Solved: A small city requires about 15 MW of power.

A current of 1.60 A flows in a wire. How many electrons are flowing past any point in the wire per second?

A service station charges a battery using a current of 6.7 A for 5.0 h. How much charge passes through the battery?

What is the current in amperes if flow across a cell membrane in The charge on the sodium is the same as on an electron, but positive

What is the resistance of a toaster if 120 V produces a current of 4.6 A?

(I) What voltage will produce 0.25 A of current through a \(4800-\Omega\) resistor? Equation Transcription: Text Transcription: 4800 - Omega

How many coulombs are there in a 75 ampere-hour car battery?

(a) What is the current in the element of an electric clothes dryer with a resistance of when it is connected to 240 V? (b) How much charge passes through the element in 50 min? (Assume direct current.)

A bird stands on a dc electric transmission line carrying 4100 A (Fig. 1834). The line has resistance per meter, and the birds feet are 4.0 cm apart. What is the potential difference between the birds feet?

A hair dryer draws 13.5 A when plugged into a 120-V line. (a) What is its resistance? (b) How much charge passes through it in 15 min? (Assume direct current.)

A 4.5-V battery is connected to a bulb whose resistance is How many electrons leave the battery per minute?

An electric device draws 5.60 A at 240 V. (a) If the voltage drops by 15%, what will be the current, assuming nothing else changes? (b) If the resistance of the device were reduced by 15%, what current would be drawn at 240 V?

What is the diameter of a 1.00-m length of tungsten wire whose resistance is

What is the resistance of a 5.4-m length of copper wire 1.5 mm in diameter?

Calculate the ratio of the resistance of 10.0 m of aluminum wire 2.2 mm in diameter, to 24.0 m of copper wire 1.8 mm in diameter

Can a 2.2-mm-diameter copper wire have the same resistance as a tungsten wire of the same length? Give numerical details

(II) A certain copper wire has a resistance of \(15.0 \Omega\). At what point along its length must the wire be cut so that the resistance of one piece is 4.0 times the resistance of the other? What is the resistance of each piece? Equation Transcription: Text Transcription: 15. 0 Omega

Compute the voltage drop along a 21-m length of household no. 14 copper wire (used in 15-A circuits). The wire has diameter 1.628 mm and carries a 12-A current.

Two aluminum wires have the same resistance. If one has twice the length of the other, what is the ratio of the diameter of the longer wire to the diameter of the shorter wire?

A rectangular solid made of carbon has sides of lengths 1.0 cm, 2.0 cm, and 4.0 cm, lying along the x, y, and z axes, respectively (Fig. 1835). Determine the resistance for current that passes through the solid in (a) the x direction, (b) the y direction, and (c) the z direction. Assume the resistivity is r = 3.0 * 105 m.

(II) A length of wire is cut in half and the two lengths are wrapped together side by side to make a thicker wire. How does the resistance of this new combination compare to the resistance of the original wire?

How much would you have to raise the temperature of a copper wire (originally at 20C) to increase its resistance by 12%?

(II) Determine at what temperature aluminum will have the same resistivity as tungsten does at \(20^{\circ}C\).

(II) A 100-W lightbulb has a resistance of about \(12\ Omega\) when cold (\(20^{\circ}C\)) and \(140\ \Omega\) when on (hot). Estimate the temperature of the filament when hot assuming an average temperature coefficient of resistivity \(\alpha = 0.0045\ (C^{\circ})^{-1}\).

A length of aluminum wire is connected to a precision 10.00-V power supply, and a current of 0.4212 A is precisely measured at 23.5C. The wire is placed in a new environment of unknown temperature where the measured current is 0.3818 A. What is the unknown temperature?

For some applications, it is important that the value of a resistance not change with temperature. For example, suppose you made a resistor from a carbon resistor and a Nichrome wire-wound resistor connected together so the total resistance is the sum of their separate resistances. What value should each of these resistors have (at 0C) so that the combination is temperature independent?

A 10.0-m length of wire consists of 5.0 m of copper followed by 5.0 m of aluminum, both of diameter 1.4 mm. A voltage difference of 95 mV is placed across the composite wire. (a) What is the total resistance (sum) of the two wires? (b) What is the current through the wire? (c) What are the voltages across the aluminum part and across the copper part?

What is the maximum power consumption of a 3.0-V portable CD player that draws a maximum of 240 mA of current?

The heating element of an electric oven is designed to produce 3.3 kW of heat when connected to a 240-V source. What must be the resistance of the element?

What is the maximum voltage that can be applied across a resistor rated at watt?

(a) Determine the resistance of, and current through, a 75-W lightbulb connected to its proper source voltage of 110 V. (b) Repeat for a 250-W bulb

An electric car has a battery that can hold 16 kWh of energy (approximately ). If the battery is designed to operate at 340 V, how many coulombs of charge would need to leave the battery at 340 V and return at 0 V to equal the stored energy of the battery?

An electric car uses a 45-kW (160-hp) motor. If the battery pack is designed for 340 V, what current would the motor need to draw from the battery? Neglect any energy losses in getting energy from the battery to the motor

A 120-V hair dryer has two settings: 950 W and 1450 W. (a) At which setting do you guess the resistance to be higher? After making a guess, determine the resistance at (b) the lower setting, and (c) the higher setting

(II) A 12-V battery causes a current of 0.60 A through a resistor. (a) What is its resistance, and (b) how many joules of energy does the battery lose in a minute?

A 120-V fish-tank heater is rated at 130 W. Calculate (a) the current through the heater when it is operating, and (b) its resistance

You buy a 75-W lightbulb in Europe, where electricity is delivered at 240 V. If you use the bulb in the United States at 120 V (assume its resistance does not change), how bright will it be relative to 75-W 120-V bulbs? [Hint: Assume roughly that brightness is proportional to power consumed.

How many kWh of energy does a 550-W toaster use in the morning if it is in operation for a total of 5.0 min? At a cost of estimate how much this would add to your monthly electric energy bill if you made toast four mornings per week.

At what does it cost to leave a 25-W porch light on day and night for a year?

What is the total amount of energy stored in a 12-V, 65 Ah car battery when it is fully charged?

An ordinary flashlight uses two D-cell 1.5-V batteries connected in series to provide 3.0 V across the bulb, as in Fig. 184b (Fig. 1836). The bulb draws 380 mA when turned on. (a) Calculate the resistance of the bulb and the power dissipated. (b) By what factor would the power increase if four D- cells in series (total 6.0 V) were used with the same bulb? (Neglect heating effects of the filament.) Why shouldnt you try this?

How many 75-W lightbulbs, connected to 120 V as in Fig. 1820, can be used without blowing a 15-A fuse?

An extension cord made of two wires of diameter 0.129 cm (no. 16 copper wire) and of length 2.7 m (9 ft) is connected to an electric heater which draws 18.0 A on a 120-V line. How much power is dissipated in the cord?

You want to design a portable electric blanket that runs on a 1.5-V battery. If you use a 0.50-mm- diameter copper wire as the heating element, how long should the wire be if you want to generate 18 W of heating power? What happens if you accidentally connect the blanket to a 9.0-V battery?

A power station delivers 750 kW of power at 12,000 V to a factory through wires with total resistance How much less power is wasted if the electricity is delivered at 50,000 V rather than 12,000 V?

A small immersion heater can be used in a car to heat a cup of water for coffee or tea. If the heater can heat 120 mL of water from 25C to 95C in 8.0 min, (a) approximately how much current does it draw from the cars 12-V battery, and (b) what is its resistance? Assume the manufacturers claim of 85% efficiency.

The current in an electromagnet connected to a 240-V line is 21.5 A. At what rate must cooling water pass over the coils for the water temperature to rise no more than 6.50 C?

Calculate the peak current in a resistor connected to a 220-V rms ac source.

An ac voltage, whose peak value is 180 V, is across a resistor. What are the rms and peak currents in the resistor?

(II) Estimate the resistance of the \(120-V_{rms}\) circuits in your house as seen by the power company, when (a) everything electrical is unplugged, and (b) two 75-W lightbulbs are on.

The peak value of an alternating current in a 1500-W device is 6.4 A. What is the rms voltage across it?

An 1800-W arc welder is connected to a ac line. Calculate (a) the peak voltage and (b) the peak current.

Each channel of a stereo receiver is capable of an average power output of 100 W into an loudspeaker (see Fig. 1814). What are the rms voltage and the rms current fed to the speaker (a) at the maximum power of 100 W, and (b) at 1.0 W when the volume is turned down?

