Solved: Using the formula power = current × voltage, find

Problem 1R Rank the circuits illustrated according to the brightness of the identical bulbs, from brightest to dimmest.

Problem 21RQ A tipped domino sends a pulse along a row of standing dominoes. Is this a good analogy for the way electric current, sound, or both travel?

Problem 1RQ What condition is necessary for the flow of heat? What analogous condition is necessary for the flow of charge?

What two things can be done to increase the amount of flow in a water pipe? Similarly, what two things can be done to increase the current in an electric circuit?

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?

Problem 2E Consider a water pipe that branches into two smaller pipes. If the flow of water is 10 gallons per minute in the main pipe and 4 gallons per minute in one of the branches, how much water per minute flows in the other branch?

Problem 2P The wattage marked on a lightbulb is not an inherent property of the bulb, but depends on the voltage to which it is connected, usually 110 or 120 V. How many amperes flow through a 60-W bulb connected in a 120-V circuit?

Problem 2R The bulbs shown are identical. An ammeter is placed in different locations, as shown. Rank the current readings in the ammeter from greatest to least.

Problem 2RQ What condition is necessary for the sustained flow of water in a pipe? What analogous condition is necessary for the sustained flow of charge in a wire?

Problem 3E Consider a circuit with a main wire that branches into two other wires. If the current is 10 A in the main wire and 4 A in one of the branches, how much current is in the other branch?

Problem 2PC Calculate the current that moves through your fingers (resistance 1000 ?) when you touch them to the terminals of a 6-V battery.

Problem 3P Rearrange the equation current = voltage/resistance to express ?resistance? in terms of current and voltage. Then solve the following: A certain device in a 120-V circuit has a current rating of 20 A. What is the resistance of the device (how many ohms)?

Problem 3PC Calculate the current in the 240-? filament of a bulb connected to a 120-V line. ?

Problem 3R All bulbs are identical in the circuits shown. An ammeter is connected next to the battery, as shown. Rank the current readings in the ammeter, from greatest to least.

Why are electrons, rather than protons, the principal charge carriers in metal wires?

Problem 4E 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.

Problem 4P Using the formula power = current × voltage, find the current drawn by a 1200-W toaster connected to 120 V. Then, using the method from the previous problem, show that the resistance of the toaster is 12 ?.

Problem 4PC Calculate the power of a device that carries 0.5 A when impressed with 120 V.

Problem 4R All bulbs are identical in the following circuits. A voltmeter is connected across a single bulb to measure the voltage drop across it. Rank the voltage readings from greatest to least.

Problem 4RQ What exactly is an ?ampere?

What happens to the brightness of light emitted by a lightbulb when the current flowing through it increases?

Problem 5PC Calculate the power of a hair dryer that operates on 120 V and draws a current of 10 A.

Problem 5R Consider the three parts of the circuit: A, the top branch with two bulbs; B, the middle branch with one bulb; C, the battery. a. Rank the current through each, from greatest to least. b. Rank the voltage across each from greatest to least.

Problem 5RQ Name two kinds of practical “electric pumps.”

Problem 6E Your friend says that a battery supplies the electrons in an electric circuit. Do you agree or disagree? Defend your answer.

Problem 6P Show that operating a 100-W lamp continuously for 1 week when the power utility rate is 15¢/kWh costs $2.52.

Problem 6PC Given that the power consumed by a device is 1200 W operating on a 120-V line, calculate the amount of current it draws.

How much energy is supplied to each coulomb of charge that flows through a 12-V battery?

Is a current-carrying wire electrically charged because of the electrons moving in it?

Problem 7P A 4-W night-light is plugged into a 120-V circuit and operates continuously for 1 year. Find the following: (a) the current it draws, (b) the resistance of its filament, (c) the energy consumed in a year. (d) Then show that for a utility rate of 15¢/kWh the cost for a year’s operation is $5.25.

Problem 7RQ Does charge flow ?through? a circuit or ?into? a circuit? Does voltage flow ?through? a circuit, or is voltage established ?across? a circuit?

Problem 8E Your tutor tells you that an ?ampere? and a ?volt? really measure the same thing and that the different terms only serve to make a simple concept seem confusing. Why should you consider getting a different tutor?

