Solved: Two wires have the same length and the same

The battery pack of a pocket calculator has a voltage of 3.0 V and delivers a current of 0.17 mA. In one hour of operation, (a) how much charge flows in the circuit and (b) how much energy does the battery deliver to the calculator circuit?

The filament in a light bulb is a resistor in the form of a thin piece of wire. The wire becomes hot enough to emit light because of the current in it. Figure 20.5 shows a flashlight that uses two 1.5-V batteries (effectively a single 3.0-V battery) to provide a current of 0.40 A in the filament. Determine the resistance of the glowing filament

In circuit A the battery that supplies energy has twice as much voltage as the battery in circuit B. However, the current in circuit A is only one-half the current in circuit B. Circuit A presents _____ the resistance to the current that circuit B does. (a) twice (b) one-half (c) the same (d) four times (e) one-fourth

Two circuits present the same resistance to the current. In one circuit the battery causing the flow of current has a voltage of 9.0 V, and the current is 3.0 A. In the other circuit the battery has a voltage of 1.5 V. What is the current in this other circuit?

The instructions for an electric lawn mower suggest that a 20-gauge extension cord can be used for distances up to 35 m, but a thicker 16-gauge cord should be used for longer distances, to keep the resistance of the wire as small as possible. The cross-sectional area of 20-gauge wire is 5.2  107 m2 , while that of 16-gauge wire is 13  107 m2 . Determine the resistance of (a) 35 m of 20-gauge copper wire and (b) 75 m of 16-gauge copper wire.

Figure 20.7a shows a cherry-red heating element on an electric stove. The element contains a wire (length 1.1 m, cross-sectional area 3.1  106 m2) through which electric charge flows. As Figure 20.7b shows, this wire is embedded within an electrically insulating material that is contained within a metal casing. The wire becomes hot in response to the flowing charge and heats the casing. The material of the wire has a resistivity of 0 6.8  105  m at T0 320 C and a temperature coefficient of resistivity of 2.0  103 (C ) 1 . Determine the resistance of the heater wire at an operating temperature of 420 C. Reason

Two materials have different resistivities. Two wires of the same length are made, one from each of the materials. Is it possible for each wire to have the same resistance? (a) Yes, if the material with the greater resistivity is used for a thinner wire. (b) Yes, if the material with the greater resistivity is used for a thicker wire. (c) It is not possible

How does the resistance of a copper wire change when both the length and diameter of the wire are doubled? (a) It decreases by a factor of two. (b) It increases by a factor of two. (c) It increases by a factor of four. (d) It decreases by a factor of four. (e) It does not change.

A resistor is connected between the terminals of a battery. This resistor is a wire, and the following five choices give possibilities for its length and radius in multiples of L0 and r0, respectively. For which one or more of the possibilities is the current in the resistor a minimum? (a) L0 and r0 (b) and (c) 2L0 and 2r0 (d) 2L0 and r0 (e) 8L0 and 2r0

In the flashlight in Figure 20.5, the current is 0.40 A, and the voltage is 3.0 V. Find (a) the power delivered to the bulb and (b) the electrical energy dissipated in the bulb in 5.5 minutes of operation.

A toaster is designed to operate with a voltage of 120 V, and a clothes dryer is designed to operate with a voltage of 240 V. Based solely on this information, which appliance uses more power? (a) The toaster (b) The dryer (c) Insufficient information is given for an answe

When an incandescent light bulb is turned on, a constant voltage is applied across the tungsten filament, which then becomes white hot. The temperature coefficient of resistivity for tungsten is a positive number. What happens to the power delivered to the bulb as the filament heats up? (a) It decreases. (b) It increases. (c) It remains constant

The drawing shows a circuit that includes a bimetallic strip (made from brass and steel; see Section 12.4) with a resistance heater wire wrapped around it. When the switch is initially closed, a current appears in the circuit because charges flow through the heater wire (which becomes hot), the strip itself, the contact point, and the light bulb. The bulb glows in response. As long as the switch remains closed, does the bulb (a) continue to glow, (b) eventually turn off permanently, or (c) flash on and off?

A stereo receiver applies a peak ac voltage of 34 V to a speaker. The speaker behaves approximately as if it had a resistance of 8.0 , as the circuit in Figure 20.12 indicates. Determine (a) the rms voltage, (b) the rms current, and (c) the average power for this circuit.

During the winter, many people use portable electric space heaters to keep warm. When the heater is located far from a 120-V wall receptacle, an extension cord is necessary (see Figure 20.13). To prevent fires, however, manufacturers sometimes caution about using extension cords. To minimize the risk of a fire, should a long extension cord used with a space heater be made from (a) larger-gauge or (b) smaller-gauge wire?

The drawing shows a circuit in which a light bulb is connected to the household ac voltage via two switches, S1 and S2 . This is the kind of wiring, for example, that allows you to turn on a carport light from either inside the house or out in the carport. Which one or more of the combinations of the switch positions will turn on the light? (a) S1 set to A and S2 set to B (b) S1 set to B and S2 set to B (c) S1 set to B and S2 set to A (d) S1 set to A and S2 set to A

Two light bulbs are designed for use with an ac voltage of 120 V and are rated at 75 W and 150 W. Which bulb, if either, has the greater filament resistance?