Determine (a) the maximum instantaneous power dissipated by a 2.2-hp pump connected to a ac power source, and (b) the maximum current passing through the pump.

A heater coil connected to a ac line has a resistance of (a) What is the average power used? (b) What are the maximum and minimum values of the instantaneous power

A 0.65-mm-diameter copper wire carries a tiny dc current of Estimate the electron drift velocity

A 4.80-m length of 2.0-mm-diameter wire carries a 750-mA dc current when 22.0 mV is applied to its ends. If the drift velocity is determine (a) the resistance R of the wire, (b) the resistivity and (c) the number n of free electrons per unit volume.

At a point high in the Earths atmosphere, in a concentration of are moving due north at a speed of Also, a concentration of is moving due south at a speed of Determine the magnitude and direction of the net current passing through unit area

What is the magnitude of the electric field across an axon membrane thick if the resting potential is

A neuron is stimulated with an electric pulse. The action potential is detected at a point 3.70 cm down the axon 0.0052 s later. When the action potential is detected 7.20 cm from the point of stimulation, the time required is 0.0063 s. What is the speed of the electric pulse along the axon? (Why are two measurements needed instead of only one?)

During an action potential, move into the cell at a rate of about How much power must be produced by the active pumping system to produce this flow against a potential difference? Assume that the axon is 10 cm long and in diameter.

A person accidentally leaves a car with the lights on. If each of the two headlights uses 40 W and each of the two taillights 6 W, for a total of 92 W, how long will a fresh 12-V battery last if it is rated at Assume the full 12 V appears across each bulb.

A sequence of potential differences V is applied across a wire and the resulting currents I are measured as follows: V (V) 0.100 0.200 0.300 0.400 0.500 I (mA) 72 142 218 290 357 (a) If this wire obeys Ohms law, graphing I vs. V will result in a straight-line plot. Explain why this is so and determine the theoretical predictions for the straight lines slope and y-intercept. (b) Plot I vs. V. Based on this plot, can you conclude that the wire obeys Ohms law (i.e., did you obtain a straight line with the expected y-intercept, within the values of the significant figures)? If so, determine the wires resistance R. (c) Calculate the wires resistivity and use Table 181 to identify the solid material from which it is composed.

What is the average current drawn by a 1.0-hp 120-V motor?

The conductance G of an object is defined as the reciprocal of the resistance R; that is, The unit of conductance is a which is also called the siemens (S). What is the conductance (in siemens) of an object that draws 440 mA of current at 3.0 V?

The heating element of a 110-V, 1500-W heater is 3.8 m long. If it is made of iron, what must its diameter be?

A particular household uses a 2.2-kW heater (on time), four 100-W lightbulbs a 3.0-kW electric stove element for a total of and miscellaneous power amounting to If electricity costs $0.115 per kWh, what will be their monthly bill (30 d)? (b) How much coal (which produces ) must be burned by a 35%- efficient power plant to provide the yearly needs of this household?

A small city requires about 15 MW of power. Suppose that instead of using high-voltage lines to supply the power, the power is delivered at 120 V. Assuming a two-wire line of 0.50-cm-diameter copper wire, estimate the cost of the energy lost to heat per hour per meter. Assume the cost of electricity is about 12 cents per kWh

A 1600-W hair dryer is designed for 117 V. (a) What will be the percentage change in power output if the voltage drops to 105 V? Assume no change in resistance. (b) How would the actual change in resistivity with temperature affect your answer

The wiring in a house must be thick enough so it does not become so hot as to start a fire. What diameter must a copper wire be if it is to carry a maximum current of 35 A and produce no more than 1.5 W of heat per meter of length?

Determine the resistance of the tungsten filament in a 75-W 120-V incandescent lightbulb (a) at its operating temperature of about 2800 K, (b) at room temperature.

Suppose a current is given by the equation \(I\) = 1.40 sin 210\(t\), where \(I\) is in amperes and \(t\) in seconds. (a) What is the frequency? (b) What is the rms value of the current? (c) If this is the current through a \(24.0-\Omega\) resistor, write the equation that describes the voltage as a function of time. Equation Transcription: Text Transcription: I t I t 24.0 - Omega

A microwave oven running at 65%efficiency delivers 950W to the interior. Find (a) the power drawn from the source, and (b) the current drawn. Assume a source voltage of 120V.

A \(1.00-\Omega\) wire is stretched uniformly to 1.50 times its original length. What is its resistance now? Equation Transcription: Text Transcription: 1.00 - Omega

220 V is applied to two different conductors made of the same material. One conductor is twice as long and twice the diameter of the second. What is the ratio of the power transformed in the first relative to the second?

An electric power plant can produce electricity at a fixed power \(P\), but the plant operator is free to choose the voltage \(V\) at which it is produced. This electricity is carried as an electric current \(I\) through a transmission line (resistance \(R\) ) from the plant to the user, where it provides the user with electric power \(P^{\prime}\). (a) Show that the reduction in power \(\Delta P=P-P^{\prime}\) due to transmission losses is given by \(\Delta P=P^{2} R / V^{2}\).(b) In order to reduce power losses during transmission, should the operator choose \(V\) to be as large or as small as possible? Equation Transcription: Text Transcription: P V I R P’ Delta = P - P’ Delta = P^2{R}/V^2 V

A 2800-W oven is connected to a 240-V source. (a) What is the resistance of the oven? (b) How long will it take to bring 120 mL of 15°C water to 100°C assuming 65% efficiency? (c) How much will this cost at 11 cents/kWh?

A proposed electric vehicle makes use of storage batteries as its source of energy. It is powered by 24 batteries, each \(12 \mathrm{~V}, 95 \mathrm{~A} \cdot \mathrm{h}\). Assume that the car is driven on level roads at an average speed of 45 km/h, and the average friction force is 440 N. Assume 100% efficiency and neglect energy used for acceleration. No energy is consumed when the vehicle is stopped, since the engine doesn’t need to idle. (a) Determine the horsepower required. (b) After approximately how many kilometers must the batteries be recharged? Equation Transcription: Text Transcription: 12 V, 95 A cdot h

A \(15.2-\Omega\) resistor is made from a coil of copper wire whose total mass is 15.5 g. What is the diameter of the wire, and how long is it? Equation Transcription: Text Transcription: 15.2 - Omega

A fish-tank heater is rated at 95 W when connected to 120 V. The heating element is a coil of Nichrome wire. When uncoiled, the wire has a total length of 3.5 m. What is the diameter of the wire?

A 100-W, 120-V lightbulb has a resistance of \(12 \Omega\) when cold (20°C) and \(140 \Omega\) when on (hot). Calculate its power consumption (a) at the instant it is turned on, and (b) after a few moments when it is hot. Equation Transcription: Text Transcription: 12 Omega 140 Omega

In an automobile, the system voltage varies from about 12 V when the car is off to about 13.8 V when the car is on and the charging system is in operation, a difference of 15%. By what percentage does the power delivered to the headlights vary as the voltage changes from 12 V to 13.8 V? Assume the headlight resistance remains constant

A tungsten filament used in a flashlight bulb operates at 0.20 A and 3.0 V. If its resistance at 20°C is \(1.5 \Omega\), what is the temperature of the filament when the flashlight is on? Equation Transcription: Text Transcription: 1.5 Omega

Lightbulb A is rated at 120 V and 40 W for household applications. Lightbulb B is rated at 12 V and 40 W for automotive applications. (a) What is the current through each bulb? (b) What is the resistance of each bulb? (c) In one hour, how much charge passes through each bulb? (d) In one hour, how much energy does each bulb use? (e) Which bulb requires larger diameter wires to connect its power source and the bulb?

An air conditioner draws 18 A at 220-V ac. The connecting cord is copper wire with a diameter of 1.628 mm. (a) How much power does the air conditioner draw? (b) If the length of the cord (containing two wires) is 3.5 m, how much power is dissipated in the wiring? (c) If no. 12 wire, with a diameter of 2.053 mm, was used instead, how much power would be dissipated in the wiring? (d) Assuming that the air conditioner is run 12 h per day, how much money per month (30 days) would be saved by using no. 12 wire? Assume that the cost of electricity is 12 cents per kWh.

An electric wheelchair is designed to run on a single 12-V battery rated to provide 100 ampere-hours (100 ). (a) How much energy is stored in this battery? (b) If the wheelchair experiences an average total retarding force (mainly friction) of 210 N, how far can the wheelchair travel on one charge?

