Integrated Concepts The classic Millikan oil drop

Problem 68PE Construct Your Own Problem Consider identical spherical conducting space ships in deep space where gravitational fields from other bodies are negligible compared to the gravitational attraction between the ships. Construct a problem in which you place identical excess charges on the space ships to exactly counter their gravitational attraction. Calculate the amount of excess charge needed. Examine whether that charge depends on the distance between the centers of the ships, the masses of the ships, or any other factors. Discuss whether this would be an easy, difficult, or even impossible thing to do in practice.

Problem 66PE Unreasonable Results A wrecking yard inventor wants to pick up cars by charging a 0.400 m diameter ball and inducing an equal and opposite charge on the car. If a car has a 1000 kg mass and the ball is to be able to lift it from a distance of 1.00 m: (a) What minimum charge must be used? (b) What is the electric field near the surface of the ball? (c) Why are these results unreasonable? (d) Which premise or assumption is responsible?

Problem 65PE Unreasonable Results (a) Two 0.500 g raindrops in a thunderhead are 1.00 cm apart when they each acquire 1.00 mC charges. Find their acceleration. (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?

Problem 63PE Integrated Concepts (a) In Figure 18.59, four equal char? ges? q lie on the corners of a square. A fifth ch? arge? q is on a mass m directly above the center of the square, at a height equal to the length d of one side of the square. Determine the magni?tude of? q in te? rms of? q , m , and d , if the Coulomb force is to equal the weight of m . (b) Is this equilibrium stable or unstable? Discuss.

Problem 61PE Integrated Concepts Figure 18.57 shows an electron passing between two charged metal plates that create an 100 N/C vertical electric field perpendicular to the electron’s original horizontal velocity. (These can be used to change the electron’s direction, such as in an oscilloscope.) The initial speed of the electron is 3.00×10? m/s , and the horizontal distance it travels in the uniform field is 4.00 cm. (a) What is its vertical deflection? (b) What is the vertical component of its final velocity? (c) At what angle does it exit? Neglect any edge effects.

Problem 62PE Integrated Concepts The classic Millikan oil drop experiment was the first to obtain an accurate measurement of the charge on an electron. In it, oil drops were suspended against the gravitational force by a vertical electric field. (See Figure 18.58.) Given the oil drop to be 1.00 µm in radius and have a density of 920 kg/m3 : (a) Find the weight of the drop. (b) If the drop has a single excess electron, find the electric field strength needed to balance its weight.

Problem 59PE Integrated Concepts The practical limit to an electric field in air is about 3.00 6? × 10? N/C. Above this strength, sparking takes place because air begins to ionize and charges flow, reducing the field. (a) Calculate the distance a free proton must travel in this field to reach 3.00% of the speed of light, starting from rest. (b) Is this practical in air, or must it occur in a vacuum?

Problem 58PE Integrated Concepts An electron has an initial velocity of 5.00 × 10? m/s in a uniform 2.00 × 10? 5 N/C strength electric field. The field accelerates the electron in the direction opposite to its initial velocity. (a) What is the direction of the electric field? (b) How far does the electron travel before coming to rest? (c) How long does it take the electron to come to rest? (d) What is the electron’s velocity when it returns to its starting point?

Problem 1Q What quantity is measured by a battery rating given in ampere-hours Explain.

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 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 3Q When a flashlight is operated, what is being used up: battery current, battery voltage, battery energy, battery power, or battery resistance? Explain.

Problem 4Q 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 6Q Can a copper wire and an aluminum wire of the same length have the same resistance? Explain.

Problem 8Q 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?

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.

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.

What happens when a lightbulb burns out?

Problem 11Q Explain why lightbulbs almost always burn out just as they are turned on and not after they have been on for some time.

Problem 12P (I) What is the diameter of a 1 00-m length of tungsten wire whose resistance is 0.32 ??

Problem 12Q Which draws more current, a 100-W lightbulb or a 75-W bulb? Which has the higher resistance?

Problem 13Q Electric power is transferred over large distances at very high voltages. Explain how the high voltage reduces power losses in the transmission lines.