An ac circuit contains only a generator and a resistor. Which one of the following changes leads to the greatest average power being delivered to the circuit? (a) Double the peak voltage of the generator and double the resistance. (b) Double the resistance. (c) Double the peak voltage of the generator. (d) Double the peak voltage of the generator and reduce the resistance by a factor of two.

Suppose that the resistances in Figure 20.14 are R1  47  and R2  86 , and the battery voltage is 24 V. Determine the equivalent resistance of the two resistors and the current in the circuit.

A 6.00- resistor and a 3.00- resistor are connected in series with a 12.0-V battery, as Figure 20.15 indicates. Assuming that the battery contributes no resistance to the circuit, find the power delivered to each of the resistors.

The power rating of a 1000-W heater specifies the power that the heater uses when it is connected to an ac voltage of 120 V. What is the total power used by two of these heaters when they are connected in series with a single ac voltage of 120 V? (a) 4000 W (b) 3000 W (c) 2000 W (d) 1000 W (e) 500 W

Most receivers allow the user to connect remote speakers (to play music in another room, for instance) in addition to the main speakers. Figure 20.21 shows that the remote speaker and the main speaker for the right stereo channel are connected to the receiver in parallel (for clarity, the speakers for the left channel are not shown). At the instant represented in the picture, the ac voltage across the speakers is 6.00 V. The main-speaker resistance is 8.00 , and the remote-speaker resistance is 4.00 .* Determine (a) the equivalent resistance of the two speakers, (b) the total current supplied by the receiver, (c) the current in each speaker, and (d) the power dissipated in each speaker

Three-way light bulbs are popular because they can provide three levels of illumination (e.g., 50 W, 100 W, and 150 W) using a 120-V socket. The socket, however, must be equipped with a special three-way switch that enables one to select the illumination level. This switch does not select different voltages, because a three-way bulb uses a single voltage of 120 V. Within the bulb are two separate filaments. When the bulb is producing its highest illumination level and one of the filaments burns out (i.e., vaporizes), the bulb shines at one of the other illumination levels (either the lowest or the intermediate one). When the bulb is set to its highest level of illumination, how are the two filaments connected, (a) in parallel or (b) in series

A car has two headlights, and their power is derived from the cars battery. The filament in one burns out, but the other headlight stays on. Are the headlights connected in series or in parallel?

Two identical light bulbs are connected to identical batteries in two different ways. In method A the bulbs are connected in parallel, and the parallel combination is connected between the one batterys terminals. In method B the bulbs are connected in series, and the series combination is connected between the other batterys terminals. What is the ratio of the power supplied by the battery in method A to the power supplied in method B? (a) (b) 4 (c) (d) 2 (e) 1

Figure 20.23a shows a circuit composed of a 24-V battery and four resistors, whose resistances are 110, 180, 220, and 250 . Find (a) the total current supplied by the battery and (b) the voltage between points A and B in the circuit.

In one of the circuits in the drawing, none of the resistors is in series or in parallel with any of the other resistors. Which circuit is it?

You have three resistors, each of which has a resistance R. By connecting all three together in various ways, which one or more of the following resistance values can you obtain? (a) 3R (b) (c) R (d

You have four resistors, each of which has a resistance R. It is possible to connect these four together so that the equivalent resistance of the combination is also R. How many ways can you do it? There is more than one way

Figure 20.25 shows a car battery whose emf is 12.0 V and whose internal resistance is 0.010 . This resistance is relatively large because the battery is old and the terminals are corroded. What is the terminal voltage when the current I drawn from the battery is (a) 10.0 A and (b) 100.0 A?

Figure 20.28 shows a circuit that contains two batteries and two resistors. Determine the current I in the circuit.

In a car, the headlights are connected to the battery and would discharge the battery if it were not for the alternator, which is run by the engine. Figure 20.29 indicates how the car battery, headlights, and alternator are connected. The circuit includes an internal resistance of 0.0100  for the car battery and its leads and a resistance of 1.20  for the headlights. For the sake of simplicity, the alternator is approximated as an additional 14.00-V battery with an internal resistance of 0.100 . Determine the currents through the car battery (IB), the headlights (I H), and the alternator (IA).

Draw the current in each branch of the circuit. Choose any direction. If your choice is incorrect, the value obtained for the current will turn out to be a negative number.

Mark each resistor with a plus sign at one end and a minus sign at the other end, in a way that is consistent with your choice for the current direction in Step 1. Outside a battery, conventional current is always directed from a higher potential (the end marked ) toward a lower potential (the end marked ).

Apply the junction rule and the loop rule to the circuit, obtaining in the process as many independent equations as there are unknown variables.

Solve the equations obtained in Step 3 simultaneously for the unknown variables. (See Appendix C.3.)

The drawing shows a circuit containing three resistors and three batteries. In preparation for applying Kirchhoffs rules, the currents in each resistor have been drawn. For these currents, write down the equations that result from applying Kirchhoffs junction rule and loop rule. Apply the loop rule to loops ABCD and BEFC.

An ideal ammeter has _________ resistance, whereas an ideal voltmeter has ________ resistance. (a) zero, zero (b) infinite, infinite (c) zero, infinite (d) infinite, zero

What would happen to the current in a circuit if a voltmeter, inadvertently mistaken for an ammeter, were inserted into the circuit? The current would (a) increase markedly (b) decrease markedly (c) remain the same.