If a wire of resistance R is stretched uniformly so that its length doubles, by what factor does the power dissipated in the wire change, assuming it remains hooked up to the same voltage source? Assume the wires volume and density remain constant.

Copper wire of diameter 0.259 cm is used to connect a set of appliances at 120 V, which draw 1450 W of power total. (a) What power is wasted in 25.0 m of this wire? (b) What is your answer if wire of diameter 0.412 cm is used?

Battery-powered electricity is very expensive compared with that available from a wall receptacle. Estimate the cost per kWh of (a) an alkaline D-cell (cost $1.70) and (b) an alkaline AA-cell (cost $1.25). These batteries can provide a continuous current of 25 mA for 820 h and 120 h, respectively, at 1.5 V. (c) Compare to the cost of a normal 120-V ac house source at $0.10/kWh.

A copper pipe has an inside diameter of 3.00 cm and an outside diameter of 5.00 cm (Fig. 18–37). What is the resistance of a 10.0-m length of this pipe?

The Tevatron accelerator at Fermilab (Illinois) is designed to carry an 11-mA beam of protons \(\left(q=1.6 \times 10^{-19} \mathrm{C}\right)\) traveling at very nearly the speed of light \(\left(3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)\) around a ring 6300 m in circumference. How many protons are in the beam? Equation Transcription: Text Transcription: (q = 1.6 x 10^-19 C) (3.0 x 10^8 m/s)

The level of liquid helium (temperature \(\approx 4 \mathrm{~K}\) ) in its storage tank can be monitored using a vertically aligned niobiumtitanium (NbTi) wire, whose length \(\ell\) spans the height of the tank. In this level-sensing setup, an electronic circuit maintains a constant electrical current \(I\) at all times in the NbTi wire and a voltmeter monitors the voltage difference \(V\) across this wire. Since the superconducting critical temperature for NbTi is 10 K, the portion of the wire immersed in the liquid helium is in the superconducting state, while the portion above the liquid (in helium vapor with a temperature above 10 K ) is in the normal state. Define \(f=x / \ell\) to be the fraction of the tank filled with liquid helium (Fig. 18-38) and \(V_{0}\) to be the value of \(V\) when the tank is empty \((f=0)\). Determine the relation between \(f\) and \(V\) (in terms of \(V_{0}\)). Equation Transcription: ? /? Text Transcription: approx 4K ell I V f = x/ell V_0 V (f = 0) f V V_0

The conductors shown are all made of copper and are at the same temperature. Which conductor would have the greatest resistance to the flow of charge entering from the left? Which would offer the least resistance?

Problem 1MCQ When connected to a battery, a light bulb glows brightly. If the battery is reversed and reconnected to the bulb, the bulb will glow (a) brighter. (c) with the same brightness. (b) dimmer. (d) not at all.

Problem 1Q When an electric cell is connected to a circuit, electrons flow away from the negative terminal in the circuit. But within the cell, electrons flow to the negative terminal. Explain.

Problem 1SL Why is Ohm’s law less of a law than Newton’s laws?

When a battery is connected to a lightbulb properly, current flows through the lightbulb and makes it glow. How much current flows through the battery compared with the lightbulb? (a) More. (b) Less. (c) The same amount. (d) No current flows through the battery.

Problem 2P (I) A service station charges a battery using a current of 6.7 A for 5.0 h. How much charge passes through the battery?

Problem 2Q When a flashlight is operated, what is being used up: battery current, battery voltage, battery energy, battery power, or battery resistance? Explain.

Problem 2SL A traditional incandescent lamp filament may have been lit to a temperature of 2700 K. A contemporary halogen incandescent lamp filament may be at around 2900 K. (a) Estimate the percent improvement of the halogen bulb over the traditional one. [Hint: See Section 14–8.] (b) To produce the same amount of light as a traditional 100-W bulb, estimate what wattage a halogen bulb should use.

Which of the following statements about Ohm’s law is true? (a) Ohm’s law relates the current through a wire to the voltage across the wire. (b) Ohm’s law holds for all materials. (c) Any material that obeys Ohm’s law does so independently of temperature. (d) Ohm’s law is a fundamental law of physics. (e) Ohm’s law is valid for superconductors.

Problem 3P (I) What is the current in amperes if 1200 Na+ ions flow across a cell membrane in 3.1 µs? The charge on the sodium is the same as on an electron, but positive.

Problem 3Q What quantity is measured by a battery rating given in ampere-hours Explain.

You find a small cylindrical resistor that measures 9.00 mm in length and 2.15 mm in diameter, and it has a color code of red, yellow, brown, and gold. What is the resistor made of primarily?

Problem 4MCQ Electrons carry energy from a battery to a light bulb. What happens to the electrons when they reach the light bulb? (a) The electrons are used up. (b) The electrons stay in the light bulb. (c) The electrons are emitted as light. (d) Fewer electrons leave the bulb than enter it. (e) None of the above.

Problem 4P (I) What is the resistance of a toaster if 120 V produces a current of 4.6 A?

Problem 4Q Can a copper wire and an aluminum wire of the same length have the same resistance? Explain.

Problem 4SL Small changes in the length of an object can be measured using a strain gauge sensor, which is a wire that when undeformed has length lo cross-sectional area A0, and resistance R0 This sensor is rigidly affixed to the object’s surface, aligning its length in the direction in which length changes are to be measured. As the object deforms, the length of the wire sensor changes by ?l. and the resulting change ? R in the sensor’s resistance is measured. Assuming that as the solid wire is deformed to a length l its density and volume remain constant (only approximately valid), show that the strain (=?l/lo) of the wire sensor, and thus of the object to which it is attached, is approximately ? R/2R0. [See Sections 18–4 and 9–5.]

Where in the circuit of Fig. is the current the largest, , (c), or Or it is the same at all points?

Problem 5P (I) What voltage will produce 0.25 A of current through a 4800-? resistor?

Problem 5Q One terminal of a car battery is said to be connected to “ground.” Since it is not really connected to the ground, what is meant by this expression?

Problem 5SL An electric heater is used to heat a room of volume 65 m3 , Air is brought into the room at 5°C and is completely replaced twice per hour. Heat loss through the walls amounts to approximately 850 kcal/h. If the air is to be maintained at 22°C, what minimum wattage must the heater have? (The specific heat of air is about kcal/kg.C°. Reread parts of Chapter 14 and Section 18–5.)

Problem 6MCQ When you double the voltage across a certain material or device, you observe that the current increases by a factor of 3. What can you conclude? (a) Ohm’s law is obeyed, because the current increases when V increases. (b) Ohm’s law is not obeyed in this case. (c) This situation has nothing to do with Ohm’s law.

Problem 6P (I) How many coulombs are there in a 75 ampere-hour car battery?

The equation \(P=V^{2} / R\) indicates that the power dissipated in a resistor decreases if the resistance is increased, whereas the equation \(P=I^{2} R\) implies the opposite. Is there a contradiction here? Explain. Equation Transcription: Text Transcription: P = v^2/R P = I^2{R}

Problem 6SL Household wiring has sometimes used aluminium instead of copper. (a) Using Table 18–1, find the ratio of the resistance of a copper wire to that of an aluminum wire of the same length and diameter. (b) Typical copper wire used for home wiring in the U.S. has a diameter of 1.63 mm. What is the resistance of 125 m of this wire? (c) What would be the resistance of the same wire if it were made of aluminum? (d) How much power would be dissipated in each wire if it carried 18 A of current? (e) What should be the diameter of the aluminum wire for it to have the same resistance as the copper wire? (f ) In Section 18–4, a statement is made about the resistance of copper and aluminum wires of the same weight. Using Table 10–1 for the densities of copper and aluminum, find the resistance of an aluminum wire of the same mass and length as the copper wire in part (b). Is the statement true?

Problem 7MCQ When current flows through a resistor, (a) some of the charge is used up by the resistor. (b) some of the current is used up by the resistor. (c) Both (a) and (b) are true. (d) Neither (a) nor (b) is true.

Problem 7P (II) (a) What is the current in the element of an electric clothes dryer with a resistance of 8.6 ? when it is connected to 240 V? (b) How much charge passes through the element in 50 min? (Assume direct current.)

What happens when a lightbulb burns out?

Problem 7SL How far can an average electron move along the wires of a 650-W toaster during an alternating current cycle? The power cord has copper wires of diameter 1.7 mm and is plugged into a standard 60-Hz 120-V ac outlet. [Hint: The maximum current in the cycle is related to the maximum drift velocity. The maximum velocity in an oscillation is related to the maximum displacement; see Chapter 11.]