Problem 8P An electric iron connected to a 110-V source draws 9 A of current. Show that the amount of heat it generates in a minute is nearly 60,000 J.

Problem 8RQ Will water flow more easily through a wide pipe or a narrow pipe? Will current flow more easily through a thick wire or a thin wire?

Problem 9E In which of the circuits shown does a current exist to light the bulb?

Does heating a metal wire increase or decrease its electrical resistance?

Does more current flow out of a battery than into it? Does more current flow into a lightbulb than out of it? Explain.

Problem 10RQ If the voltage impressed across a circuit is held constant while the resistance doubles, what change occurs in the current?

Problem 10P In periods of peak demand, power companies lower their voltage. This saves them power (and saves you money!). To see the effect, consider a 1200-W coffeemaker 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, it is the resistance of the toaster, not its power, that remains constant.)

Problem 11E Something gets “used up” in a battery that eventually dies and goes flat. One friend says that current is used up. Another friend says that energy is used up. Who, if either, do you agree with, and why?

Problem 12E Suppose you leave your car lights on while at a movie. When you return, your battery is too “weak” to start your car. A friend gives you a jump-start with his battery and battery cables. What physics is occurring here?

Problem 12RQ How does wetness affect the resistance of your body?

If the resistance of a circuit remains constant while the voltage across the circuit decreases to half its former value, what change occurs in the current?

Your friend says that, when jump-starting a dead battery, you should connect your live battery in parallel with the dead battery, which, in effect, replaces the dead one. Do you agree?

Problem 13RQ What is the function of the round third prong in a modern household electric plug?

Problem 14E An electron moving in a wire collides repeatedly with atoms and travels an average distance between collisions called the ?mean free path?. If the mean free path is less in some metals, what can you say about the resistance of these metals? For a given conductor, what can be done to lengthen the mean free path?

Problem 14RQ Does a battery produce dc or ac? Does the generator at a power station produce dc or ac?

What does it mean to say that a certain current is 60 Hz?

Problem 16E Only a small percentage of the electric energy fed into a common lightbulb is transformed into light. What happens to the remaining energy?

Problem 16RQ What property of a diode enables it to convert ac to pulsed dc?

Problem 18RQ What is the error in saying that electrons in a common battery-driven circuit travel at about the speed of light?

Problem 18E A simple lie detector consists of an electric circuit, often from one finger to another. A sensitive meter shows the current chat flows when a small voltage is applied. How does this technique indicate that a person is lying? (And when does this technique ?not? indicate when someone is lying?)

Problem 19E Why are thick wires rather than thin wires usually used to carry large currents?

Why does a wire that carries electric current become hot?

Problem 20E Why does the filament of a lightbulb glow while the connecting wires do not?

Problem 20RQ What is meant by ?drift velocity?

Problem 21E It is commonly said that a certain resistor draws a certain current. Does this mean that the resistor “attracts” the current? Defend your answer.

A toaster has a heating element of 15 ? and is connected to a 120-V outlet. Show that the current drawn by the toaster is 8 A.

Problem 5P 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 that you forget to turn the headlights off in your parked automobile. If each of the two headlights draws 3 A, how long will it be before your battery is “dead”?

Problem 9P Show in the previous problem that 540 C of charge flow through the iron in 1 minute.

Problem 15E Why is the current in an incandescent bulb greater immediately after it is turned on than it is a few moments later? (That’s why bulbs usually burn out just as they are being turned on.)

Problem 17E Why are all compact fluorescent lamps more efficient than incandescent lamps?

Problem 17RQ A diode converts ac to pulsed dc. What electrical device smoothes the pulsed dc to a smoother dc?

What condition is necessary for the flow of heat? What analogous condition is necessary for the flow of charge?

Flow of Charge and Electric Current What condition is necessary for the sustained flow of water in a pipe? What analogous condition is necessary for the sustained flow of charge in a wire?

Flow of Charge and Electric Current Why are electrons, rather than protons, the principal charge carriers in metal wires?

Flow of Charge and Electric Current What exactly is an ampere?

Voltage Sources Name two kinds of practical "electric pumps."

