Chapter 27 - Circuits

A portion of a circuit is shown, with the values of the currents given for some branches. What is the direction and value of the current i? *insert picture* A. ↓,6A B. ↑,6A C. ↓,4A D. ↑,4A E. ↓,2A

A. ↓,6A

Two identical batteries, each with an emf of 18V and an internal resistance of 1Ω, are wired in parallel by connecting their positive terminals together and connecting their negative terminals together. The combination is then wired across a 4-Ω resistor. The current in each battery is: A. 1.0A B. 2.0A C. 4.0A D. 3.6A E. 7.2A

B. 2.0A

Each of the resistors in the diagram has a resistance of 12Ω. The resistance of the entire circuit is: A. 5.76Ω B. 25Ω C. 48Ω D. 120Ω E. none of these

B. 25Ω

A galvanometer has an internal resistance of 12Ω and requires 0.01A for full scale deflection. To convert it to a voltmeter reading 3V full scale, one must use a series resistance of: A. 102Ω B. 288Ω C. 300Ω D. 360Ω E. 412Ω

B. 288Ω

In the figure, voltmeter V1 reads 600V, voltmeter V2 reads 580V, and ammeter A reads 100A. The power wasted in the transmission line connecting the power house to the consumer is: A. 1kW B. 2kW C. 58kW D. 59kW E. 60kW

B. 2kW

A charged capacitor is being discharged through a resistor. At the end of one time constant the charge has been reduced by (1−1/e) = 63% of its initial value. At the end of two time constants the charge has been reduced by what percent of its initial value? A. 82% B. 86% C. 100% D. Between 90% and 100% E. Need to know more data to answer the question

B. 86%

A certain voltmeter has an internal resistance of 10,000Ω and a range from 0 to 12V. To extend its range to 120V, use a series resistance of: A. 1,111Ω B. 90,000Ω C. 100,000Ω D. 108,000Ω E. 120,000Ω

B. 90,000Ω

A certain galvanometer has a resistance of 100Ω and requires 1mA for full scale deflection. To make this into a voltmeter reading 1V full scale, connect a resistance of: A. 1000Ω in parallel B. 900Ω in series C. 1000Ω in series D. 10Ω in parallel E. 0.1Ω in series

B. 900Ω in series

Two wires made of the same material have the same lengths but different diameters. They are connected in parallel to a battery. The quantity that is NOT the same for the wires is: A. the end-to-end potential difference B. the current C. the current density D. the electric field E. the electron drift velocity

B. the current

Two wires made of the same material have the same lengths but different diameters. They are connected in series to a battery. The quantity that is the same for the wires is: A. the end-to-end potential difference B. the current C. the current density D. the electric field E. the electron drift velocity

B. the current

Two identical batteries, each with an emf of 18V and an internal resistance of 1Ω, are wired in parallel by connecting their positive terminals together and connecting their negative terminals together. The combination is then wired across a 4-Ω resistor. The current in the 4-Ω resistor is: A. 1.0A B. 2.0A C. 4.0A D. 3.6A E. 7.2A

C. 4.0A

Four 20-Ω resistors are connected in series and the combination is connected to a 20-V emf device. The potential difference across any one of the resistors is: A. 1V B. 4V C. 5V D. 20V E. 80V

C. 5V

The equivalent resistance between points 1 and 2 of the circuit shown is: *INSERT PICTURE* A. 3Ω B. 4Ω C. 5Ω D. 6Ω E. 7Ω

C. 5Ω

An initially uncharged capacitor C is connected in series with resistor R. This combination is then connected to a battery of emf V0. Su fficient time elapses so that a steady state is reached. Which of the following statements is NOT true? A. The time constant is independent of V0 B. The final charge on C is independent of R C. The total thermal energy generated by R is independent of R D. The total thermal energy generated by R is independent of V0 E. The initial current (just after the battery was connected) is independent of C