Problem 8MCQ The unit kilowatt-hour is a measure of (a) the rate at which energy is transformed. (b) power. (c) an amount of energy. (d) the amount of power used per second.

(II) A bird stands on a dc electric transmission line carrying (Fig. . The line has \(2.5 \times 10^{-5} \Omega\) resistance per meter, and the bird's feet are apart. What is the potential difference between the bird's feet? Equation transcription: Text transcription: 2.5 times 10^{-5} Omega

If the resistance of a small immersion heater (to heat water for tea or soup, Fig. 18–32) was increased, would it speed up or slow down the heating process? Explain.

Problem 8SL Capacitance of an axon. (a) Do an order-of-magnitude estimate for the capacitance of an axon 10 cm long of radius 10 ? The thickness of the membrane is about 10-8m, and the dielectric constant is about 3. (b) By what factor does the concentration (number of ions per volume) of Na+ ions in the cell change as a result of one action potential?

Problem 9MCQ Why might a circuit breaker open if you plug too many electrical devices into a single circuit? (a) The voltage becomes too high. (b) The current becomes too high. (c) The resistance becomes too high. (d) A circuit breaker will not “trip” no matter how many electrical devices you plug into the circuit.

Problem 9P (II) A hair dryer draws 13.5 A when plugged into a 120-V line. (a) What is its resistance? (b) How much charge passes through it in 15 min? (Assume direct current.)

Problem 9Q If a rectangular solid made of carbon has sides of lengths a, 2a, and 3a, to which faces would you connect the wires from a battery so as to obtain (a) the least resistance, (b) the greatest resistance?

Problem 10MCQ Nothing happens when birds land on a power line, yet we are warned not to touch a power line with a ladder. What is the difference? (a) Birds have extremely high internal resistance compared to humans. (b) There is little to no voltage drop between a bird’s two feet, but there is a significant voltage drop between the top of a ladder touching a power line and the bottom of the ladder on the ground. (c) Dangerous current comes from the ground only. (d)Most birds don’t understand the situation.

Problem 10P (II) A 4.5-V battery is connected to a bulb whose resistance Is 1.3 ?. How many electrons leave the battery per minute?

Problem 10Q Explain why light bulbs almost always burn out just as they are turned on and not after they have been on for some time.

Problem 11MCQ When a light switch is turned on, the light comes on immediately because (a) the electrons coming from the power source move through the initially empty wires very fast. (b) the electrons already in the wire are instantly “pushed” by a voltage difference. (c) the light bulb may be old with low resistance. It would take longer if the bulb were new and had high resistance. (d) the electricity bill is paid. The electric company can make it take longer when the bill is unpaid.

Problem 11P (II) An electric device draws 5.60 A at 240 V. (a) If the voltage drops by 15%, what will be the current, assuming nothing else changes? (b) If the resistance of the device were reduced by 15%, what current would be drawn at 240 V?

Problem 11Q Which draws more current, a 100-W lightbulb or a 75-W bulb? Which has the higher resistance?

(I) What is the diameter of a 1.00-m length of tungsten wire whose resistance is \(0.32\ \Omega\).

Problem 12Q Electric power is transferred over large distances at very high voltages. Explain how the high voltage reduces power losses in the transmission lines.

Problem 13P (I) What is the resistance of a 5.4-m length of copper wire 1.5 mm in diameter?

Problem 13Q A 15-A fuse blows out repeatedly. Why is it dangerous to replace this fuse with a 25-A fuse?

Problem 14P (II) Calculate the ratio of the resistance of 10.0 m of aluminum wire 2.2 mm in diameter, to 24.0 m of copper wire 1.8 mm in diameter.

Problem 15P (II) Can a 2.2-mm-diameter copper wire have the same resistance as a tungsten wire of the same length? Give numerical details.

Problem 15Q Driven by ac power, the same electrons pass back and forth through your reading lamp over and over again. Explain why the light stays lit instead of going out after the first pass of electrons.

Problem 16P (II) A certain copper wire has a resistance of 15.0 ?. At what point along its length must the wire be cut so that the resistance of one piece is 4.0 times the resistance of the other? What is the resistance of each piece?

The heating element in a toaster is made of Nichrome wire. Immediately after the toaster is turned on, is the current magnitude \(\left(I_{\mathrm{rms}}\right)\) in the wire increasing, decreasing, or staying constant? Explain. Equation Transcription: Text Transcription: (I_rms)

Problem 17P (II) Compute the voltage drop along a 21-m length of household no. 14 copper wire (used in 15-A circuits). The wire has diameter 1.628 mm and carries a 12-A current.

Problem 17Q Is current used up in a resistor? Explain.

Problem 18EA If 1 million electrons per second pass a point in a wire, what is the current?

How many coulombs is \(1.00 \ \mathrm A \cdot \mathrm h\)?

Problem 18EC What is the resistance of a lightbulb if 0.50 A flows through it when 120 V is connected across it?

Return to the Chapter-Opening Question, page 501, and answer it again now. Try to explain why you may have answered differently the first time.

A copper wire has a resistance of \(10\ \Omega\). What would its resistance be if it had the same diameter but was only half as long? (a) \(20\ \Omega\), (b) \(10\ \Omega\), (c) \(5\ \Omega\), (d) \(1\ \Omega\), (e) none of these.

Copper wires in houses typically have a diameter of about . How long a wire would have a \(1.0-\Omega\) resistance? Equation transcription: Text transcription: 1.0-Omega

Problem 18EG The resistance of the tungsten filament of a common incandescent light bulb is how many times greater at its operating temperature of 2800 K than its resistance at room temperature? (a) Less than 1% greater; (b) roughly 10% greater; (c) about2 times greater; (d) roughly 10 times greater; (e) more than 100 times greater.

Problem 18EH Since 1 kWh = 3.6 X 106 J, how much mass must be lifted against gravity through one meter to do the equivalent amount of work?

How many 60-W 120-V lightbulbs can operate on a 20-A line? (a) 2; (b) 3; (c) 6; (d) 20; (e) 40.

Problem 18P (II) Two aluminum wires have the same resistance. If one has twice the length of the other, what is the ratio of the diameter of the longer wire to the diameter of the shorter wire?

Problem 18Q Why is it more dangerous to turn on an electric appliance when you are standing outside in bare feet than when you are inside wearing shoes with thick soles?

(II) A rectangular solid made of carbon has sides of lengths 1.0 cm, 2.0 cm, and 4.0 cm, lying along the , and axes, respectively (Fig. 18-35). Determine the resistance for current that passes through the solid in the direction, (b) the direction, and the direction. Assume the resistivity is \(p=3.0 \times 10^{-5} \Omega . m\). Equation transcription: Text transcription: p=3.0 times 10^{-5} Omega . m

Problem 19Q Compare the drift velocities and electric currents in two wires that are geometrically identical and the density of atoms is similar, but the number of free electrons per atom in the material of one wire is twice that in the other.

Problem 20P (II) A length of wire is cut in half and the two lengths are wrapped together side by side to make a thicker wire. How does the resistance of this new combination compare to the resistance of the original wire?

A voltage V is connected across a wire of length \(\ell\) and radius r. How is the electron drift speed affected if (a) \(\ell\) is doubled, (b) r is doubled, (c) V is doubled, assuming in each case that other quantities stay the same?

Problem 21P (II) How much would you have to raise the temperature of a copper wire (originally at 20°C) to increase its resistance by 12%?

Problem 22P (II) Determine at what temperature aluminum will have the same resistivity as tungsten does at 20°C.

Problem 23P (II) A 100-W lightbulb has a resistance of about 12.? when cold (20°C) and 140 ? when on (hot). Estimate the temperature of the filament when hot assuming an average temperature coefficient of resistivity ? =0.0045 (C°)-1

(III) A length of aluminum wire is connected to a precision 10.00-V power supply, and a current of 0.4212 A is precisely measured at \(23.5^{\circ}C\). The wire is placed in a new environment of unknown temperature where the measured current is 0.3818 A. What is the unknown temperature?

Problem 25P (III) For some applications, it is important that the value of a resistance not change with temperature. For example, suppose you made a 3.20 – k ? resistor from a carbon resistor and a Nichrome wire-wound resistor connected together so the total resistance is the sum of their separate resistances. What value should each of these resistors have (at 0°C) so that the combination is temperature independent?