The time constant  of a series RC circuit is measured in seconds (s) and is given by   RC, where the resistance R is measured in ohms () and the capacitance C is measured in farads (F). Verify that an ohm times a farad is equivalent to a second

The drawings show two different resistorcapacitor arrangements. The time constant for arrangement A is 0.20 s. What is the time constant for arrangement B? (a) 0.050 s (b) 0.10 s (c) 0.20 s (d) 0.40 s (e) 0.80 s

A circuit contains a 48-V battery and a single light bulb whose resistance is 240 . A second, identical, light bulb can be wired either in series or in parallel with the first one (see Figure 20.42). Determine the power delivered to a single bulb when the circuit contains (a) only one bulb, (b) two bulbs in series, and (c) two bulbs in parallel. Assume that the battery has no internal resistance.

How is the power P that is delivered to a light bulb related to the bulbs resistance R and the voltage V across it?

When there is only one light bulb in the circuit, what is the voltage V?

The more power delivered to a light bulb, the brighter it is. When two bulbs are wired in series, does the brightness of each bulb increase, decrease, or remain the same relative to the brightness when only a single bulb is in the circuit?

When two bulbs are wired in parallel, does the brightness of each bulb increase, decrease, or remain the same relative to the brightness when only a single bulb is in the circuit?

For the circuit in Figure 20.43, use Kirchhoffs junction rule and loop rule to find the currents through the three resistors

Notice that there are two loops, labeled 1 and 2, in this circuit. Does it matter that there is no battery in loop 1, but only two resisto

The currents through the three resistors are labeled as I1, I2 and I3. Does it matter which direction, left-to-right or right-to-left, has been chosen for each current?

When we place the and signs at the ends of each resistor, does it matter which end is and which is ? An

When we evaluate the potential drops and rises around a closed loop, does it matter which direction, clockwise or counterclockwise, is chosen for the evaluation?

In 2.0 s, 1.9  1019 electrons pass a certain point in a wire. What is the current I in the wire?

Which one of the following graphs correctly represents Ohms law, where V is the voltage and I is the current? (a) A (b) B (c) C (d) D

Two wires are made from the same material. One wire has a resistance of 0.10 . The other wire is twice as long as the first wire and has a radius that is half as much. What is the resistance of the second wire? (a) 0.40  (b) 0.20  (c) 0.10  (d) 0.050  (e) 0.80

A single resistor is connected across the terminals of a battery. Which one or more of the following changes in voltage and current leaves unchanged the electric power dissipated in the resistor? (A) Doubling the voltage and reducing the current by a factor of two (B) Doubling the voltage and increasing the resistance by a factor of four (C) Doubling the current and reducing the resistance by a factor of four (a) A, B, C (b) A, B (c) B, C (d) A (e) B

The average power dissipated in a 47- resistor is 2.0 W. What is the peak value I0 of the ac current in the resistor?

For the circuit shown in the drawing, what is the voltage V1 across resistance R1? (a) (d) (b) (e)

For the circuit shown in the drawing, what is the ratio of the current I1 in resistance R1 to the current I2 in resistance R2? (a) (d) (b) (e) (c)

In the following three arrangements each resistor has the same resistance R. Rank the equivalent resistances of the arrangements in descending order (largest first). (a) A, B, C (b) B, A, C (c) B, C, A (d) A, C, B (e) C, B, A R R R R R R R R R R R R A B

A battery has an emf of V and an internal resistance of r. What resistance R, when connected across the terminals of this battery, will cause the terminal voltage of the battery to be (a) (b) (c) (d) (e)

When applying Kirchhoffs rules, one of the essential steps is to mark each resistor with plus and minus signs to label how the potential changes from one end of the resistor to the other. The circuit in the drawing contains four resistors, each marked with the associated plus and minus signs. However, one resistor is marked incorrectly. Which one is it? (a) (b) (c) (d)

Three capacitors are identical, each having a capacitance C. Two of them are connected in series. Then, this series combination is connected in parallel with the third capacitor. What is the equivalent capacitance of the entire connection? (a) (b) (c) 3C (d) (e)

The time constant of an RC circuit is 2.6 s. How much time t is required for the capacitor (uncharged initially) to gain one-half of its full equilibrium charge?

A defibrillator is used during a heart attack to restore the heart to its normal beating pattern (see Section 19.5). A defibrillator passes 18 A of current through the torso of a person in 2.0 ms. (a) How much charge moves during this time? (

An especially violent lightning bolt has an average current of 1.26  103 A lasting 0

A battery charger is connected to a dead battery and delivers a current of 6.0 A for 5.0 hours, keeping the voltage across the battery terminals at 12 V in the process. How much energy is delivered to the battery?

A coffee-maker contains a heating element that has a resistance of 14 . This heating element is energized by a 120-V outlet. What is the current in the heating element?

Suppose that the resistance between the walls of a biological cell is 5.0  109 . (a) What is the current when the potential difference between the walls is 75 mV? (b) If the current is composed of Na ions (q e), how many such ions flow in 0.50 s? *

A car battery has a rating of 220 ampere hours (A h). This rating is one indication of the total charge that the battery can provide to a circuit before failing. (a) What is the total charge (in coulombs) that this battery can provide? (b) Determine the maximum current that the battery can provide for 38 minutes.