Voltage Sources How much energy is supplied to each coulomb of charge that flows through a 12-V battery?

Voltage Sources Does electric charge flow across a circuit or through a circuit? Does voltage flow across a circuit or is it impressed across a circuit?

Electrical Resistance Will water flow more easily through a wide pipe or a narrow pipe? Will current flow more easily through a thick Wire or a thin wire?

Electrical Resistance Does heating a metal wire increase or decrease its electrical resistance?

What is the unit of electrical resistance?

Ohm's Law If the voltage impressed across a circuit is held constant while the resistance doubles, what change occurs in the current?

Ohm's Law If the resistance of a circuit remains constant while the voltage across the circuit decreases to half its former value, what change occurs in the current?

How does wetness affect the resistance of your body?

What is the function of the round third prong in a modern household electrical plug?

Direct Current and Alternating Current Does a battery produce dc or ac? Does the generator at a power station produce dc or ac?

What does it mean to say that a certain current is 60 Hz?

What property of a diode enables it to convert ac to pulsed dc?

Direct Current and Alternating Current A diode converts ac to pulsed dc. What electrical device smoothes the pulsed dc to a smoother dc?

Speed and Source of Electrons in a Circuit Why does a wire that carries electric current become hot?

Speed and Source of Electrons in a Circuit What is the error in saying that electrons in a common battery-driven circuit travel at about the speed of light?

Speed and Source of Electrons in a Circuit What is meant by drift velocity?

Speed and Source of Electrons in a Circuit A tipped domino sends a pulse along a row of standing dominoes. Is this a good analogy for the way electric current, sound, or both travel?

Speed and Source of Electrons in a Circuit What is the error in saying that the source of electrons in a circuit is the battery or generator?

Speed and Source of Electrons in a Circuit When you make your household electric payment at the end of the month, which are you billed for: voltage, current, power, or energy?

Speed and Source of Electrons in a Circuit From where do the electrons originate that produce an electric shock when you touch a charged conductor?

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

Electric Power Which of these is a unit of power and which is a unit of energy: a watt, a kilowatt, a kilowatt-hour?

Lamps How does the heat emitted by lamps affect their efficiency?

Electric Circuits In a circuit of two lamps in series, if the current through one lamp is 1 A, what is the current through the other lamp? Defend your answer.

In a circuit of two lamps in parallel, if there is a voltage of 6 V across one lamp, what is the voltage across the other lamp?

Electric Circuits If a voltage of 6 V is impressed across the circuit in the preceding question and the voltage across the first lamp is 2 V, what is the voltage across the second lamp? Defend your answer.

Electric Circuits How does the sum of the currents through the branches of a simple parallel circuit compare with the current in the voltage source?

What is the function of fuses or circuit breakers in a circuit?

\(\text { Obm's law: } I=\frac{V}{R}\) 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

\(\text { Obm's law: } I=\frac{V}{R}\) When you touch your fingers (resistance \(1000 \Omega\)) to the terminals of a 6-V battery, show that the small current moving through your fingers is 0.006A. Text Transcription: Ohms’ law: I = V/R 1000 Omega

Calculate the current in the \(240 - \Omega\) filament of a bulb connected to a 120-V line. \(\text { Power }=I \times V\)

An electric toy draws 0.5 A from a 120-V outlet. Show that the toy consumes 60 W of power.

\(\text { Power }=I \times V\) 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

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?

The wattage marked on a lightbulb is not an inherent property of the bulb but depends on the voltage to which it is connected, usually 110 V or 120 V. How many amperes flow through a 60-W bulb connected in a 120-V circuit?

Rearrange the equation current = voltage/resistance toexpress resistance in terms of current and voltage. Then solve the following: A certain device in a 120-V circuit has a current rating of 20 A. What is the resistance of the device (how many ohms)?

Using the formula \(power = current \times voltage\), find the current drawn by a 1200-W toaster connected to 120 V. Then, using the method from the preceding problem, show that the resistance of the toaster is \(12 \Omega\).

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 that you forget to turn the headlights off in your parked automobile. If each of the two headlights draws 3 A, how long will it be before your battery is "dead"?

