?\(\text { Power }=I \times V\)An electric toy draws 0.5 A from a 120-V outlet. Show

Suppose you could expend 10 joules of work to push a 1-coulomb charged particle against an electric field. What would be its change of voltage? If the particle is released, what will be its kinetic energy as it flies past its starting position?

The potential difference between a storm cloud and the ground is 100 million volts. If a charge of 2 C flashes in a bolt from cloud to Earth, show that the change of potential energy of the charge is \(2 \times 10^{8} \mathrm{~J}\). Text Transcription: 2 x 10^8 J

The current driven by voltage V in a circuit of resistance R is given by Ohm’s law, \(I=\frac{V}{R}\). Show that the resistance of a circuit carrying current I and driven by voltage V is given by the equation \(R=\frac{V}{I}\). Text Transcription: I = V/R R = V/I

The same voltage V is impressed on each of the branches of a parallel circuit. The voltage source provides a total current \(I_{\text {total }}\) to the circuit and “sees” a total equivalent resistance of \(R_{\mathrm{eq}}\) in the circuit. That is, \(V=I_{\text {total }} R_{\mathrm{eq}}\). The total current is equal to the sum of the currents through each branch of the parallel circuit. In a circuit with n branches, \(I_{\text {total }}=I_{1}+I_{2}+I_{3}+\cdots+I_{n}\). Use Ohm’s law \(\left(I=\frac{V}{R}\right)\) and show that the equivalent resistance of a parallel circuit with n branches is given by \(\frac{1}{R_{\mathrm{eq}}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}} \cdots+\frac{1}{R_{n}}\) Text Transcription: I_total R_eq V = I_totalR_eq I_total = I1_ + I_2 + I_3 + . . . + I_n 1/r_eq = 1/R_1 + 1/R_2 + 1/R_3 … _+ 1/R_n (I = V/R)

The power in watts marked on a light bulb is not an inherent property of the bulb; rather, it depends on the voltage to which it is connected, usually 110 or 120 V. (a) Show that the current in a 300-W bulb connected in a 120-V circuit is 2.5 A. (b) Compute the resistance of the bulb’s filament. (c) Assuming this resistance does not change, compute the bulb’s power output if the bulb is instead connected to a 24-V battery.

Rearrange the formula Current = voltage/resistance \(\left(I=\frac{V}{R}\right)\) to express resistance in terms of current and voltage. Then consider the following: A certain device in a 120-V circuit has a current rating of 20 A. Show that the resistance of the device is \(6 \Omega\). Text Transcription: (I = V/R) 6 omega

Three 6-ohm \(6 \Omega\) resistors are arranged in a triangle as shown. A voltage source of 12 V is impressed across one of the resistors. (a) How much current is in that resistor? (b) How much current is in each of the other two resistors? Text Transcription: 6 omega

Using the formula Power = current \(\times\) voltage, show that the current drawn by a 1200-W hair dryer connected to 120 V is 10 A. Then use the same method you used to solve the previous problem, and show that the resistance of the hair dryer is \(12 \Omega\). Text Transcription: 12 omega

The power of an electric circuit is given by the formula P = IV. Use Ohm’s law to express V and show that power can be expressed by the equation \(P=I^{2} R\). Text Transcription: P = I^2R

A dehumidifier with a resistance of \(20 \Omega\) draws 6.0 A when connected to an electrical outlet. Show that the power consumed by the iron is 720 W. Text Transcription: 20 omega

An electric space heater dissipates 1320 W of power via electromagnetic radiation and convection when connected to 120 V. When current is unknown, power can be expressed as \(P=\frac{V^{2}}{R}\). Use this formula to show that the resistance of the space heater is about \(11 \Omega\). Text Transcription: P = V^2/R 11 omega

The total charge that an automobile battery can supply without being recharged is given in terms of ampere-hours. A typical 12-V battery has a rating of 60 ampere-hours (60 A for 1 h, 30 A for 2 h, and so on). Suppose you forget to turn off the headlights in your parked automobile. If each of the two headlights draws 3 A, show that your battery will go dead in about 10 h.

Show that it costs 7 cents to operate a 25-W porch light for 24 h if electric energy costs 12\(\text{¢}\) per kW.h. Text Transcription: cent

Suppose you operate a 100-W lamp continuously for 1 week when the power utility rate is 12\(\text{¢}\)/kW.h. Show that the cost is $2.02. Text Transcription: cent

An electric dryer connected to a 120-V source draws 8.4 A of current. Show that the amount of heat generated in 1 min is about 60 kJ.