Problem 26P (III) A 10.0-m length of wire consists of 5.0 m of copper followed by 5.0 m of aluminum, both of diameter 1.4 mm. A voltage difference of 95 mV is placed across the composite wire. (a) What is the total resistance (sum) of the two wires? (b) What is the current through the wire? (c) What are the voltages across the aluminum part and across the copper part?

Problem 27P (I) What is the maximum power consumption of a 3.0-V portable CD player that draws a maximum of 240 mA of current?

Problem 28P (I) The heating element of an electric oven is designed to produce 3.3 kW of heat when connected to a 240-V source. What must be the resistance of the element?

(I) What is the maximum voltage that can be applied across a \(3.9-k \Omega\) resistor rated at \(\frac{1}{4}\) watt? Equation transcription: Text transcription: 3.9-k Omega frac{1}{4}

Problem 30P (I) (a) Determine the resistance of, and current through, a 75-W lightbulb connected to its proper source voltage of 110 V. (b) Repeat for a 250-W bulb.

Problem 31P (I) An electric car has a battery that can hold 16 kWh of energy (approximately 6X 107 J). If the battery is designed to operate at 340 V, how many coulombs of charge would need to leave the battery at 340 V and return at 0 V to equal the stored energy of the battery?

Problem 32P (I) An electric car uses a 45-kW (160-hp) motor. If the battery pack is designed for 340V, what current would the motor need to draw from the battery? Neglect any energy losses in getting energy from the battery to the motor.

Problem 33P (II) A 120-V hair dryer has two settings: 950 W and 1450W. (a) At which setting do you guess the resistance to be higher? After making a guess, determine the resistance at (b) the lower setting, and (c) the higher setting.

Problem 34P (II) A 12-V battery causes a current of 0.60 A through a resistor. (a) What is its resistance, and (b) how many joules of energy does the battery lose in a minute?

Problem 35P (II) A 120-V fish-tank heater is rated at 130W. Calculate (a) the current through the heater when it is operating, and (b) its resistance.

Problem 36P (II) You buy a 75-W lightbulb in Europe, where electricity is delivered at 240 V. If you use the bulb in the United States at 120 V (assume its resistance does not change), how bright will it be relative to 75-W 120-V bulbs? [Hint: Assume roughly that brightness is proportional to power consumed.]

(II) How many kWh of energy does a 550-W toaster use in the morning if it is in operation for a total of 5.0 min? At a cost of 9.0 cents/kWh, estimate how much this would add to your monthly electric energy bill if you made toast four mornings per week.

Problem 38P (II) At $0.095/kWh, what does it cost to leave a 25-W porch light on day and night for a year?

Problem 39P (II) What is the total amount of energy stored in a 12-V, 65Ah car battery when it is fully charged?

(II) An ordinary flashlight uses two D-cell 1.5-V batteries connected in series to provide 3.0 V across the bulb, as in Fig. 18–4b (Fig. 18–36). The bulb draws 380 mA when turned on. (a) Calculate the resistance of the bulb and the power dissipated. (b) By what factor would the power increase if four D-cells in series (total 6.0 V) were used with the same bulb? (Neglect heating effects of the filament.)Why shouldn’t you try this?

(II) How many 75-W lightbulbs, connected to 120 V as in Fig. 18–20, can be used without blowing a 15-A fuse?

Problem 42P (II) An extension cord made of two wires of diameter 0.129 cm (no. 16 copper wire) and of length 2.7 m (9 ft) is connected to an electric heater which draws 18.0 A on a 120-V line. How much power is dissipated in the cord?

(II) You want to design a portable electric blanket that runs on a 1.5-V battery. If you use a 0.50-mm-diameter copper wire as the heating element, how long should the wire be if you want to generate 18 W of heating power?What happens if you accidentally connect the blanket to a 9.0-V battery?

Problem 44P (II) A power station delivers 750 kW of power at 12,000 V to a factory through wires with total resistance 3.0 ?. How much less power is wasted if the electricity is delivered at 50,000 V rather than 12,000 V?

Problem 45P (III) A small immersion heater can be used in a car to heat a cup of water for coffee or tea. If the heater can heat 120 mL of water from 25°C to 95°C in 8.0 min, (a) approximately how much current does it draw from the car’s 12-V battery, and (b) what is its resistance? Assume the manufacturer’s claim of 85% efficiency.

Problem 46P (III) The current in an electromagnet connected to a 240V line is 21.5 A. At what rate must cooling water pass over the coils for the water temperature to rise no more than 6.50 C°?

Problem 47P (I) Calculate the peak current in a 2.7-k? resistor connected to a 220-V rms ac source.

Problem 48P (I) An ac voltage, whose peak value is 180V, is across a 310-? resistor. What are the rms and peak currents in the resistor?

(II) Estimate the resistance of the \(120-V_{rms}\) circuits in your house as seen by the power company, when (a) everything electrical is unplugged, and (b) two 75-W lightbulbs are on.

Problem 50P (II) The peak value of an alternating current in a 1500-W device is 6.4 A. What is the rms voltage across it?

(II) An 1800-W arc welder is connected to a \(660-V_{rms}\) ac line. Calculate (a) the peak voltage and (b) the peak current.

(II) Each channel of a stereo receiver is capable of an average power output of into an\(8-\Omega\) loudspeaker (see Fig. 18-14). What are the rms voltage and the rms current fed to the speaker at the maximum power of , and at when the volume is turned down? Equation transcription: Text transcription: 8-Omega

Problem 53P (II) Determine (a) the maximum instantaneous power dissipated by a 2.2-hp pump connected to a 240 –V rms ac power source, and (b) the maximum current passing through the pump.

Problem 54P (II) A heater coil connected to a 240 –V rms ac line has a Resistance 38 ? of (a) What is the average power used? (b) What are the maximum and minimum values of the instantaneous power?

(II) A 0.65-mm-diameter copper wire carries a tiny dc current of \(2.7\ \mu A\). Estimate the electron drift velocity.

(II) A 4.80-m length of 2.0-mm-diameter wire carries a 750-mA dc current when 22.0 mV is applied to its ends. If the drift velocity is \(1.7 \times 10^{-5} \ \mathrm {m/s}\) determine (a) the resistance R of the wire, (b) the resistivity \(\rho\) and (c) the number n of free electrons per unit volume.

Problem 57P (III) At a point high in the Earth’s atmosphere, He2+ ions in a concentration of 2.4 X 1012/m3 are moving due north at a speed of 2.0 X 106 m/s. Also, a 7.0 X 1011/m3 concentration of O2 ions is moving due south at a speed of 6.2 X 106 m/s. Determine the magnitude and direction of the net current passing through unit area

Problem 58P (I) What is the magnitude of the electric field across an axon membrane 1.0 X 10-8 m thick if the resting potential is -70 mV?

Problem 59P (II) A neuron is stimulated with an electric pulse. The action potential is detected at a point 3.70 cm down the axon 0.0052 s later. When the action potential is detected 7.20 cm from the point of stimulation, the time required is 0.0063 s. What is the speed of the electric pulse along the axon? (Why are two measurements needed instead of only one?)

Problem 60P (III) During an action potential, Na+ ions move into the cell at a rate of about 3X 10-7 mol/m2 .s. How much power must be produced by the “active Na+ pumping” system to produce this flow against a +30 -mV potential difference? Assume that the axon is 10 cm long and 20 mm in diameter.

Problem 61GP A person accidentally leaves a car with the lights on. If each of the two headlights uses 40 W and each of the two taillights 6W, for a total of 92W, how long will a fresh 12-V battery last if it is rated at Assume the full 12 V appears across each bulb.

A sequence of potential differences V is applied across a wire (diameter = 0.32 mm, length = 11 cm) and the resulting currents I are measured as follows: (a) If this wire obeys Ohm’s law, graphing I vs. V will result in a straight-line plot. Explain why this is so and determine the theoretical predictions for the straight line’s slope and y-intercept. (b) Plot I vs. V. Based on this plot, can you conclude that the wire obeys Ohm’s law (i.e., did you obtain a straight line with the expected y-intercept, within the values of the significant figures)? If so, determine the wire’s resistance R. (c) Calculate the wire’s resistivity and use Table 18–1 to identify the solid material from which it is composed.

Problem 63GP What is the average current drawn by a 1.0-hp 120-V motor? (1 hp=746 W.)

Problem 64GP The conductance G of an object is defined as the reciprocal of the resistance R; that is G=1/R. The unit of conductance is a mho(=ohm-1), which is also called the siemens (S). What is the conductance (in siemens) of an object that draws 440 mA of current at 3.0 V?

The heating element of a 110-V, 1500-W heater is 3.8 m long. If it is made of iron, what must its diameter be?