C. The total thermal energy generated by R is independent of R

Resistor 1 has twice the resistance of resistor 2. The two are connected in parallel and a potential difference is maintained across the combination. The rate of thermal energy generation in 1 is: A. the same as that in 2 B. twice that in 2 C. half that in 2 D. four times that in 2 E. one-fourth that in 2

C. half that in 2

For any circuit the number of independent equations containing emf's, resistances, and currents equals: A. the number of junctions B. the number of junctions minus 1 C. the number of branches D. the number of branches minus 1 E. the number of closed loops

C. the number of branches

In the diagrams, all light bulbs are identical and all emf devices are identical. In which circuit (A, B, C, D, E) will the bulbs glow with the same brightness as in circuit X? *INSERT PICTURE*

D

The positive terminals of two batteries with emf's of E1 and E2, respectively, are connected together. Here E2 > E1. The circuit is completed by connecting the negative terminals. If each battery has an internal resistance r, the rate with which electrical energy is converted to chemical energy in the smaller battery is: A. E2 1/r B. E2 1/2r C. (E2 −E1)E1/r D. (E2 −E1)E1/2r E. E2 2/2r

D. (E2 −E1)E1/2r

In the circuit shown, the capacitor is initially uncharged. At time t = 0, switch S is closed. If τ denotes the time constant, the approximate current through the 3Ω resistor when t = τ/10 is: A. 0.38A B. 0.50A C. 0.75A D. 1.0A E. 1.5A

D. 1.0A

Two identical batteries, each with an emf of 18V and an internal resistance of 1Ω, are wired in parallel by connecting their positive terminals together and connecting their negative terminals together. The combination is then wired across a 4-Ω resistor. The potential difference across the 4-Ω resistor is: A. 4.0V B. 8.0V C. 14V D. 16V E. 29V

D. 16V

A battery with an emf of 24V is connected to a 6-Ω resistor. As a result, current of 3A exists in the resistor. The terminal potential difference of the battery is: A. 0 B. 6V C. 12V D. 18V E. 24V

D. 18V

Four wires meet at a junction. The first carries 4A into the junction, the second carries 5A out of the junction, and the third carries 2A out of the junction. The fourth carries: A. 7A out of the junction B. 7A into the junction C. 3A out of the junction D. 3A into the junction E. 1A into the junction

D. 3A into the junction

By using only two resistors, R1 and R2, a student is able to obtain resistances of 3Ω,4Ω, 12Ω, and 16Ω. The values of R1 and R2 (in ohms) are: A. 3, 4 B. 2, 12 C. 3, 16 D. 4, 12 E. 4, 16

D. 4, 12

Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the switch S is open. The values of the emf E, resistance R, and capacitance C for each of the circuits are circuit 1: E = 18V,R =3Ω, C =1µF circuit 2: E = 18V,R =6Ω, C =9µF circuit 3: E = 12V,R =1Ω, C =7µF circuit 4: E = 10V,R =5Ω, C =7µF Rank the circuits according to the current just after switch S is closed least to greatest. A. 1, 2, 3, 4 B. 4, 3, 2, 1 C. 4, 2, 3, 1 D. 4, 2, 1, 3 E. 3, 1, 2, 4

D. 4, 2, 1, 3

To make a galvanometer into an ammeter, connect: A. a high resistance in parallel B. a high resistance in series C. a low resistance in series D. a low resistance in parallel E. a source of emf in series

D. a low resistance in parallel

A certain ammeter has an internal resistance of 1Ω and a range from 0 to 50mA. To make its range from 0 to 5A, use: A. a series resistance of 99Ω B. an extremely large (say 106 Ω ) series resistance C. a resistance of 99Ω in parallel D. a resistance of 1/99Ω in parallel E. a resistance of 1/1000Ω in parallel

D. a resistance of 1/99Ω in parallel

"The sum of the emf's and potential differences around a closed loop equals zero" is a consequence of: A. Newton's third law B. Ohm's law C. Newton's second law D. conservation of energy E. conservation of charge