For the electric dryer of the previous problem, show that the number of coulombs that flow through in 1 minute is approximately 500 C.

An incandescent light bulb with an operating resistance of \(95 \Omega\) is labeled “150 W.” Is this bulb designed for use in a 120-V circuit or a 220-V circuit? Defend your answer. Text Transcription: 95 omega

In periods of peak demand, power companies lower their voltage in order to save power (and save you money). To see the effect, consider a 1200-W toaster that draws 10 A when connected to 120 V. Suppose the voltage is lowered by 10% to 108 V. By how much does the current decrease? By how much does the power decrease? (CAUTION: The 1200-W label is valid only when 120 V is applied. When the voltage is lowered, the resistance of the toaster, not its power, remains constant. Also, when metal wire such as the toaster coil cools, its resistance drops also, which we will ignore here.)

The three pairs of same-size metal spheres have different charges on their surfaces, as indicated. The members of each pair are brought together, allowed to touch, and then separated. Rank, from greatest to least, the total amount of charge on the pairs of spheres after separation.

Rank, from brightest to dimmest, the identical bulbs in the following circuits.

The bulbs are identical. Ammeters are placed in different locations, as shown. Rank, from greatest to least, the current readings in the three ammeters.

All bulbs are identical in the circuits. An ammeter is connected next to each battery, as shown. Rank, from greatest to least, the current readings in the three ammeters.

All bulbs are identical in the circuits. A voltmeter is connected across a single bulb in each circuit to measure the voltage drop across it, as shown. Rank, from greatest to least, the voltage readings in the three voltmeters.

Consider the three parts of the circuit. First rank, from greatest to least, the current through each part. Then rank, from greatest to least, the voltage across each part: (a) The top branch with two bulbs. (b) The lower branch with one bulb. (c) The battery.

At the atomic level, what is meant by saying something is electrically charged?

Why is charge usually transferred by electrons rather than by protons?

Why are objects with vast numbers of electrons normally not electrically charged?

If you scuff electrons from your shoes while walking across a silk rug, are you negatively or positively charged?

Why do clothes often cling together after tumbling in a clothes dryer?

An electroscope is a simple device consisting of a metal ball that is attached by a conductor to two thin metal foils protected from air disturbances in a jar, as shown. When the ball is touched by a charged body, the foils that normally hang straight down spread apart. Why? (Electroscopes are useful not only for detecting charges but also for measuring the quantity of charge: the greater the charge transferred to the ball, the greater the foils diverge.)

The leaves of a charged electroscope collapse in time. At higher altitudes, they collapse more rapidly. Can you think of an explanation? (Hint: The existence of cosmic rays was first indicated by this observation.)

If electrons were positive and protons were negative, would Coulomb’s law be written the same or differently?

When you double the distance between a pair of charged particles, what happens to the force between them? Does it depend on the sign of the charges? What law supports your answer?

When you double the charge on only one of a pair of particles, what effect does this have on the force that each exerts on the other? Does the effect depend on the sign of the charge?

When you double the charge on both particles in a pair, what effect does this have on the force between them? Does it depend on the sign of the charge?

If you rub an inflated balloon against your hair and place it against a metal door, by what mechanism does the balloon stick? Explain.

If you rub an inflated balloon against your hair and place it against a wooden door, by what mechanism does the balloon stick? Explain.

When a car is moved into a painting chamber, a mist of paint is sprayed around its body. When the body is given a sudden electric charge and mist is attracted to it—presto— the car is quickly and uniformly painted. What does the phenomenon of polarization have to do with this?

By what specific means do the bits of fine threads align in the electric fields in Figure 8.11?

Suppose that the strength of the electric field about an isolated point charge has a certain value at a distance of 1 m. How does the electric field strength compare at a distance of 2 m from the point charge? What law guides your answer?

Suppose an investigator places first a free electron and then a free proton into an electric field between oppositely charged conducting plates. (a) How do the forces acting on the electron and those acting on the proton compare? (b) How do the particles’ accelerations compare? (c) How do their directions of travel compare?

Why is voltage often referred to as an electric pressure, especially when electric circuits and water flow in pipes are compared?