Problem 66GP (a) A particular household uses a 2.2-kW heater 2.0 h/day (“on” time), four 100-W lightbulbs 6.0 h/day, a 3.0-kW electric stove element for a total of 1.0 h/day, and miscellaneous power amounting to 2.0 kWh/day. If electricity costs $0.115 per kWh, what will be their monthly bill (30 d)? (b) How much coal (which produces 7500 kcal/kg ) must be burned by a 35%-efficient power plant to provide the yearly needs of this household?

A small city requires about 15 MW of power. Suppose that instead of using high-voltage lines to supply the power, the power is delivered at 120 V. Assuming a two-wire line of 0.50-cm-diameter copper wire, estimate the cost of the energy lost to heat per hour per meter. Assume the cost of electricity is about 12 cents per kWh.

Problem 68GP A 1600-W hair dryer is designed for 117 V. (a) What will be the percentage change in power output if the voltage drops to 105 V? Assume no change in resistance. (b) How would the actual change in resistivity with temperature affect your answer?

Problem 69GP The wiring in a house must be thick enough so it does not become so hot as to start a fire. What diameter must a copper wire be if it is to carry a maximum current of 35 A and produce no more than 1.5 W of heat per meter of length?

Problem 70GP Determine the resistance of the tungsten filament in a 75-W 120-V incandescent light bulb (a) at its operating temperature of about 2800 K, (b) at room temperature.

Problem 71GP Suppose a current is given by the equation I=1.40 sin 210t, where I is in amperes and t in seconds. (a) What is the frequency? (b) What is the rms value of the current? (c) If this is the current through a 24.0-omega resistor, write the equation that describes the voltage as a function of time.

Problem 72GP A microwave oven running at 65%efficiency delivers 950W to the interior. Find (a) the power drawn from the source, and (b) the current drawn. Assume a source voltage of 120V.

A \(1.00 \Omega\) wire is stretched uniformly to 1.50 times its original length. What is its resistance now? Equation transcription: Text transcription: 1.00 Omega

Problem 74GP 220 V is applied to two different conductors made of the same material. One conductor is twice as long and twice the diameter of the second. What is the ratio of the power transformed in the first relative to the second?

An electric power plant can produce electricity at a fixed power , but the plant operator is free to choose the voltage at which it is produced. This electricity is carried as an electric current through a transmission line (resistance from the plant to the user, where it provides the user with electric power (a) Show that the reduction in power \(\Delta P=P-P\) due to transmission losses is given by \(\Delta P=P^{2} R / V^{2}\)(b) In order to reduce power losses during transmission, should the operator choose to be as large or as small as possible? Equation transcription: Text transcription: Delta P=P-P Delta P=P^{2} R / V^{2}

Problem 76GP A 2800-W oven is connected to a 240-V source. (a) What is the resistance of the oven? (b) How long will it take to bring 120 mL of 15°C water to 100°C assuming 65% efficiency? (c) How much will this cost at 11 cents/kWh?

Problem 77GP A proposed electric vehicle makes use of storage batteries as its source of energy. It is powered by 24 batteries, each 12V, Assume that the car is driven on level roads at an average speed of and the average friction force is 440 N. Assume 100% efficiency and neglect energy used for acceleration. No energy is consumed when the vehicle is stopped, since the engine doesn’t need to idle. (a) Determine the horsepower required. (b) After approximately how many kilometers must the batteries be recharged?

A \(15.2-\Omega\) resistor is made from a coil of copper wire whose total mass is What is the diameter of the wire, and how long is it? Equation transcription: Text transcription: 15.2-Omega

Problem 79GP A fish-tank heater is rated at 95 W when connected to 120V. The heating element is a coil of Nichrome wire. When uncoiled, the wire has a total length of 3.5 m. What is the diameter of the wire?

A lightbulb has a resistance of \(12 \Omega\) when cold \(\left(20^{0} \mathrm{C}\right)\) and \(140 \Omega\) when on (hot). Calculate its power consumption at the instant it is turned on, and after a few moments when it is hot. Equation transcription: Text transcription: 12 Omega (20^{0}{C}) 140 Omega

Problem 81GP In an automobile, the system voltage varies from about 12 V when the car is off to about 13.8 V when the car is on and the charging system is in operation, a difference of 15%. By what percentage does the power delivered to the headlights vary as the voltage changes from 12V to 13.8 V? Assume the headlight resistance remains constant.

A tungsten filament used in a flashlight bulb operates at and . If its resistance at \(20^{\circ} \mathrm{C}\) is \(1.5 \Omega\), what is the temperature of the filament when the flashlight is on? Equation transcription: Text transcription: 20^{circ}{C} 1.5 Omega

Problem 83GP Light Bulb A is rated at 120 V and 40 W for household applications. Light Bulb B is rated at 12V and 40 W for automotive applications. (a) What is the current through each bulb? (b) What is the resistance of each bulb? (c) In one hour, how much charge passes through each bulb? (d) In one hour, how much energy does each bulb use? (e) Which bulb requires larger diameter wires to connect its power source and the bulb?

Problem 84GP An air conditioner draws 18 A at 220-V ac. The connecting cord is copper wire with a diameter of 1.628 mm. (a) How much power does the air conditioner draw? (b) If the length of the cord (containing two wires) is 3.5 m, how much power is dissipated in the wiring? (c) If no. 12 wire, with a diameter of 2.053 mm, was used instead, how much power would be dissipated in the wiring? (d) Assuming that the air conditioner is run 12 h per day, how much money per month (30 days) would be saved by using no. 12 wire? Assume that the cost of electricity is 12 cents per kWh.

Problem 85GP An electric wheelchair is designed to run on a single 12-V battery rated to provide 100 ampere-hours (100 A.h ). (a) How much energy is stored in this battery? (b) If the wheelchair experiences an average total retarding force (mainly friction) of 210 N, how far can the wheelchair travel on one charge?

Problem 86GP If a wire of resistance R is stretched uniformly so that its length doubles, by what factor does the power dissipated in the wire change, assuming it remains hooked up to the same voltage source? Assume the wire’s volume and density remain constant.

Problem 87GP Copper wire of diameter 0.259 cm is used to connect a set of appliances at 120 V, which draw 1450 W of power total. (a) What power is wasted in 25.0 m of this wire? (b) What is your answer if wire of diameter 0.412 cm is used?

Problem 88GP Battery-powered electricity is very expensive compared with that available from a wall receptacle. Estimate the cost per kWh of (a) an alkaline D-cell (cost $1.70) and (b) an alkaline AA-cell (cost $1.25). These batteries can provide a continuous current of 25 mA for 820 h and 120 h, respectively, at 1.5 V. (c) Compare to the cost of a normal 120-V ac house source at $0.10/kWh.

A copper pipe has an inside diameter of 3.00 cm and an outside diameter of 5.00 cm (Fig. 18–37).What is the resistance of a 10.0-m length of this pipe?

The Tevatron accelerator at Fermilab (Illinois) is designed to carry an beam of protons \(\left(q=1.6 \times 10^{-19} C\right)\) traveling at very nearly the speed of light \(\left(3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)\) around a ring in circumference. How many protons are in the beam? Equation transcription: Text transcription: (q=1.6 times 10^{-19} C) (3.0 times 10^{8}{~m} /{s})

The level of liquid helium (temperature \(\approx 4 k\)) in its storage tank can be monitored using a vertically aligned niobiumtitanium (NbTi) wire, whose length spans the height of the tank. In this level-sensing setup, an electronic circuit maintains a constant electrical current at all times in the NbTi wire and a voltmeter monitors the voltage difference across this wire. Since the superconducting critical temperature for is , the portion of the wire immersed in the liquid helium is in the superconducting state, while the portion above the liquid (in helium vapor with temperature above is in the normal state. Define \(f=x / l\) to be the fraction of the tank filled with liquid helium (Fig. and \(V_{0}\) to be the value of when the tank is empty \((f=0)\). Determine the relation between and (in terms of \(V_{0}\) ). Equation transcription: Text transcription: approx 4 k f=x / l (f=0) V{0}

Problem 14Q When electric lights are operated on low-frequency ac (say, 5 Hz), they flicker noticeably. Why?

A current of 1.60 A flows in a wire. How many electrons are flowing past any point in the wire per second?

A service station charges a battery using a current of 6.7 A for 5.0 h. How much charge passes through the battery?

What is the current in amperes if flow across a cell membrane in The charge on the sodium is the same as on an electron, but positive

What is the resistance of a toaster if 120 V produces a current of 4.6 A?