A resistor is connected across the terminals of a 9.0-V battery, which delivers 1.1  105 J of energy to the resistor in six hours. What is the resistance of the resistor?

The resistance of a bagel toaster is 14 . To prepare a bagel, the toaster is operated for one minute from a 120-V outlet. How much energy is delivered to the toaster?

A beam of protons is moving toward a target in a particle accelerator. This beam constitutes a current whose value is 0.50 A. (a) How many protons strike the target in 15 s? (b) Each proton has a kinetic energy of 4.9  1012 J. Suppose the target is a 15-gram block of aluminum, and all the kinetic energy of the protons goes into heating it up. What is the change in temperature of the block that results from the 15-s bombardment of protons?

The resistance and the magnitude of the current depend on the path that the current takes. The drawing shows three situations in which the current takes different paths through a piece of material. Each of the rectangular pieces is made from a material whose resistivity is  1.50  102  m, and the unit of length in the drawing is L0  5.00 cm. Each piece of material is connected to a 3.00-V battery. Find (a) the resistance and (b) the current in each case.

Two wires are identical, except that one is aluminum and one is copper. The aluminum wire has a resistance of 0.20 . What is the resistance of the copper wire?

A cylindrical wire has a length of 2.80 m and a radius of 1.03 mm. It carries a current of 1.35 A, when a voltage of 0.0320 V is applied across the ends of the wire. From what material in Table 20.1 is the wire made?

A coil of wire has a resistance of 38.0  at 25 C and 43.7  at 55 C. What is the temperature coefficient of resistivity?

A large spool in an electricians workshop has 75 m of insulationcoated wire coiled around it. When the electrician connects a battery to the ends of the spooled wire, the resulting current is 2.4 A. Some weeks later, after cutting off various lengths of wire for use in repairs, the electrician finds that the spooled wire carries a 3.1-A current when the same battery is connected to it. What is the length of wire remaining on the spool?

Two wires have the same length and the same resistance. One is made from aluminum and the other from copper. Obtain the ratio of the cross-sectional area of the aluminum wire to the cross-sectional area of the copper wire.

High-voltage power lines are a familiar sight throughout the country. The aluminum wire used for some of these lines has a cross-sectional area of 4.9  104 m2 . What is the resistance of ten kilometers of this wire?

The temperature coefficient of resistivity for the metal gold is 0.0034 (C ) 1 , and for tungsten it is 0.0045 (C ) 1 . The resistance of a gold wire increases by 7.0% due to an increase in temperature. For the same increase in temperature, what is the percentage increase in the resistance of a tungsten wire? *

A tungsten wire has a radius of 0.075 mm and is heated from 20.0 to 1320 C. The temperature coefficient of resistivity is  4.5  103 (C ) 1 . When 120 V is applied across the ends of the hot wire, a current of 1.5 A is produced. How long is the wire? Neglect any effects due to thermal expansion of the wire. *

Two wires have the same cross-sectional area and are joined end to end to form a single wire. One is tungsten, which has a temperature coefficient of resistivity of  0.0045 (C ) 1 . The other is carbon, for which  0.0005 (C ) 1 . The total resistance of the composite wire is the sum of the resistances of the pieces. The total resistance of the composite does not change with temperature. What is the ratio of the lengths of the tungsten and carbon sections? Ignore any changes in length due to thermal expansion. * 2

Two cylindrical rods, one copper and the other iron, are identical in lengths and cross-sectional areas. They are joined end to end to form one long rod. A 12-V battery is connected across the free ends of the copperiron rod. What is the voltage between the ends of the copper rod?

A digital thermometer employs a thermistor as the temperaturesensing element. A thermistor is a kind of semiconductor and has a large negative temperature coefficient of resistivity . Suppose that  0.060 (C ) 1 for the thermistor in a digital thermometer used to measure the temperature of a patient. The resistance of the thermistor decreases to 85% of its value at the normal body temperature of 37.0 C. What is the patients temperature? Sec

An electric blanket is connected to a 120-V outlet and consumes 140 W of power. What is the resistance of the heater wire in the blanket?

The heating element in an iron has a resistance of 24 . The iron is plugged into a 120-V outlet. What is the power delivered to the iron?

A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow-dryer is 11 A, and that of the vacuum cleaner is 4.0 A. Determine the power consumed by (a) the blow-dryer and (b) the vacuum cleaner. (c) Determine the ratio of the energy used by the blow-dryer in 15 minutes to the energy used by the vacuum cleaner in one-half hour.

There are approximately 110 million households that use TVs in the United States. Each TV uses, on average, 75 W of power and is turned on for 6.0 hours a day. If electrical energy costs $0.12 per kWh, how much money is spent every day in keeping 110 million TVs turned on?

An MP3 player operates with a voltage of 3.7 V, and is using 0.095 W of power. Find the current being supplied by the players battery.

In doing a load of clothes, a clothes dryer uses 16 A of current at 240 V for 45 min. A personal computer, in contrast, uses 2.7 A of current at 120 V. With the energy used by the clothes dryer, how long (in hours) could you use this computer to surf the Internet?

An electric heater used to boil small amounts of water consists of a 15- coil that is immersed directly in the water. It operates from a 120-V socket. How much time is required for this heater to raise the temperature of 0.50 kg of water from 13 C to the normal boiling point?