Show that operating a 100-W lamp continuously for 1 week when the power utility rate is 15¢/kWh costs $2.52.

A 4-W night-light is plugged into a 120-V circuit and oper- ates continuously for 1 year. Find the following: (a) the current it draws, (6) the resistance of its filament, (¢) the energy consumed in a year. (d) Then show that for a utility rate of 15/kWh the cost for a year's operation is $5.25.

An electric iron connected to a 110-V source draws 9 A of current. Show that the amount of heat it generates in a minute is nearly 60,000 J.

Show in the preceding problem that 540 C of charge flows through the iron in 1 minute.

In periods of peak demand, power companies lower their voltage. This saves them power (and saves you money!). To see the effect, consider a 1200-W coffeemaker 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 current is lowered, so the power output of the toaster's heating coils drops, which cools the coil and lowers its resistance. However, for this problem assume the change in resistance is slight.)

The bulbs shown are identical. An ammeter is placed in different locations, as shown. Rank the current readings in the ammeter, from greatest to least.

Rank the circuits illustrated according to the brightness of the identical bulbs, from brightest to dimmest.

\(54\). All bulbs are identical in the circuits shown. An ammeter is connected next to the battery, as shown. Rank the current readings in the ammeter, from greatest to least. Equation Transcription: Text Transcription: 54

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

Consider the three parts of the circuit: A, the top branch with two bulbs; B, the middle branch with one bulb; C, the battery. a. Rank the currents through each, from greatest to least. b. Rank the voltages across each, from greatest to least.

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

What two things can be done to increase the amount of flow in a water pipe? Similarly, what two things can be done to increase the current in an electric circuit?

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

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 systems exhibits behavior more analogous to an electric circuit? Explain.

What happens to the brightness of light emitted by a lightbulb when the current flowing through it increases?

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

Your friend says that a battery supplies the electrons in an electric circuit. Do you agree or disagree? Defend your answer.

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

Is a current-carrying wire electrically charged because of the electrons moving in it?

Your tutor tells you that an ampere and a volt really measure the same thing and that the different terms only serve to make a simple concept seem confusing. Why should you consider getting a different tutor?

In which of the circuits shown 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 lightbulb than out of it? Explain.

Something gets “used up” in a battery that eventually dies and goes flat. One friend says that current is used up. Another friend says that energy is used up. Who, if either, do you agree with, and why?

Suppose you leave your car lights on while you see a movie. When you return, your battery is too “weak” to start your car. A friend gives you a jump-start with his battery and battery cables. What physics is occurring here?

Your friend says that, when jump-starting a dead battery, you should connect your live battery in parallel with the dead battery, which, in effect, replaces the dead one. Do you agree?

An electron moving in a wire collides repeatedly with atoms and travels an average distance between collisions called the mean free path. If the mean free path is less in some metals, what can you say about the resistance of these metals? For a given conductor, what can be done to lengthen the mean free path?

Why is the current in an incandescent bulb greater immediately after it is turned on than it is a few moments later? (That’s why bulbs usually burn out just as they are being turned on.)

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

Why are all compact fluorescent lamps more efficient than incandescent lamps?

Why are thick wires rather than thin wires usually used to carry large currents?

Why does the filament of a lightbulb glow but the connecting wires do not?

Will a lamp with a thick filament draw more current or less current than a lamp with a thin filament?

What causes electric shock: current or voltage?

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

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

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

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

What unit signifies (a) joule per coulomb, (b) coulomb per second, (c) \(watt \cdot second\)?

Which is the same for a 10-\(\Omega\) and a 20-\(\Omega\) resistor in series in a series circuit: current or voltage?

Which is the same for a 10-\(\Omega\) and a 20-\(\Omega\) resistor in parallel in a parallel circuit: current or voltage?

The damaging effects of electric shock result from the amount of current that flows in the body. Why, then, do we see signs that read “Danger-High Voltage” rather than “Danger-High Current”?

Comment on the warning sign shown in the sketch.

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.”

Which will do less damage: plugging a 110-V hairdryer into a 220-V circuit or plugging a 220-V hairdryer into a 110-V circuit? Defend your answer.