What voltage will produce 0.25 A of current through a 4800 resistor?

How many coulombs are there in a 75 ampere-hour car battery?

(a) What is the current in the element of an electric clothes dryer with a resistance of when it is connected to 240 V? (b) How much charge passes through the element in 50 min? (Assume direct current.)

A bird stands on a dc electric transmission line carrying 4100 A (Fig. 1834). The line has resistance per meter, and the birds feet are 4.0 cm apart. What is the potential difference between the birds feet?

A hair dryer draws 13.5 A when plugged into a 120-V line. (a) What is its resistance? (b) How much charge passes through it in 15 min? (Assume direct current.)

A 4.5-V battery is connected to a bulb whose resistance is How many electrons leave the battery per minute?

An electric device draws 5.60 A at 240 V. (a) If the voltage drops by 15%, what will be the current, assuming nothing else changes? (b) If the resistance of the device were reduced by 15%, what current would be drawn at 240 V?

What is the diameter of a 1.00-m length of tungsten wire whose resistance is

What is the resistance of a 5.4-m length of copper wire 1.5 mm in diameter?

Calculate the ratio of the resistance of 10.0 m of aluminum wire 2.2 mm in diameter, to 24.0 m of copper wire 1.8 mm in diameter

Can a 2.2-mm-diameter copper wire have the same resistance as a tungsten wire of the same length? Give numerical details

A certain copper wire has a resistance of At what point along its length must the wire be cut so that the resistance of one piece is 4.0 times the resistance of the other? What is the resistance of each piece?

Compute the voltage drop along a 21-m length of household no. 14 copper wire (used in 15-A circuits). The wire has diameter 1.628 mm and carries a 12-A current.

Two aluminum wires have the same resistance. If one has twice the length of the other, what is the ratio of the diameter of the longer wire to the diameter of the shorter wire?

(II) A rectangular solid made of carbon has sides of lengths 1.0 cm, 2.0 cm, and 4.0 cm, lying along the x, y, and z axes, respectively (Fig. 18–35). Determine the resistance for current that passes through the solid in (a) the x direction, (b) the y direction, and (c) the z direction. Assume the resistivity is \(\rho=3.0 \times 10^{-5}\ \Omega \cdot m\).

A length of wire is cut in half and the two lengths are wrapped together side by side to make a thicker wire. How does the resistance of this new combination compare to the resistance of the original wire?

How much would you have to raise the temperature of a copper wire (originally at 20C) to increase its resistance by 12%?

Determine at what temperature aluminum will have the same resistivity as tungsten does at 20C

A 100-W lightbulb has a resistance of about when cold (20C) and when on (hot). Estimate the temperature of the filament when hot assuming an average temperature coefficient of resistivity

A length of aluminum wire is connected to a precision 10.00-V power supply, and a current of 0.4212 A is precisely measured at 23.5C. The wire is placed in a new environment of unknown temperature where the measured current is 0.3818 A. What is the unknown temperature?

For some applications, it is important that the value of a resistance not change with temperature. For example, suppose you made a resistor from a carbon resistor and a Nichrome wire-wound resistor connected together so the total resistance is the sum of their separate resistances. What value should each of these resistors have (at 0C) so that the combination is temperature independent?

A 10.0-m length of wire consists of 5.0 m of copper followed by 5.0 m of aluminum, both of diameter 1.4 mm. A voltage difference of 95 mV is placed across the composite wire. (a) What is the total resistance (sum) of the two wires? (b) What is the current through the wire? (c) What are the voltages across the aluminum part and across the copper part?

What is the maximum power consumption of a 3.0-V portable CD player that draws a maximum of 240 mA of current?

The heating element of an electric oven is designed to produce 3.3 kW of heat when connected to a 240-V source. What must be the resistance of the element?

What is the maximum voltage that can be applied across a resistor rated at watt?

(a) Determine the resistance of, and current through, a 75-W lightbulb connected to its proper source voltage of 110 V. (b) Repeat for a 250-W bulb

An electric car has a battery that can hold 16 kWh of energy (approximately ). If the battery is designed to operate at 340 V, how many coulombs of charge would need to leave the battery at 340 V and return at 0 V to equal the stored energy of the battery?

(I) An electric car uses a 45-kW (160-hp) motor. If the battery pack is designed for 340V, what current would the motor need to draw from the battery? Neglect any energy losses in getting energy from the battery to the motor.

(II) A 120-V hair dryer has two settings: 950 W and 1450W. (a) At which setting do you guess the resistance to be higher? After making a guess, determine the resistance at (b) the lower setting, and (c) the higher setting.

(II) A 12-V battery causes a current of 0.60 A through a resistor. (a) What is its resistance, and (b) how many joules of energy does the battery lose in a minute?

(II) A 120-V fish-tank heater is rated at 130W. Calculate (a) the current through the heater when it is operating, and (b) its resistance.

You buy a 75-W lightbulb in Europe, where electricity is delivered at 240 V. If you use the bulb in the United States at 120 V (assume its resistance does not change), how bright will it be relative to 75-W 120-V bulbs? [Hint: Assume roughly that brightness is proportional to power consumed.

How many kWh of energy does a 550-W toaster use in the morning if it is in operation for a total of 5.0 min? At a cost of estimate how much this would add to your monthly electric energy bill if you made toast four mornings per week.

At what does it cost to leave a 25-W porch light on day and night for a year?

What is the total amount of energy stored in a 12-V, 65 Ah car battery when it is fully charged?

An ordinary flashlight uses two D-cell 1.5-V batteries connected in series to provide 3.0 V across the bulb, as in Fig. 184b (Fig. 1836). The bulb draws 380 mA when turned on. (a) Calculate the resistance of the bulb and the power dissipated. (b) By what factor would the power increase if four D-cells in series (total 6.0 V) were used with the same bulb? (Neglect heating effects of the filament.) Why shouldnt you try this?

How many 75-W lightbulbs, connected to 120 V as in Fig. 1820, can be used without blowing a 15-A fuse?

An extension cord made of two wires of diameter 0.129 cm (no. 16 copper wire) and of length 2.7 m (9 ft) is connected to an electric heater which draws 18.0 A on a 120-V line. How much power is dissipated in the cord?

You want to design a portable electric blanket that runs on a 1.5-V battery. If you use a 0.50-mm-diameter copper wire as the heating element, how long should the wire be if you want to generate 18 W of heating power? What happens if you accidentally connect the blanket to a 9.0-V battery?

A power station delivers 750 kW of power at 12,000 V to a factory through wires with total resistance How much less power is wasted if the electricity is delivered at 50,000 V rather than 12,000 V?

A small immersion heater can be used in a car to heat a cup of water for coffee or tea. If the heater can heat 120 mL of water from 25C to 95C in 8.0 min, (a) approximately how much current does it draw from the cars 12-V battery, and (b) what is its resistance? Assume the manufacturers claim of 85% efficiency.

The current in an electromagnet connected to a 240-V line is 21.5 A. At what rate must cooling water pass over the coils for the water temperature to rise no more than 6.50 C?

Calculate the peak current in a resistor connected to a 220-V rms ac source.

An ac voltage, whose peak value is 180 V, is across a resistor. What are the rms and peak currents in the resistor?

Estimate the resistance of the circuits in your house as seen by the power company, when (a) everything electrical is unplugged, and (b) two 75-W lightbulbs are on

The peak value of an alternating current in a 1500-W device is 6.4 A. What is the rms voltage across it?

An 1800-W arc welder is connected to a ac line. Calculate (a) the peak voltage and (b) the peak current.

Each channel of a stereo receiver is capable of an average power output of 100 W into an loudspeaker (see Fig. 1814). What are the rms voltage and the rms current fed to the speaker (a) at the maximum power of 100 W, and (b) at 1.0 W when the volume is turned down?

Determine (a) the maximum instantaneous power dissipated by a 2.2-hp pump connected to a ac power source, and (b) the maximum current passing through the pump.

A heater coil connected to a ac line has a resistance of (a) What is the average power used? (b) What are the maximum and minimum values of the instantaneous power

A 0.65-mm-diameter copper wire carries a tiny dc current of Estimate the electron drift velocity

A 4.80-m length of 2.0-mm-diameter wire carries a 750-mA dc current when 22.0 mV is applied to its ends. If the drift velocity is determine (a) the resistance R of the wire, (b) the resistivity and (c) the number n of free electrons per unit volume.