The rear window of a van is coated with a layer of ice at 0 C. The density of ice is 917 kg/m3 . The driver of the van turns on the rearwindow defroster, which operates at 12 V and 23 A. The defroster directly heats an area of 0.52 m2 of the rear window. What is the maximum thickness of ice coating this area that the defroster can melt in 3.0 minutes?

A piece of Nichrome wire has a radius of 6.5  104 m. It is used in a laboratory to make a heater that uses 4.00  102 W of power when connected to a voltage source of 120 V. Ignoring the effect of temperature on resistance, estimate the necessary length of wire.

Tungsten has a temperature coefficient of resistivity of 0.0045 (C ) 1 . A tungsten wire is connected to a source of constant voltage via a switch. At the instant the switch is closed, the temperature of the wire is 28 C, and the initial power delivered to the wire is P0. At what wire temperature will the power that is delivered to the wire be decreased to

The rms current in a copy machine is 6.50 A, and the resistance of the machine is 18.6 . What are (a) the average power and (b) the peak power delivered to the machine?

The rms current in a 47- resistor is 0.50 A. What is the peak value of the voltage across this resistor?

A 550-W space heater is designed for operation in Germany, where household electrical outlets supply 230 V (rms) service. What is the power output of the heater when plugged into a 120-V (rms) electrical outlet in a house in the United States? Ignore the effects of temperature on the heaters resistance.

Review Conceptual Example 7 as an aid in solving this problem. A portable electric heater uses 18 A of current. The manufacturer recommends that an extension cord attached to the heater receive no more than 2.0 W of power per meter of length. What is the smallest radius of copper wire that can be used in the extension cord? (Note: An extension cord contains two wires.)

The average power used by a stereo speaker is 55 W. Assuming that the speaker can be treated as a 4.0- resistance, find the peak value of the ac voltage applied to the speaker.

The recovery time of a hot water heater is the time required to heat all the water in the unit to the desired temperature. Suppose that a 52-gal (1.00 gal  3.79  103 m3) unit starts with cold water at 11 C and delivers hot water at 53 C. The unit is electric and utilizes a resistance heater (120 V ac, 3.0 ) to heat the water. Assuming that no heat is lost to the environment, determine the recovery time (in hours) of the unit.

A light bulb is connected to a 120.0-V wall socket. The current in the bulb depends on the time t according to the relation I  (0.707 A) sin [(314 Hz)t]. (a) What is the frequency f of the alternating current? (b) Determine the resistance of the bulbs filament. (c) What is the average power delivered to the light bulb?

To save on heating costs, the owner of a greenhouse keeps 660 kg of water around in barrels. During a winter day, the water is heated by the sun to 10.0 C. During the night the water freezes into ice at 0.0 C in nine hours. What is the minimum ampere rating of an electric heating system (240 V) that would provide the same heating effect as the water does?

Three resistors, 25, 45, and 75 , are connected in series, and a 0.51-A current passes through them. What are (a) the equivalent resistance and (b) the potential difference across the three resistors?

A 60.0-W lamp is placed in series with a resistor and a 120.0-V source. If the voltage across the lamp is 25 V, what is the resistance R of the resistor?

The current in a series circuit is 15.0 A. When an additional 8.00- resistor is inserted in series, the current drops to 12.0 A. What is the resistance in the original circuit?

Multiple-Concept Example 9 discusses the physics principles used in this problem. Three resistors, 2.0, 4.0, and 6.0 , are connected in series across a 24-V battery. Find the power delivered to each resistor.

The current in a 47- resistor is 0.12 A. This resistor is in series with a 28- resistor, and the series combination is connected across a battery. What is the battery voltage?

Multiple-Concept Example 9 reviews the concepts that are important to this problem. A light bulb is wired in series with a 144- resistor, and they are connected across a 120.0-V source. The power delivered to the light bulb is 23.4 W. What is the resistance of the light bulb? Note that there are two possible answers.

Three resistors are connected in series across a battery. The value of each resistance and its maximum power rating are as follows: 2.0  and 4.0 W, 12.0  and 10.0 W, and 3.0  and 5.0 W. (a) What is the greatest voltage that the battery can have without one of the resistors burning up? (b) How much power does the battery deliver to the circuit in (a)?

One heater uses 340 W of power when connected by itself to a battery. Another heater uses 240 W of power when connected by itself to the same battery. How much total power do the heaters use when they are both connected in series across the battery?

Two resistances, R1 and R2, are connected in series across a 12-V battery. The current increases by 0.20 A when R2 is removed, leaving R1 connected across the battery. However, the current increases by just 0.10 A when R1 is removed, leaving R2 connected across the battery. Find (a) R1 and (b) R2.

A coffee-maker (14 ) and a toaster (19 ) are connected in parallel to the same 120-V outlet in a kitchen. How much total power is supplied to the two appliances when both are turned on?

For the three-way bulb (50 W, 100 W, 150 W) discussed in Conceptual Example 11, find the resistance of each of the two filaments. Assume that the wattage ratings are not limited by significant figures, and ignore any heating effects on the resistances.