D. conservation of energy

The emf of a battery is equal to its terminal potential difference: A. under all conditions B. only when the battery is being charged C. only when a large current is in the battery D. only when there is no current in the battery E. under no conditions

D. only when there is no current in the battery

Nine identical wires, each of diameter d and length L, are connected in series. The combination has the same resistance as a single similar wire of length L but whose diameter is: A. 3d B. 9d C. d/3 D. d/9 E. d/81

C. d/3

The terminal potential difference of a battery is less than its emf: A. under all conditions B. only when the battery is being charged C. only when the battery is being discharged D. only when there is no current in the battery E. under no conditions

C. only when the battery is being discharged

In the diagrams, all light bulbs are identical and all emf devices are identical. In which circuit (A, B, C, D, E) will the bulbs be dimmest? *INSERT PICTURE*

D

A 120-V power line is protected by a 15-A fuse. What is the maximum number of "120V, 500W" light bulbs that can be operated at full brightness from this line? A. 1 B. 2 C. 3 D. 4 E. 5

C. 3

Four 20-Ω resistors are connected in series and the combination is connected to a 20-V emf device. The current in any one of the resistors is: A. 0.25A B. 1.0A C. 4.0A D. 5.0A E. 100A

A. 0.25A

Resistances of 2.0Ω,4 .0Ω, and 6.0Ω and a 24-V emf device are all in parallel. The current in the 2.0-Ω resistor is: A. 12A B. 4.0A C. 2.4A D. 2.0A E. 0.50A

A. 12A

A battery with an emf of 12V and an internal resistance of 1Ω is used to charge a battery with an emf of 10V and an internal resistance of 1Ω. The current in the circuit is: A. 1A B. 2A C. 4A D. 11A E. 22A

A. 1A

A 3-Ω and a 1.5-Ω resistor are wired in parallel and the combination is wired in series to a 4-Ω resistor and a 10-V emf device. The potential difference across the 3-Ω resistor is: A. 2.0V B. 6.0V C. 8.0V D. 10V E. 12V

A. 2.0V

Nine identical wires, each of diameter d and length L, are connected in parallel. The combination has the same resistance as a single similar wire of length L but whose diameter is: A. 3d B. 9d C. d/3 D. d/9 E. d/81

A. 3d

A total resistance of 3.0Ω is to be produced by combining an unknown resistor R with a 12Ω resistor. What is the value of R and how is it to be connected to the 12Ω resistor? A. 4.0Ω, parallel B. 4.0Ω, series C. 2.4Ω, parallel D. 2.4Ω, series E. 9.0Ω, series

A. 4.0Ω, parallel

Resistances of 2.0Ω,4 .0Ω, and 6.0Ω and a 24-V emf device are all in series. The potential difference across the 2.0-Ω resistor is: A. 4V B. 8V C. 12V D. 24V E. 48V

A. 4V

If a circuit has L closed loops, B branches, and J junctions the number of independent loop equations is: A. B−J +1 B. B−J C. B D. L E. L−J

A. B−J +1

A resistor with resistance R1 and a resistor with resistance R2 are connected in parallel to an ideal battery with emf E. The rate of thermal energy generation in the resistor with resistance R1 is: A. E2/R1 B. E2R1/(R1 + R2)2 C. E2/(R1 + R2) D. E2/R2 E. E2R1/R2^2

A. E2/R1

When switch S is open, the ammeter in the circuit shown reads 2.0A. When S is closed, the ammeter reading: A. increases slightly B. remains the same C. decreases slightly D. doubles E. halves

A. increases slightly

A series circuit consists of a battery with internal resistance r and an external resistor R. If these two resistances are equal (r = R) then the thermal energy generated per unit time by the internal resistance r is: A. the same as by R B. half that by R C. twice that by R D. one-third that by R E. unknown unless the emf is given