At a point high in the Earths atmosphere, in a concentration of are moving due north at a speed of Also, a concentration of is moving due south at a speed of Determine the magnitude and direction of the net current passing through unit area

What is the magnitude of the electric field across an axon membrane thick if the resting potential is

A neuron is stimulated with an electric pulse. The action potential is detected at a point 3.70 cm down the axon 0.0052 s later. When the action potential is detected 7.20 cm from the point of stimulation, the time required is 0.0063 s. What is the speed of the electric pulse along the axon? (Why are two measurements needed instead of only one?)

During an action potential, move into the cell at a rate of about How much power must be produced by the active pumping system to produce this flow against a potential difference? Assume that the axon is 10 cm long and in diameter.

A person accidentally leaves a car with the lights on. If each of the two headlights uses 40 W and each of the two taillights 6 W, for a total of 92 W, how long will a fresh 12-V battery last if it is rated at Assume the full 12 V appears across each bulb.

A sequence of potential differences V is applied across a wire and the resulting currents I are measured as follows: V (V) 0.100 0.200 0.300 0.400 0.500 I (mA) 72 142 218 290 357 (a) If this wire obeys Ohms law, graphing I vs. V will result in a straight-line plot. Explain why this is so and determine the theoretical predictions for the straight lines slope and y-intercept. (b) Plot I vs. V. Based on this plot, can you conclude that the wire obeys Ohms law (i.e., did you obtain a straight line with the expected y-intercept, within the values of the significant figures)? If so, determine the wires resistance R. (c) Calculate the wires resistivity and use Table 181 to identify the solid material from which it is composed.

What is the average current drawn by a 1.0-hp 120-V motor?

The conductance G of an object is defined as the reciprocal of the resistance R; that is, The unit of conductance is a which is also called the siemens (S). What is the conductance (in siemens) of an object that draws 440 mA of current at 3.0 V?

The heating element of a 110-V, 1500-W heater is 3.8 m long. If it is made of iron, what must its diameter be?

A particular household uses a 2.2-kW heater (on time), four 100-W lightbulbs a 3.0-kW electric stove element for a total of and miscellaneous power amounting to If electricity costs $0.115 per kWh, what will be their monthly bill (30 d)? (b) How much coal (which produces ) must be burned by a 35%-efficient power plant to provide the yearly needs of this household?

A small city requires about 15 MW of power. Suppose that instead of using high-voltage lines to supply the power, the power is delivered at 120 V. Assuming a two-wire line of 0.50-cm-diameter copper wire, estimate the cost of the energy lost to heat per hour per meter. Assume the cost of electricity is about 12 cents per kWh.

A 1600-W hair dryer is designed for 117 V. (a) What will be the percentage change in power output if the voltage drops to 105 V? Assume no change in resistance. (b) How would the actual change in resistivity with temperature affect your answer

The wiring in a house must be thick enough so it does not become so hot as to start a fire. What diameter must a copper wire be if it is to carry a maximum current of 35 A and produce no more than 1.5 W of heat per meter of length?

Determine the resistance of the tungsten filament in a 75-W 120-V incandescent lightbulb (a) at its operating temperature of about 2800 K, (b) at room temperature.

Suppose a current is given by the equation where I is in amperes and t in seconds. (a) What is the frequency? (b) What is the rms value of the current? (c) If this is the current through a resistor, write the equation that describes the voltage as a function of time

A microwave oven running at 65% efficiency delivers 950 W to the interior. Find (a) the power drawn from the source, and (b) the current drawn. Assume a source voltage of 120 V.

A wire is stretched uniformly to 1.50 times its original length. What is its resistance now?

220 V is applied to two different conductors made of the same material. One conductor is twice as long and twice the diameter of the second. What is the ratio of the power transformed in the first relative to the second?

An electric power plant can produce electricity at a fixed power P, but the plant operator is free to choose the voltage V at which it is produced. This electricity is carried as an electric current I through a transmission line (resistance R) from the plant to the user, where it provides the user with electric power (a) Show that the reduction in power due to transmission losses is given by (b) In order to reduce power losses during transmission, should the operator choose V to be as large or as small as possible?

A 2800-W oven is connected to a 240-V source. (a) What is the resistance of the oven? (b) How long will it take to bring 120 mL of 15C water to 100C assuming 65% efficiency? (c) How much will this cost

A proposed electric vehicle makes use of storage batteries as its source of energy. It is powered by 24 batteries, each 12 V, Assume that the car is driven on level roads at an average speed of and the average friction force is 440 N. Assume 100% efficiency and neglect energy used for acceleration. No energy is consumed when the vehicle is stopped, since the engine doesnt need to idle. (a) Determine the horsepower required. (b) After approximately how many kilometers must the batteries be recharged?

A resistor is made from a coil of copper wire whose total mass is 15.5 g. What is the diameter of the wire, and how long is it?

A fish-tank heater is rated at 95 W when connected to 120 V. The heating element is a coil of Nichrome wire. When uncoiled, the wire has a total length of 3.5 m. What is the diameter of the wire?

A 100-W, 120-V lightbulb has a resistance of when cold (20C) and when on (hot). Calculate its power consumption (a) at the instant it is turned on, and (b) after a few moments when it is hot.

In an automobile, the system voltage varies from about 12 V when the car is off to about 13.8 V when the car is on and the charging system is in operation, a difference of 15%. By what percentage does the power delivered to the headlights vary as the voltage changes from 12 V to 13.8 V? Assume the headlight resistance remains constant

A tungsten filament used in a flashlight bulb operates at 0.20 A and 3.0 V. If its resistance at 20C is what is the temperature of the filament when the flashlight is on?

Lightbulb A is rated at 120 V and 40 W for household applications. Lightbulb B is rated at 12 V and 40 W for automotive applications. (a) What is the current through each bulb? (b) What is the resistance of each bulb? (c) In one hour, how much charge passes through each bulb? (d) In one hour, how much energy does each bulb use? (e) Which bulb requires larger diameter wires to connect its power source and the bulb?

An air conditioner draws 18 A at 220-V ac. The connecting cord is copper wire with a diameter of 1.628 mm. (a) How much power does the air conditioner draw? (b) If the length of the cord (containing two wires) is 3.5 m, how much power is dissipated in the wiring? (c) If no. 12 wire, with a diameter of 2.053 mm, was used instead, how much power would be dissipated in the wiring? (d) Assuming that the air conditioner is run 12 h per day, how much money per month (30 days) would be saved by using no. 12 wire? Assume that the cost of electricity is 12 cents per kWh.

An electric wheelchair is designed to run on a single 12-V battery rated to provide 100 ampere-hours (100 ). (a) How much energy is stored in this battery? (b) If the wheelchair experiences an average total retarding force (mainly friction) of 210 N, how far can the wheelchair travel on one charge?

If a wire of resistance R is stretched uniformly so that its length doubles, by what factor does the power dissipated in the wire change, assuming it remains hooked up to the same voltage source? Assume the wires volume and density remain constant.

Copper wire of diameter 0.259 cm is used to connect a set of appliances at 120 V, which draw 1450 W of power total. (a) What power is wasted in 25.0 m of this wire? (b) What is your answer if wire of diameter 0.412 cm is used?

Battery-powered electricity is very expensive compared with that available from a wall receptacle. Estimate the cost per kWh of (a) an alkaline D-cell (cost $1.70) and (b) an alkaline AA-cell (cost $1.25). These batteries can provide a continuous current of 25 mA for 820 h and 120 h, respectively, at 1.5 V. (c) Compare to the cost of a normal 120-V ac house source at

A copper pipe has an inside diameter of 3.00 cm and an outside diameter of 5.00 cm (Fig. 1837). What is the resistance of a 10.0-m length of this pipe

The Tevatron accelerator at Fermilab (Illinois) is designed to carry an 11-mA beam of protons traveling at very nearly the speed of light around a ring 6300 m in circumference. How many protons are in the beam

The level of liquid helium (temperature ) in its storage tank can be monitored using a vertically aligned niobium titanium (NbTi) wire, whose length spans the height of the tank. In this level-sensing setup, an electronic circuit maintains a constant electrical current I at all times in the NbTi wire and a voltmeter monitors the voltage difference V across this wire. Since the superconducting critical temperature for NbTi is 10 K, the portion of the wire immersed in the liquid helium is in the superconducting state, while the portion above the liquid (in helium vapor with temperature above 10 K) is in the normal state. Define to be the fraction of the tank filled with liquid helium (Fig. 1838) and to be the value of V when the tank is empty Determine the relation between f and V (in terms of )