Why might the wingspans of birds be a consideration in determining the spacing between parallel wires on power poles?

One example of a water system is a garden hose that waters a garden. Another is the cooling system of an automobile. Which of these exhibits behavior more analogous to an electric circuit? Explain.

How is a hydraulic pump that produces sustained water flow analogous to a battery or generator?

What is the difference between electric potential difference and voltage.

Why is a good conductor of electricity also a good conductor of heat?

Which travels at nearly the speed of light in an electric circuit: electrons, electric field, or both?

Which flows through an electric circuit: voltage, electric charge, resistance, or all three?

Would you expect to find dc or ac in the filament of a light bulb in your home? In the headlight of an automobile?

Comment on the warning sign in the sketch.

Which has the higher resistance: a lamp filament with no current or one carrying current? Or do both have the same resistance?

Only a small percentage of the electric energy supplied to a common light bulb is transformed into light. What happens to the remaining energy?

What is the effect on the current in a wire if both the voltage across it and its resistance are doubled? If both are halved? Let Ohm’s law guide your thinking.

Why is a bird perched on a high-voltage wire safe, even though the wires are not insulated?

Say the bird perched on a high-voltage wire reaches over with its foot and touches another wire. Why is it in trouble?

What does it mean to say that an electric appliance is “grounded”?

If a current of one- or two-tenths of an ampere were to pass into one of your hands and out the other, you would probably be electrocuted. However, if the same current were to pass into your hand and out the elbow above the same hand, you could survive, even though the current might be large enough to burn your flesh. Explain.

Consider a water pipe that branches into two smaller pipes. If the flow of water is 10 liters per minute in the main pipe and 4 liters per minute in one of the branches, how much water per minute flows in the other branch?

Consider a circuit with a main wire that branches into two other wires. If the current is 10 amperes in the main wire and 4 amperes in one of the branches, how much current is in the other branch?

Are automobile headlights wired in parallel or in series? What is your evidence?

As more lanes are added to toll booths, the resistance to vehicles passing through is reduced. How is this similar to what happens when more branches are added to a parallel circuit?

(a) Which is the same for a \(10-\Omega\) and a \(20-\Omega\) resistor connected in series in a series circuit: current or voltage? (b) Which is the same for a \(10-\Omega\) and a \(20-\Omega\) resistor connected in parallel in a parallel circuit: current or voltage? Text Transcription: 10 - omega 20 - omega

If several bulbs are connected in series to a battery, they may feel warm to the touch even though they are not visibly glowing. What is your explanation?

Which is less damaging: plugging a 110-V appliance into a 220-V circuit or plugging a 220-V appliance into a 110-V circuit? Explain.

What unit of measurement is meant by (a) joule per coulomb, (b) coulomb per second, and (c) watt-second?

What happens to the brightness of light emitted by a light bulb when the current in the filament increases?

Why are LED lamps more efficient than incandescent lamps?

Is it correct to say that the energy from a car battery ultimately comes from fuel in the gas tank? Defend your answer.

A car’s headlight dissipates 40 W on low beam and 50 W on high beam. Is there more or less resistance in the high beam filament?

The proportionality constant k in Coulomb’s law is huge in ordinary units, whereas the proportionality constant G in Newton’s law of gravitation is tiny. What does this indicate about the relative strengths of these two forces?

A friend says that the reason one’s hair stands out while one is touching a charged Van de Graaff generator is simply that the hair strands become charged and are light enough so that the repulsion between strands is visible. Do you agree or disagree?

Your tutor tells you that an ampere and a volt really measure the same thing, and the different terms only make a simple concept seem confusing. Why should you find another tutor?

The circuit within an incandescent bulb is shown at the left. Which of the battery arrangements will light the bulb?

In which of the following circuits does a current exist to light the bulb?

Does more current “flow” out of a battery than into it? Does more current “flow” into a light bulb than out of it? Explain.

Sometimes you hear someone say that a particular appliance “uses up” electricity. What is it that the appliance actually consumes, and what becomes of it?

Does a lamp with a thick filament draw more current or less current than a lamp with a thin filament? Defend your answer.

Does a lamp with a thick filament draw more current or less current than a lamp with a thin filament? Defend your answer.

Is the following label on a household product cause for concern? “Caution: This product contains tiny, electrically charged particles moving at speeds in excess of 100,000,000 kilometers per hour.”