Problem 14Q A 15-A fuse blows out repeatedly. Why is it dangerous to replace this fuse with a 25-A fuse?

Problem 15Q When electric lights are operated on low-frequency ac (say, 5 Hz), they flicker noticeably. Why?

Problem 16Q 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 17Q The heating element in a toaster is made of Nichrome wire. Immediately after the toaster is turned on, is the current magnitude (/rms) in the wire increasing, decreasing, or staying constant? Explain.

Problem 18Q Is current used up in a resistor? Explain.

Problem 32P (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) 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 \(\rho=3.0 \times 10^{-5} \Omega . m\). Equation Transcription: Text Transcription: \rho=3.0 \times 10^-5 \Omega . m

Problem 34P (II) At S0.095/kWh, what does it cost to leave a 25-W porch light on day and night for a year?

Problem 44P (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 46P (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.

Problem 52P (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 55P (Ill) 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 57GP What is the average current drawn by a 1.0-hp 120-V motor? (1 hp=746 W.)

Problem 58GP 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 rated at Assume the full 12 V appears across each bulb.

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?

Problem 1P A current of 1.30 A flows in a wire. How many electrons are flowing past any point in the wire per second?

Problem 67GP A microwave oven running at 65%efficiency delivers 950W to the interior. Find (a) the power drawn from the source, and (P) the current drawn. Assume a source voltage of 120V.

Problem 3P What is the current in amperes if 1200 Na+ ions flow across a cell membrane in 3.5 ?s? The charge on the sodium is the same as on an electron, but positive.

Problem 69GP 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?

Problem 4P What is the resistance of a toaster if 120 V produces a current of 4.2 A?

Problem 74GP A 100-W, 120-V lightbulb has a resistance of 12 a when cold (20°C) and 140a when on (hot). Calculate its power consumption (a) at the instant it is turned on. and (P) after a few moments when it is hot.

Problem 5P What voltage will produce 0.25 A of current through a 3800-? resistor?

Problem 75GP The Tevatron accelerator at Fermilab (Illinois) is designed to carry an 11-mA beam of protons (q=1.6 x 10-19C) travelling at very nearly the speed of light (3.0 x 108 m/s) around a ring 6300 m in circumference,. How many protons are in the beam?

Problem 5Q When you turn on a water faucet, the water usually flows immediately. You don’t have to wait for water to flow from the faucet valve to the spout. Why not? Is the same thing true when you connect a wire to the terminals of a battery?

Problem 76GP 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? (cf) 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.

(II) A hair dryer draws \(7.5 \mathrm{~A}\) when plugged into a \(120-\mathrm{V}\) line. (a) What is its resistance? (b) How much charge passes through it in \(15 \mathrm{~min}\) ? (Assume direct current.)

Problem 78GP 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.

Problem 7P An electric clothes dryer has a heating element with a resistance of 9.6 ?. (a) What is the current in the element when it is connected to 240 V? (b) How much charge passes through the element in 50 min?

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?

Problem 8P A 9.0-V battery is connected to a bulb whose resistance is 1.6 ?. How many electrons leave the battery per minute?

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?

(II) A bird stands on a dc electric transmission line carrying 2800 A (Fig. 18–34). The line has \(2.5 \times 10^{-5} \Omega\) resistance per meter, and the bird’s feet are 4.0 cm apart. What is the potential difference between the bird’s feet? Equation Transcription: Text Transcription: 2.5 \times 10^-5 \Omega

Problem 83GP 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 a. what is the temperature of the filament when the flashlight is on?

Problem 10P An electric device draws 6.50 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 11P 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?

What is the resistance of a 3.5-m length of copper wire 1.5 mm in diameter?

(II) Calculate the ratio of the resistance of \(10.0 \mathrm{~m}\) of aluminum wire \(2.0 \mathrm{~mm}\) in diameter, to \(20.0 \mathrm{~m}\) of copper wire \(2.5 \mathrm{~mm}\) in diameter.