The drawing shows three different resistors in two different circuits. The battery has a voltage of V  24.0 V, and the resistors have values of R1  50.0 , R2  25.0 , and R3  10.0 . (a) For the circuit on the left, determine the current through and the voltage across each resistor. (b) Repeat part (a) for the circuit on the righ

The drawing shows a circuit that contains a battery, two resistors, and a switch. What is the equivalent resistance of the circuit when the switch is (a) open and (b) closed? What is the total power delivered to the resistors when the switch is (c) open and (d) closed?

A 16- loudspeaker, an 8.0- loudspeaker, and a 4.0- loudspeaker are connected in parallel across the terminals of an amplifier. Determine the equivalent resistance of the three speakers, assuming that they all behave as resistors.

Two resistors, 42.0 and 64.0 , are connected in parallel. The current through the 64.0- resistor is 3.00 A. (a) Determine the current in the other resistor. (b) What is the total power supplied to the two resistors?

Two identical resistors are connected in parallel across a 25-V battery, which supplies them with a total power of 9.6 W. While the battery is still connected, one of the resistors is heated so that its resistance doubles. The resistance of the other resistor remains unchanged. Find (a) the initial resistance of each resistor and (b) the total power delivered to the resistors after one resistor has been heated.

A coffee cup heater and a lamp are connected in parallel to the same 120-V outlet. Together, they use a total of 111 W of power. The resistance of the heater is 4.0  102 . Find the resistance of the lamp.

Two resistors have resistances R1 and R2. When the resistors are connected in series to a 12.0-V battery, the current from the battery is 2.00 A. When the resistors are connected in parallel to the battery, the total current from the battery is 9.00 A. Determine R1 and R2.

A cylindrical aluminum pipe of length 1.50 m has an inner radius of 2.00  103 m and an outer radius of 3.00  103 m. The interior of the pipe is completely filled with copper. What is the resistance of this unit? (Hint: Imagine that the pipe is connected between the terminals of a battery and decide whether the aluminum and copper parts of the pipe are in series or in parallel.)

The drawing shows two circuits, and the same battery is used in each. The two resistances RA in circuit A are the same, and the two resistances RB in circuit B are the same. Knowing that the same total power is delivered in each circuit, find the ratio RB/RA for the circuits.

The rear window defogger of a car consists of thirteen thin wires (resistivity  88.0  108  m) embedded in the glass. The wires are connected in parallel to the 12.0-V battery, and each has a length of 1.30 m. The defogger can melt 2.10  102 kg of ice at 0 C into water at 0 C in two minutes. Assume that all the power delivered to the wires is used immediately to melt the ice. Find the cross-sectional area of each wire. S

A 60.0- resistor is connected in parallel with a 120.0- resistor. This parallel group is connected in series with a 20.0- resistor. The total combination is connected across a 15.0-V battery. Find (a) the current and (b) the power delivered to the 120.0- resistor.

A 14- coffee maker and a 16- frying pan are connected in series across a 120-V source of voltage. A 23- bread maker is also connected across the 120-V source and is in parallel with the series combination. Find the total current supplied by the source of voltage.

Find the equivalent resistance between points A and B in the drawing.

Determine the equivalent resistance between the points A and B for the group of resistors in the drawing.

The circuit in the drawing contains three identical resistors. Each resistor has a value of 10.0 . Determine the equivalent resistance between the points a and b, b and c, and a and c.

Find the equivalent resistance between the points A and B in the drawing.

Each resistor in the three circuits in the drawing has the same resistance R, and the batteries have the same voltage V. The values for R and V are 9.0  and 6.0 V, respectively. Determine the total power delivered by the battery in each of the three circuits.

Eight different values of resistance can be obtained by connecting together three resistors (1.00, 2.00, and 3.00 ) in all possible ways. What are the values?

Determine the power supplied to each of the resistors in the drawing.

The circuit in the drawing contains five identical resistors. The 45-V battery delivers 58 W of power to the circuit. What is the resistance R of each resistor?

The circuit shown in the drawing is constructed with six identical resistors and an ideal battery. When the resistor R4 is removed from the circuit, the current in the battery decreases by 1.9 A. Determine the resistance of each resistor.

A battery has an internal resistance of 0.50 . A number of identical light bulbs, each with a resistance of 15 , are connected in parallel across the battery terminals. The terminal voltage of the battery is observed to be one-half the emf of the battery. How many bulbs are connected?

A 1.40- resistor is connected across a 9.00-V battery. The voltage between the terminals of the battery is observed to be only 8.30 V. Find the internal resistance of the battery

When a light bulb is connected across the terminals of a battery, the battery delivers 24 W of power to the bulb. A voltage of 11.8 V exists between the terminals of the battery, which has an internal resistance of 0.10 . What is the emf of the battery?

A battery has an internal resistance of 0.012  and an emf of 9.00 V. What is the maximum current that can be drawn from the battery without the terminal voltage dropping below 8.90 V?

A battery delivering a current of 55.0 A to a circuit has a terminal voltage of 23.4 V. The electric power being dissipated by the internal resistance of the battery is 34.0 W. Find the emf of the battery.