The equivalent resistance of a pair of resistors depends on how they’re connected. Suppose you wish to connect a pair of resistors in such a way that their equivalent resistance is less than the resistance of either one. Should you connect them in series or in parallel?

A friend says that a battery provides not a source of constant current, but a source of constant voltage. Do you agree or disagree, and why?

A friend says that adding bulbs in series to a circuit provides more obstacles to the flow of charge, so there is less current with more bulbs, but that adding bulbs in parallel provides more paths, so more current can flow. Do you agree or disagree, and why?

Consider a pair of flashlight bulbs connected to a battery. Do they glow brighter if they are connected in series or in parallel? Does the battery run down faster if they are connected in series or in parallel?

In the circuit shown, how do the three identical light bulbs compare in brightness? Which light bulb draws the most current? What happens if bulb A is unscrewed? If bulb C is unscrewed?

As more and more bulbs are connected in series to a flashlight battery, what happens to the brightness of each bulb? Assuming that heating inside the battery is negligible, what happens to the brightness of each bulb when more and more bulbs are connected in parallel?

A battery has internal resistance, so when the current it supplies goes up, the voltage it supplies goes down. If too many bulbs are connected in parallel across a battery, does their brightness diminish? Explain.

Are these circuits equivalent to one another? Why or why not?

Your friend says that electric current takes the path of least resistance. In the case of a parallel circuit, why is it more accurate to say that most current travels the path of least resistance?

Consider a pair of incandescent bulbs, a 60-W bulb and a 100-W bulb. If the bulbs are connected in series in a circuit, across which bulb is the greater voltage drop? If the bulbs are connected in parallel?

Electric Circuits In a circuit consisting of two lamps connected in series, if the current in one lamp is 1 A, what is the current in the other lamp?

Electric Circuits If 6 V were impressed across the circuit in question 26, and the voltage across the first lamp were 2 V, what would be the voltage across the second lamp?

Electric Circuits How does the total current through the branches of a parallel circuit compare with the current through the voltage source?

Electric Circuits As more lanes are opened at a fast-food restaurant, the resistance to the motion of people and cars trying to get through is reduced. How is this similar to what happens when more branches are added to a parallel circuit?

Electric Power What is the relationship among electric power, current, and voltage?

Write a letter to your favorite uncle and bring him up to speed on your progress with physics. Apply some of the terms in this chapter to practical examples, and tell him how you’re learning to distinguish among them and how that contributes to your understanding.

Demonstrate charging by friction and discharging from pointed objects with a friend who stands at the far end of a carpeted room. Wearing your leather shoes, scuff your way across the rug until your noses are close together. This can be a delightfully tingling experience, depending on the dryness of the air and how pointed your noses are.

Briskly rub a comb against your hair or a woolen garment, and bring it near a small, smooth stream of running water. Is the stream of water charged? (Before you say yes, note the behavior of the stream when an opposite charge is brought nearby.)

A car battery is actually a series of cells. A single electric cell can be made by placing two plates of different materials that have different affinities for electrons in a conducting solution. You can make a simple 1.5-V cell by placing a strip of copper and a strip of zinc in a tumbler of salt water. The voltage of a cell depends on the materials used and on the conducting solution they are placed in, not on the size of the plates. An easier cell to construct is the citrus cell. Stick a paperclip and a piece of copper wire into a lemon. Hold the ends of the wire close together, but not touching, and place the ends on your tongue. The slight tingle you feel and the metallic taste you experience result from a small current of electricity pushed by the citrus cell through the wires when your moist tongue closes the circuit.

\(\text { Coulombs Law: } F=k \frac{q_{1} q_{2}}{d^{2}}\) Two point charges, each with 0.1 C of charge, are 0.1 m apart. Knowing that k is \(9 \times 10^{9} \mathrm{\ N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}\) (the proportionality constant for Coulomb’s law), show that the force between the charges is \(9 \times 10^{9} \mathrm{\ N}\). Text Transcription: Coulombs Law: F = k q_1 q_2/d^2 9 times 10^9 N cdot m^2 / C^2 9 times 10^9 N

\(\text { Ohms Law: } I=\frac{V}{R}\) A toaster has a heating element of \(15\ \Omega\) and is connected to a 120-V outlet. Show that the current drawn by the toaster is 8 A. Text Transcription: Ohms Law: I = V/R 15 Omega