Problem 15P Can a 2.5-mm-diameter copper wire have the same resistance as a tungsten wire of the same length? Give numerical details.

Problem 16P A certain copper wire has a resistance of 10.0 ?. 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?

Problem 17P How much would you have to raise the temperature of a copper wire (originally at 20°C) to increase its resistance by 15%?

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

Problem 19P 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 ? = 0.0060 (C°)?1.

Different lamps might have batteries connected in either of the two arrangements shown in Fig. 18–33. What would be the advantages of each scheme?

Problem 20P Compute the voltage drop along a 26-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.

(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?

(II) 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 \(20.0^{\circ} \mathrm{C}\). The wire is placed in a new environment of unknown temperature where the measured current is 0.3618 A. What is the unknown temperature?

Problem 24P A 10.0-m length of wire consists of 5.0 m of copper followed by 5.0 m of aluminum, both of diameter 1.0 mm. A voltage difference of 85 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?

(III) For some applications, it is important that the value of a resistance not change with temperature. For example, suppose you made a \(4.70-\mathrm{k} \Omega\) 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 \(0^{\circ} \mathrm{C}\)) so that the combination is temperature independent?

(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?

Problem 27P What is the maximum power consumption of a 3.0-V portable CD player that draws a maximum of 320 mA of current?

(I) What is the maximum voltage that can be applied across a \(2.7-k \Omega\) resistor rated at \(\frac{1}{4}\) watt? Equation Transcription: Text Transcription: 2.7-k \Omega \frac{1 4

Problem 30P A 115-V fish-tank heater is rated at 110W. Calculate (a) the current through the heater when it is operating, and (b) its resistance?

Problem 29P (a) Determine the resistance of, and current through, a 75-W lightbulb connected to its proper source voltage of 120 V. (b) Repeat for a 440-W bulb.

Problem 31P A 120-V hair dryer has two settings: 850 W and 1250 W. (a) At which setting do you expect the resistance to be higher? After making a guess, determine the resistance at (b) the lower setting; and (c) the higher setting.

Problem 33P How many kWh of energy does a 550-W toaster use in the morning if it is in operation for a total of 15min? 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.

(II) An ordinary flashlight uses two D-cell 1.5-V batteries connected in series as in Fig. 18–4b (Fig. 18–36).The bulb draws 450 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 were used with the same bulb? (Neglect heating effects of the filament.) Why shouldn’t you try this?

(II) What is the total amount of energy stored in a \(12-\mathrm{V}\), \(85-\mathrm{A} \cdot \mathrm{h}\) car battery when it is fully charged?

(II) How many 100-W lightbulbs, connected to 120 V as in Fig. 18–20, can be used without blowing a 15-A fuse?

Problem 38P 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 15.0 A on a 120-V line. How much power is dissipated in the cord?

Problem 39P A power station delivers 620 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?

(III) The current in an electromagnet connected to a 240-V line is 17.5 A. At what rate must cooling water pass over the coils if the water temperature is to rise by no more than \(7.50 \ C^\circ\)?

Problem 41P 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 60% efficiency.

(1) Calculate the peak current in a \(2.2-\mathrm{k} \Omega\) resistor connected to a \(220-\mathrm{V}\) rms ac source.

An ac voltage, whose peak value is 180 V, is across a \(330-\Omega\) resistor. What are the rms and peak currents in the resistor?

(II) The peak value of an alternating current in a 1500-W device is 5.4 A. What is the rms voltage across it?

Problem 47P (a) What is the maximum instantaneous power dissipated by a 3.0-hp pump connected to a 240-Vrms ac power source? (b) What is the maximum current passing through the pump?

Problem 48P A heater coil connected to a 240-Vrms ac line has a resistance of 34 ?. (a) What is the average power used? (b)What are the maximum and minimum values of the instantaneous power?

Problem 49P A 0.65-mm-diameter copper wire carries a tiny current of 2.3 ?A. What is the electron drift speed in the wire?