A. the same as by R

A 3-Ω and a 1.5-Ω resistor are wired in parallel and the combination is wired in series to a 4-Ω resistor and a 10-V emf device. The current in the 3-Ω resistor is: A. 0.33A B. 0.67A C. 2.0A D. 3.3A E. 6.7A

B. 0.67A

Resistor 1 has twice the resistance of resistor 2. They are connected in parallel to a battery. The ratio of the thermal energy generation rate in 1 to that in 2 is: A. 1 : 4 B. 1 : 2 C. 1 : 1 D. 2 : 1 E. 4 : 1

B. 1 : 2

Four 20-Ω resistors are connected in parallel and the combination is connected to a 20-V emf device. The current in any one of the resistors is: A. 0.25A B. 1.0A C. 4.0A D. 5.0A E. 100A

B. 1.0A

In an antique automobile, a 6-V battery supplies a total of 48W to two identical headlights in parallel. The resistance (in ohms) of each bulb is: A. 0.67 B. 1.5 C. 3 D. 4 E. 8

B. 1.5

In the circuit shown, both resistors have the same value R. Suppose switch S is initially closed. When it is then opened, the circuit has a time constant τa. Conversely, suppose S is initially open. When it is then closed, the circuit has a time constant τb. The ratio τa/τb is: A. 1 B. 2 C. 0.5 D. 0.667 E. 1.5

B. 2

Four 20-Ω resistors are connected in parallel and the combination is connected to a 20-V emf device. The current in the device is: A. 0.25A B. 1.0A C. 4.0A D. 5.0A E. 100

C. 4.0A

The resistance of resistor 1 is twice the resistance of resistor 2. The two are connected in parallel and a potential difference is maintained across the combination. Then: A. the current in 1 is twice that in 2 B. the current in 1 is half that in 2 C. the potential difference across 1 is twice that across 2 D. the potential difference across 1 is half that across 2 E. none of the above are true

B. the current in 1 is half that in 2

Resistor 1 has twice the resistance of resistor 2. The two are connected in series and a potential difference is maintained across the combination. The rate of thermal energy generation in 1 is: A. the same as that in 2 B. twice that in 2 C. half that in 2 D. four times that in 2 E. one-fourth that in 2

B. twice that in 2

Suppose the current charging a capacitor is kept constant. Which graph below correctly gives the potential difference V across the capacitor as a function of time? *INSERT IMAGE*

C

Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the switch S is open. The values of the emf E, resistance R, and capacitance C for each of the circuits are circuit 1: E = 18V,R =3Ω, C =1µF circuit 2: E = 18V,R =6Ω, C =9µF circuit 3: E = 12V,R =1Ω, C =7µF circuit 4: E = 10V,R =5Ω, C =7µF Rank the circuits according to the time after switch S is closed for the capacitors to reach half their final charges, least to greatest. A. 1, 2, 3, 4 B. 4, 3, 2, 1 C. 1, 3, 4, 2 D. 1 and 2 tied, then 4, 3 E. 4, 3, then 1 and 2 tied

C. 1, 3, 4, 2

The current in the 5.0-Ω resistor in the circuit shown is: *INSERT PICTURE* A. 0.42A B. 0.67A C. 1.5A D. 2.4A E. 3.0A

C. 1.5A

A certain capacitor, in series with a 720-Ω resistor, is being charged. At the end of 10ms its charge is half the final value. The capacitance is about: A. 9.6µF B. 14µF C. 20µF D. 7.2F E. 10F

C. 20µF

The resistance of resistor 1 is twice the resistance of resistor 2. The two are connected in series and a potential difference is maintained across the combination. Then: A. the current in 1 is twice that in 2 B. the current in 1 is half that in 2 C. the potential difference across 1 is twice that across 2 D. the potential difference across 1 is half that across 2 E. none of the above are true