Why are the wingspans of birds a consideration in determining the spacing between parallel wires in a power line?

Estimate the number of electrons that a power company delivers annually to the homes of a typical town of 40,000 people.

If electrons flow very slowly through a circuit, why doesn’t it take a noticeably long time for a lamp to glow when you turn on a distant switch?

Why is the speed of an electrical signal so much greater than the speed of sound?

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

\(97\). What happens to the brightness of bulb \(A\) when the switch is closed and bulb \(B\) lights up? Equation Transcription: Text Transcription: 97 A B

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

In the circuit shown, how do the brightnesses of the identical lightbulbs compare? Which bulb draws the most current? What will happen if bulb \(A\) is unscrewed? If bulb \(C\) is unscrewed? Equation Transcription: Text Transcription: A C

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?

What changes occur in the line current when more devices are introduced in a series circuit? In a parallel circuit? Why are your answers different?

Why is there no effect on other branches in a parallel circuit when one branch of the circuit is opened or closed?

When a pair of identical resistors are connected in series, which of the following is the same for both resistors: (a) voltage across each, (b) power dissipated in each, (c) current through each? Do any of your answers change if the resistors are different from each other?

When two identical resistors are connected in parallel, which of the following is the same for both resistors: (a) voltage across each, (b) power dissipated in each, (c) current through each? Do any of your answers change if the resistors are different from each other?

Batteries do have internal resistance, which is not always negligible. It shows when the current a battery supplies increases, whereupon the voltage it supplies decreases. Taking internal resistance of the battery into consideration, will the brightness of many bulbs diminish when connected in parallel? Defend your answer.

Are these three circuits equivalent? Why or why not?

Figure 23.19 shows a fuse placed in a household circuit. In what other locations might a fuse be placed in this circuit to be useful, melting only if a problem arises?

A simple lie detector consists of an electric circuit, often from one finger to another. A sensitive meter shows the current that flows when a small voltage is applied. How does this technique indicate that a person is lying? (And when doesn’t this technique indicate when someone is lying?)

It is commonly said that a certain resistor draws a certain current. Does this mean that the resistor “attracts” the current? Defend your answer.

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

To connect a pair of resistors so that their combined (equivalent) resistance will be greater than the resistance of either one, should you connect them in series or in parallel?

To connect a pair of resistors so that their combined (equivalent) resistance will be less than the resistance of either one, should you connect them in series or in parallel?

If a glowing incandescent lightbulb is jarred and oxygen leaks inside, the bulb will momentarily brighten considerably before burning out. Putting excess current through a lightbulb will also burn it out. What physical change occurs when a lightbulb burns out?

Your friend says that the equivalent (combined) resistance of resistors connected in series is always greater than the resistance of the largest resistor. Do you agree?

Your friend says that the equivalent (combined) resistance of resistors connected in parallel is always less than the resistance of the smallest resistor. Do you agree?

Your electronics friend needs a 20-\(\Omega\) resistor but has only 40-\(\Omega\) resistors. He tells you that he can combine them to produce a 20-\(\Omega\) resistor. How?

Your electronics friend needs a 10-\(\Omega\) resistor but has only 40-\(\Omega\) ones. How can he combine them to produce an equivalent resistance of 10 \(\Omega\)?

Is the resistance of a 100-W bulb greater or less than the resistance of a 60-W bulb? Assuming the filaments in each bulb are the same length and made of the same material, which bulb has the thicker filament?

If a 60-W bulb and a 100-W bulb are connected in series in a circuit, across which bulb will there be a greater voltage drop? How about if they are connected in parallel?

(a) What single resistor would be equivalent to the resistors in this arrangement? (b) If \(24\) volts were applied across points \(A \text { and } B\), how much current would there be in the circuit? (c) How much current in the \(12\)-ohm resistor? Equation Transcription: Text Transcription: 24 A and B 12

Three \(6\)-ohm resistors are arranged in a triangle as shown. A voltage source of \(12 \mathrm{~V}\) 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? (c) How much current is in the voltage source? (d) What is the equivalent resistance of the circuit (what single resistor connected to the voltage source could replace the three resistors)? Equation Transcription: Text Transcription: 6 12 V