connected across the ends of the wire, find the current in the wire.

Salamat A.
Numerade Educator

Problem 54

A given copper wire has a resistance of 5.00$\Omega$ at $20.0^{\circ} \mathrm{C}$ while a tungsten wire of the same diameter has a resistance of $4,75 \Omega$ at $20.0^{\circ} \mathrm{C}$ . At what temperature will the two wires have the same resistance?

Mayukh B.
Numerade Educator

Problem 55

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 A.
Numerade Educator

Problem 56

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 between its feet.

Mayukh B.
Numerade Educator

Problem 57

An experiment is conducted to measure the clectrical resistivity of Nichrome in the form of wires with different lengths vand cross-sectional areas. For one set of measurements, a student uses 30.0 -gauge wire, which has a cross-sectional arca of $7.30 \times 10^{-8} \mathrm{m}^{2}$ . The student measures the potential differcnce across the wirc 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.

Salamat A.
Numerade Educator

Problem 58

A 50.0 -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 B.
Numerade Educator

Problem 59

You are cooking breakfast for yourself and a friend using a $1.20-\mathrm{kW}$ waffle iron and a 0.500 -kW coffecpot. Usually, you operate these appliances from a 110 . -V outlet for 0.500 h each day. (a) At 12.0 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 $2.40-\mathrm{kW}$ wattle iron that will enable you to cook twice as many what 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?

Salamat A.
Numerade Educator

Problem 60

The current in a conductor varies in time as shown in Figure $\mathrm{P} 17.60$ . (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?

Mayukh B.
Numerade Educator

Problem 61

A $120 .$ -V motor has mechanical power output of 2.50 $\mathrm{hp}$ . It is 90.0$\%$ efficient in converting power that it takes in by clectrical transmission into mechanical power. (a) Find the current in the motor. (b) Find the energy delivered to the motor by electrical transmission in 3.00 $\mathrm{h}$ of operation. (c) If the electric company charges $\$ 0.110 / \mathrm{kWh}$ , what does it cost to run the motor for 3.00 $\mathrm{h}$ ?

Salamat A.
Numerade Educator

Problem 62

A Nichrome heating element in an oven has a resistance of 8.0$\Omega$ at $20.0^{\circ} \mathrm{C}$ . (a) What is its resistance at $350^{\circ} \mathrm{C}$ ?
(b) What assumption did you have to make to obtain your answer to part (a)?

Mayukh B.
Numerade Educator

Problem 63

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 A.
Numerade Educator

Problem 64

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 B.
Numerade Educator

Problem 65

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 A.
Numerade Educator

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 Topic $10 . )$ (b) Compare the two results for a $2.00-\mathrm{m}$ -long copper wire of radius $0.100 \mathrm{mm},$ starting at $20.0^{\circ} \mathrm{C}$ and heated to $100.0^{\circ} \mathrm{C}$ .

Mayukh B.
Numerade Educator

Problem 67

An $x$ -ray tube used for cancer therapy operates at4.0 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 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 $50 .^{\circ} \mathrm{C} ?$

Salamat A.
Numerade Educator

Problem 68

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 -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.

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