When a dry-cell flashlight battery with an internal resistance of 0.33  is connected to a 1.50- light bulb, the bulb shines dimly. However, when a lead-acid wet-cell battery with an internal resistance of 0.050  is connected, the bulb is noticeably brighter. Both batteries have the same emf. Find the ratio Pwet /Pdry of the power delivered to the bulb by the wet-cell battery to the power delivered by the dry-cell battery

Consider the circuit in the drawing. Determine (a) the magnitude of the current in the circuit and (b) the magnitude of the voltage between the points labeled A and B. (c) State which point, A or B, is at the higher potentia

The drawing shows a portion of a larger circuit. Current flows left to right in each resistor. What is the current in the resistor R?

Find the magnitude and the direction of the current in the 2.0- resistor in the drawing

Using Kirchhoffs loop rule, find the value of the current I in part c of the drawing, where R  5.0 . (Note: Parts a and b of the drawing are used in the online tutorial help that is provided for this problem in the WileyPLUS homework management program.)

Determine the current (both magnitude and direction) in the 8.0- and 2.0- resistors in the drawing.

Determine the voltage across the 5.0- resistor in the drawing. Which end of the resistor is at the higher potential?

Find the current in the 4.00- resistor in the drawing. Specify the direction of the current.

None of the resistors in the circuit shown in the drawing is connected in series or in parallel with one another. Find (a) the current I5 and the resistances (b) R2 and (c) R3.

The coil of a galvanometer has a resistance of 20.0 , and its meter deflects full scale when a current of 6.20 mA passes through it. To make the galvanometer into a nondigital ammeter, a 24.8-m shunt resistor is added to it. What is the maximum current that this ammeter can read?

The coil of wire in a galvanometer has a resistance of RC  60.0 . The galvanometer exhibits a full-scale deflection when the current through it is 0.400 mA. A resistor is connected in series with this combination so as to produce a nondigital voltmeter. The voltmeter is to have a full-scale deflection when it measures a potential difference of 10.0 V. What is the resistance of this resistor?

Nondigital voltmeter A has an equivalent resistance of 2.40  105  and a full-scale voltage of 50.0 V. Nondigital voltmeter B, using the same galvanometer as voltmeter A, has an equivalent resistance of 1.44  105 . What is its full-scale voltage?

A galvanometer with a coil resistance of 9.00  is used with a shunt resistor to make a nondigital ammeter that has an equivalent resistance of 0.40 . The current in the shunt resistor is 3.00 mA when the galvanometer reads full scale. Find the full-scale current of the galvanometer

Two scales on a nondigital voltmeter measure voltages up to 20.0 and 30.0 V, respectively. The resistance connected in series with the galvanometer is 1680  for the 20.0-V scale and 2930  for the 30.0-V scale. Determine the coil resistance and the full-scale current of the galvanometer that is used in the voltmeter.

In measuring a voltage, a voltmeter uses some current from the circuit. Consequently, the voltage measured is only an approximation to the voltage present when the voltmeter is not connected. Consider a circuit consisting of two 1550- resistors connected in series across a 60.0-V battery. (a) Find the voltage across one of the resistors. (b) A nondigital voltmeter has a full-scale voltage of 60.0 V and uses a galvanometer with a full-scale deflection of 5.00 mA. Determine the voltage that this voltmeter registers when it is connected across the resistor used in part (a).

Two capacitors are connected in parallel across the terminals of a battery. One has a capacitance of 2.0 F and the other a capacitance of 4.0 F. These two capacitors together store 5.4  105 C of charge. What is the voltage of the battery?

Three parallel plate capacitors are connected in series. These capacitors have identical geometries. However, they are filled with three different materials. The dielectric constants of these materials are 3.30, 5.40, and 6.70. It is desired to replace this series combination with a single parallel plate capacitor. Assuming that this single capacitor has the same geometry as each of the other three capacitors, determine the dielectric constant of the material with which it is filled.

Three capacitors are connected in series. The equivalent capacitance of this combination is 3.00 F. Two of the individual capacitances are 6.00 F and 9.00 F. What is the third capacitance (in F)?

Two capacitors are connected to a battery. The battery voltage is V  60.0 V, and the capacitances are C1  2.00 F and C2  4.00 F. Determine the total energy stored by the two capacitors when they are wired (a) in parallel and (b) in series.

Determine the equivalent capacitance between A and B for the group of capacitors in the drawing.

A 2.00-F and a 4.00-F capacitor are connected to a 60.0-V battery. What is the total charge supplied to the capacitors when they are wired (a) in parallel and (b) in series with each other?

Suppose that two capacitors (C1 and C2) are connected in series. Show that the sum of the energies stored in these capacitors is equal to the energy stored in the equivalent capacitor. [Hint: The energy stored in a capacitor can be expressed as q2 /(2C).]

A 3.00-F and a 5.00-F capacitor are connected in series across a 30.0-V battery. A 7.00-F capacitor is then connected in parallel across the 3.00-F capacitor. Determine the voltage across the 7.00-F capacitor.

A 7.0-F and a 3.0-F capacitor are connected in series across a 24-V battery. What voltage is required to charge a parallel combination of the two capacitors to the same total energy?

The drawing shows two capacitors that are fully charged (C1  2.00 F, q1  6.00 C; C2  8.00 F, q2  12.0 C). The switch is closed, and charge flows until equilibrium is reestablished (i.e., until both capacitors have the same voltage across their plates). Find the resulting voltage across either capacitor.