Problem 50P A 5.80-m length of 2.0-mm-diameter wire carries a 750-mA current when 22.0 mV is applied to its ends. If the drift speed is 1.7 × 10?5m/s, determine (a) the resistance R of the wire, (b) the resistivity ?, and (c) the number n of free electrons per unit volume.

(III) At a point high in the Earth’s atmosphere, \(\mathrm{He}^{2}+\) ions in a concentration of \(2.8 X 10^{12} / m^{3}\) are moving due north at a speed of \(2.0 X 10^{6} \mathrm{~m} / \mathrm{s}\). Also, a \(7.0 X 10^{11} / \mathrm{m}^{3}\) concentration of \(O_{2}^{-}\) ions is moving due south at a speed of \(7.2 X 10^{6} \mathrm{~m} / \mathrm{s}\). Determine the magnitude and direction of the net current passing through unit area \(\left(A / m^{2}\right)\). Equation Transcription: Text Transcription: He^2+ 2.8 X 10^12/m^3 2.0 X 10^6m/s 7.0 X 1011/m3 O^2- 7.2 X 10^6m/s (A/m^2)

Problem 53P A neuron is stimulated with an electric pulse. The action potential is detected at a point 3.40 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?)

(III) Estimate how much energy is required to transmit one action potential along the axon of Example 18–15. [Hint: the energy to transmit one pulse is equivalent to the energy stored by charging the axon capacitance; see Section 17–9]. What minimum average power is required for \(10^{4}\) neurons each transmitting 100 pulses per second? Equation Transcription: Text Transcription: 10^4

How many coulombs are there in 1.00 ampere-hour?

Problem 59GP The heating element of a 110-V, 1500-W heater is 5.4 m long. If it is made of iron, what must its diameter be?

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 \(mho \left(=\mathrm{ohm}^{-1}\right)\), which is also called the siemens (S). What is the conductance (in siemens) of an object that draws \(730 \mathrm{~mA}\) of current at \(3.0 \mathrm{~V}\) ?

Problem 61GP A small city requires about 10 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 10 cents per kWh.

Problem 64GP A 1200-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?

(a) A particular household uses a \(1.8-\mathrm{kW}\) heater \(3.0 \mathrm{~h} /\) day ("on" time), four \(100-\mathrm{W}\) lightbulbs \(6.0 \mathrm{~h} /\) day, a \(3.0-\mathrm{kW}\) electric stove element for a total of \(1.4 \mathrm{~h} /\) day, and miscellaneous power amounting to \(2.0 \mathrm{kWh} /\) day. If electricity costs $0.105 per \(\mathrm{kWh}\), what will be their monthly bill \((30 \mathrm{~d})\)? (b) How much coal (which produces \(7000 \mathrm{kcal} / \mathrm{kg}\) ) must be burned by a 35%-efficient power plant to provide the yearly needs of this household?

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 1.8 W of heat per meter of length?

Problem 66GP Suppose a current is given by the equation I = 1.80 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 42.0-? resistor, write the equation that describes the voltage as a function of time.

A \(1.00-\Omega\) wire is stretched uniformly to 3.00 times its original length. What is its resistance now?

Problem 70GP An electric heater is used to heat a room of volume 62 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 850kcal/h. If the air is to be maintained at 20°C, what minimum wattage must the heater have? (The specific heat of air is about 0.17 kcal/kg·C°.)

Problem 71GP A 2200-W oven is hooked 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 75% efficiency? (c) How much will this cost at 11 cents/kWh?

Problem 72GP A projected electric vehicle makes use of storage batteries as its source of energy. Its mass is 1560 kg and it is powered by 24 batteries, each 12 V, 95 A·h. Assume that the car is driven on level roads at an average speed of 45 km/h, and the average friction force is 240 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 \(12.5-\Omega\) resistor is made from a coil of copper wire whose total mass is 18.0 g. What is the diameter of the wire, and how long is it?

Problem 77GP 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 3.8 m. What is the diameter of the wire?

Problem 80GP Copper wire of diameter 0.259 cm is used to connect a set of appliances at 120 V, which draw 2250 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 82GP 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?