\(\text { Ohms Law: } I=\frac{V}{R}\) Show that when you touch your wet fingers (resistance \(1000 \ \Omega\)) to the terminals of a 6-V battery, the small current moving through your fingers is 0.006 A. Text Transcription: Ohms Law: I = V/R 1000 Omega

\(\text { Ohms Law: } I=\frac{V}{R}\) Calculate the current in the \(240-\Omega\) filament of a bulb connected to a 120-V line. Text Transcription: Ohms Law: I = V/R 240-Omega

\(\text { Power }=I \times V\) An electric toy draws 0.5 A from a 120-V outlet. Show that the toy consumes \(60 \mathrm{\ W}\) of power. Text Transcription: Power = I times V 60 W

\(\text { Power }=I \times V\) Calculate the power of a hair dryer that operates on 120 V and draws a current of 10 A. Text Transcription: Power = I times V

Two pellets, each with a charge of 1 microcoulomb \(\left(10^{-6} C\right)\), are located 3 cm (0.03 m) apart. Show that the electric force between them is 10 N. Text Transcription: (10^-6 C)

Two point charges are separated by 4 cm. The attractive force between them is 20 N. Show that when they are separated by 8 cm, the force between them is 5 N. (Why can you solve this problem without knowing the magnitudes of the charges?)

Show that if the charges attracting each other in the preceding problem have equal magnitudes, each charge has a magnitude of 1.9 microcoulombs \(\left(1.9 \times 10^{-6}\ C\right)\) . Text Transcription: (1.9 times 10^-6 C)

A droplet of ink in an industrial ink-jet printer carries a charge of \(1.6 \times 10^{-10} \ C\) and is deflected onto paper by a force of \(3.2 \times 10^{-4} \ N\). Show that the strength of the electric field \(\left(E=\frac{F}{q}\right)\) required to produce this force is \(2 \times 10^{6} \mathrm{\ N} / \mathrm{C}\). Text Transcription: 1.6 times 10^-10 C 3.2 times 10^-4 N (E=F/q) 2 times 10^6 N/C

A 12-V battery moves 4 C of charge from one terminal to the other. Show that the battery does 48 J of work.

Electric Charge Which part of an atom is positively charged, and which part is negatively charged?

Electric Charge How does the charge of one electron compare with that of another electron?

Electric Charge How do the masses of electrons compare with the masses of protons?

Electric Charge How does the number of protons in a simple atomic nucleus compare with the number of electrons that orbit the nucleus?

Electric Charge What kind of charge does an object acquire when electrons are stripped from it?

Electric Charge What is meant by saying that charge is conserved?

Coulomb’s Law How is Coulomb’s law similar to Newton’s law of gravitation? How is it different?

Coulomb’s Law How does a coulomb of charge compare with the charge of a single electron?

Coulomb’s Law How does the magnitude of electrical force between a pair of charged particles change when the particles are moved twice as far apart? Three times as far apart?

Coulomb’s Law How does an electrically polarized object differ from an electrically charged object?

Electric Field Give two examples of common force fields.

Electric Field How is the direction of an electric field defined?

Electric Potential In terms of the units that measure them, distinguish between electric potential energy and electric potential.

Electric Potential A balloon may easily be charged to several thousand volts. Does that mean it has several thousand joules of energy? Explain.

Voltage Sources What condition is necessary for a sustained flow of electric charge through a conducting medium?

Voltage Sources How much energy is given to each coulomb of charge passing through a 6-V battery?

Electric Current Does electric charge flow across a circuit or through a circuit? Does voltage flow across a circuit or is it impressed across a circuit?

Electric Current Distinguish between dc and ac.

Electric Current Does a battery produce dc or ac? Does the generator at a power station produce dc or ac?

Electrical Resistance Which has the greater resistance, a thick wire or a thin wire of the same length?

Electrical Resistance What is the unit of electrical resistance?

Ohm’s Law What is the effect on current through a circuit of steady resistance when the voltage is doubled? What if both voltage and resistance are doubled?

Ohm’s Law Which has the greater electrical resistance, wet skin or dry skin?

Ohm’s Law What is the function of the third prong on the plug of an electric appliance?

Ohm’s Law What is the source of electrons that produces a shock when you touch a charged conductor?