In a heart pacemaker, a pulse is delivered to the heart 81 times per minute. The capacitor that controls this pulsing rate discharges through a resistance of 1.8  106 . One pulse is delivered every time the fully charged capacitor loses 63.2% of its original charge. What is the capacitance of the capacitor?

A circuit contains a resistor in series with a capacitor, the series combination being connected across the terminals of a battery, as in Figure 20.37a. The time constant for charging the capacitor is 1.5 s when the resistor has a resistance of 2.0  104 . What would the time constant be if the resistance had a value of 5.2  104 ?

The circuit in the drawing contains two resistors and two capacitors that are connected to a battery via a switch. When the switch is closed, the capacitors begin to charge up. What is the time constant for the charging process?

How many time constants must elapse before a capacitor in a series RC circuit is charged to 80.0% of its equilibrium charge?

Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 0.72 s. What is the time constant when they are connected with the same resistor, as in part b?

Each of the four circuits in the drawing consists of a single resistor whose resistance is either R or 2R, and a single battery whose voltage is either V or 2V. The unit of voltage in each circuit is V  12.0 V and the unit of resistance is R  6.00 . Determine (a) the power supplied to each resistor and (b) the current delivered to each resistor.

You have three capacitors: C1  67 F, C2  45 F, and C3  33 F. Determine the maximum equivalent capacitance you can obtain by connecting two of the capacitors in parallel and then connecting the parallel combination in series with the remaining capacitor.

A fax machine uses 0.110 A of current in its normal mode of operation, but only 0.067 A in the standby mode. The machine uses a potential difference of 120 V. In one minute (a) how much more charge passes through the machine in the normal mode than in the standby mode, and (b) how much more energy is used?

In the Arctic, electric socks are useful. A pair of socks uses a 9.0-V battery pack for each sock. A current of 0.11 A is drawn from each battery pack by wire woven into the socks. Find the resistance of the wire in one sock.

For the circuit shown in the drawing, find the current I through the 2.00- resistor and the voltage V of the battery to the left of this resistor.

In Section 12.3 it was mentioned that temperatures are often measured with electrical resistance thermometers made of platinum wire. Suppose that the resistance of a platinum resistance thermometer is 125  when its temperature is 20.0 C. The wire is then immersed in boiling chlorine, and the resistance drops to 99.6 . The temperature coefficient of resistivity of platinum is  3.72  103 (C ) 1 . What is the temperature of the boiling chlorine?

The circuit in the drawing shows two resistors, a capacitor, and a battery. When the capacitor is fully charged, what is the magnitude q of the charge on one of its plates?

A galvanometer has a full-scale current of 0.100 mA and a coil resistance of 50.0 . This instrument is used with a shunt resistor to form a nondigital ammeter that will register full scale for a current of 60.0 mA. Determine the resistance of the shunt resistor.

An 86- resistor and a 67- resistor are connected in series across a battery. The voltage across the 86- resistor is 27 V. What is the voltage across the 67- resistor?

The current in the 8.00- resistor in the drawing is 0.500 A. Find the current in (a) the 20.0- resistor and in (b) the 9.00- resistor.

A 75.0- and a 45.0- resistor are connected in parallel. When this combination is connected across a battery, the current delivered by the battery is 0.294 A. When the 45.0- resistor is disconnected, the current from the battery drops to 0.116 A. Determine (a) the emf and (b) the internal resistance of the battery

An extension cord is used with an electric weed trimmer that has a resistance of 15.0 . The extension cord is made of copper wire that has a cross-sectional area of 1.3 106 m2 . The combined length of the two wires in the extension cord is 92 m. (a) Determine the resistance of the extension cord. (b) The extension cord is plugged into a 120-V socket. What voltage is applied to the trimmer itself

The total current delivered to a number of devices connected in parallel is the sum of the individual currents in each device. Circuit breakers are resettable automatic switches that protect against a dangerously large total current by opening to stop the current at a specified safe value. A 1650-W toaster, a 1090-W iron, and a 1250-W microwave oven are turned on in a kitchen. As the drawing shows, they are all connected through a 20-A circuit breaker (which has negligible resistance) to an ac voltage of 120 V. (a) Find the equivalent resistance of the three devices. (b) Obtain the total current delivered by the source and determine whether the breaker will open to prevent an accident.

A wire has a resistance of 21.0 . It is melted down, and from the same volume of metal a new wire is made that is three times longer than the original wire. What is the resistance of the new wire?

The filament in an incandescent light bulb is made from tungsten. The light bulb is plugged into a 120-V outlet and draws a current of 1.24 A. If the radius of the tungsten wire is 0.0030 mm, how long must the wire be?

A sheet of gold foil (negligible thickness) is placed between the plates of a capacitor and has the same area as each of the plates. The foil is parallel to the plates, at a position one-third of the way from one to the other. Before the foil is inserted, the capacitance is C0. What is the capacitance after the foil is in place? Express your answer in terms of C0.

An aluminum wire is hung between two towers and has a length of 175 m. A current of 125 A exists in the wire, and the potential difference between the ends of the wire is 0.300 V. The density of aluminum is 2700 kg/m3 . Find the mass of the wire.

According to Equation 20.7, an ac voltage V is given as a function of time t by V  V0 sin 2ft, where V0 is the peak voltage and f is the frequency (in hertz). For a frequency of 60.0 Hz, what is the smallest value of the time at which the voltage equals one-half of the peak value?