C. the potential difference across 1 is twice that across 2

A battery is connected across a parallel combination of two identical resistors. If the potential difference across the terminals is V and the current in the battery is i, then: A. the potential difference across each resistor is V and the current in each resistor is i B. the potential difference across each resistor is V/2 and the current in each resistor is i/2 C. the potential difference across each resistor is V and the current in each resistor is i/2 D. the potential difference across each resistor is V/2 and the current in each resistor is i E. none of the above are true

C. the potential difference across each resistor is V and the current in each resistor is i/2

A battery has an emf of 9V and an internal resistance of 2Ω. If the potential difference across its terminals is greater than 9V: A. it must be connected across a large external resistance B. it must be connected across a small external resistance C. the current must be out of the positive terminal D. the current must be out of the negative terminal E. the current must be zero

D. the current must be out of the negative terminal

The circuit shown was wired for the purpose of measuring the resistance of the lamp L. Inspection shows that: A. voltmeter V and rheostat R should be interchanged B. the circuit is satisfactory C. the ammeter A should be in parallel with R, not L D. the meters, V and A, should be interchanged E. L and V should be interchanged

D. the meters, V and A, should be interchanged

A battery is connected across a series combination of two identical resistors. If the potential difference across the terminals is V and the current in the battery is i, then: A. the potential difference across each resistor is V and the current in each resistor is i B. the potential difference across each resistor is V/2 and the current in each resistor is i/2 C. the potential difference across each resistor is V and the current in each resistor is i/2 D. the potential difference across each resistor is V/2 and the current in each resistor is i E. none of the above are true

D. the potential difference across each resistor is V/2 and the current in each resistor is i

In the context of the loop and junctions rules for electrical circuits a junction is: A. where a wire is connected to a resistor B. where a wire is connected to a battery C. where only two wires are joined D. where three or more wires are joined E. where a wire is bent

D. where three or more wires are joined

A certain capacitor, in series with a resistor, is being charged. At the end of 10ms its charge is half the final value. The time constant for the process is about: A. 0.43ms B. 2.3ms C. 6.9ms D. 10ms E. 14ms

E. 14ms

In the diagram, the current in the 3-Ω resistor is 4A. The potential difference between points 1 and 2 is: *INSERT PICTURE* A. 0.75V B. 0.8V C. 1.25V D. 12V E. 20V

E. 20V

A certain voltmeter has an internal resistance of 10,000Ω and a range from 0 to 100V. To give it a range from 0 to 1000V, one should connect: A. 100,000Ω in series B. 100,000Ω in parallel C. 1000Ω in series D. 1000Ω in parallel E. 90,000Ω in series

E. 90,000Ω in series

In the diagram R1 >R 2 >R 3. Rank the three resistors according to the current in them, least to greatest. A. 1, 2, 3 B. 3, 2, 1 C. 1, 3, 2 D. 3, 1, 3 E. All are the same

E. All are the same

"The sum of the currents into a junction equals the sum of the currents out of the junction" is a consequence of: A. Newton's third law B. Ohm's law C. Newton's second law D. conservation of energy E. conservation of charge

E. conservation of charge

In the capacitor discharge formula q = q0e−t/RC the symbol t represents: A. the time constant B. the time it takes for C to lose the fraction 1/e of its initial charge C. the time it takes for C to lose the fraction (1−1/e) of its initial charge D. the time it takes for C to lose essentially all of its initial charge E. none of the above

E. none of the above

Two 110-V light bulbs, one "25W" and the other "100W", are connected in series to a 110V source. Then: A. the current in the 100-W bulb is greater than that in the 25-W bulb B. the current in the 100-W bulb is less than that in the 25-W bulb C. both bulbs will light with equal brightness D. each bulb will have a potential difference of 55V E. none of the above

E. none of the above

The time constant RC has units of: A. second/farad B. second/ohm C. 1/second D. second/watt E. none of these

E. none of these