Deck 27: Circuits

Question 1

A battery has an emf of 9V and an internal resistance of 2 $\Omega$ . 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

Answer 1

the current must be out of the negative terminal

Question 2

Resistances of 2.0 $\Omega$ , 4.0 $\Omega$ , and 6.0 $\Omega$ and a 24-V emf device are all in series. The potential difference across the 2.0- $\Omega$ resistor is:

A) 4 V
B) 8 V
C) 12 V
D) 24 V
E) 48 V

Answer 2

4 V

Question 3

Four 20- $\Omega$ 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) 0.25 A
B) 1.0 A
C) 4.0 A
D) 5.0 A
E) 100 A

Answer 3

0.25 A

Question 4

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 energy dissipated 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

Question 5

A battery of emf 24 V is connected to a 6- $\Omega$ resistor. As a result, current of 3 A exists in the resistor. The terminal potential difference of the battery is:

A) 0
B) 6 V
C) 12 V
D) 18 V
E) 24 V

Question 6

Two 110-V light bulbs, one "25 W" and the other "100 W", are connected in series to a 110 V 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 55 V
E) none of the above

Question 7

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

Question 8

"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

Question 9

A battery with an emf of 12 V and an internal resistance of 1 $\Omega$ is used to charge a battery with an emf of 10 V and an internal resistance of 1 $\Omega$ . The current in the circuit is:

A) 1 A
B) 2 A
C) 4 A
D) 11 A
E) 22 A

Question 10

The current in the 5.0- $\Omega$ resistor in the circuit shown is:

A) 0.42 A
B) 0.67 A
C) 1.5 A
D) 2.4 A
E) 3.0 A

Question 11

Four 20- $\Omega$ 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) 1 V
B) 4 V
C) 5 V
D) 20 V
E) 80 V

Question 12

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

Question 13

In the diagram R₁ > R₂ > R₃. 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, 2
E) All are the same

Question 14

In the diagram, the current in the 3- $\Omega$ resistor is 4 A. The potential difference between points 1 and 2 is:

A) 0.75 V
B) 0.8 V
C) 1.25 V
D) 12 V
E) 20 V

Question 15

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

Question 16

The terminal potential difference of a battery is less greater 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

Question 17

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

Question 18

Two wires made of the same material have the same length 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

Question 19

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 dissipation 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

Question 20

The positive terminals of two batteries with emf's of ε₁ and ε₂, respectively, are connected together. Here ε₁ > ε_2. The circuit is completed by connecting the negative terminals. If each battery has an internal resistance of r, the rate in watts at which electrical energy is converted to chemical energy in the smaller battery is:

A)
B)
C)
D)
E)

Question 21

Four 20- $\Omega$ resistors are connected in parallel and the combination is connected to a 20-V emf device. The current in the device is:

A) 0.25 A
B) 1.0 A
C) 4.0 A
D) 5.0 A
E) 100 A

Question 22

Resistances of 2.0 $\Omega$ , 4.0 $\Omega$ , and 6.0 $\Omega$ and a 24-V battery are all in series. The current in the 2.0 $\Omega$ resistor is:

A) 12 A
B) 4.0 A
C) 2.4 A
D) 2.0 A
E) 0.50 A

Question 23

Two identical batteries, each with an emf of 18 V and an internal resistance of 1 $\Omega$ , are wired in parallel by connecting their positive terminals together and connecting their negative terminals together. The combination is then wired across a 4- $\Omega$ resistor. The current in each battery is:

A) 1.0 A
B) 2.0 A
C) 4.0 A
D) 3.6 A
E) 7.2 A

Question 24

Two identical batteries, each with an emf of 18 V and an internal resistance of 1 $\Omega$ , are wired in parallel by connecting their positive terminals together and connecting their negative terminals together. The combination is then wired across a 4- $\Omega$ resistor. The potential difference across the 4- $\Omega$ resistor is:

A) 4.0 V
B) 8.0 V
C) 14 V
D) 16 V
E) 29 V

Question 25

Two identical batteries, each with an emf of 18 V and an internal resistance of 1 $\Omega$ , are wired in parallel by connecting their positive terminals together and connecting their negative terminals together. The combination is then wired across a 4- $\Omega$ resistor. The current in the 4- $\Omega$ resistor is:

A) 1.0 A
B) 2.0 A
C) 4.0 A
D) 3.6 A
E) 7.2 A

Question 26

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

Question 27

Four 20- $\Omega$ 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) 0.25 A
B) 1.0 A
C) 4.0 A
D) 5.0 A
E) 100 A

Question 28

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

Question 29

Two wires made of the same material have the same length but different diameter. 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

Question 30

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

Question 31

The equivalent resistance between points 1 and 2 of the circuit shown is:

A) 3 $\Omega$
B) 4 $\Omega$
C) 5 $\Omega$
D) 6 $\Omega$
E) 7 $\Omega$

Question 32

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

Question 33

"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

Question 34

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

Question 35

Each of the resistors in the diagram is 12 $\Omega$ . The resistance of the entire circuit is:

A) 5.76 $\Omega$
B) 25 $\Omega$
C) 48 $\Omega$
D) 120 $\Omega$
E) none of these

Question 36

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

Question 37

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 dissipation 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

Question 38

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

Question 39

Two wires are made of the same material and have the same length but different radii. They are joined end-to-end and a potential difference is maintained across the combination. Of the following the quantity that is the same for both wires is:

A) potential difference
B) current
C) current density
D) electric field
E) conduction electron drift speed

Question 40

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?

A) $\downarrow$ , 6A
B) $\uparrow$ , 6A
C) $\downarrow$ , 4A
D) $\uparrow$ , 4A
E) $\downarrow$ , 2A

Question 41

A certain voltmeter has an internal resistance of 10,000 $\Omega$ and a range from 0 to 100 V. To give it a range from 0 to 1000 V, one should connect:

A) 100,000 $\Omega$ in series
B) 100,000 $\Omega$ in parallel
C) 1000 $\Omega$ in series
D) 1000 $\Omega$ in parallel
E) 90,000 $\Omega$ in series

Question 42

A galvanometer has an internal resistance of 12 $\Omega$ and requires 0.01 A for full scale deflection. To convert it to a voltmeter reading 3 V full scale, one must use a series resistance of:

A) 102 $\Omega$
B) 288 $\Omega$
C) 300 $\Omega$
D) 360 $\Omega$
E) 412 $\Omega$

Question 43

A resistor with resistance R1 and a resistor with resistance R2 are connected in parrallel to an ideal battery with emf ε. The rate of thermal energy generation in the resistor with resistance R1 is:

A) ε²/R₁
B) ε² R¹/(R₁ + R₂)²
C) ε² /(R₁ + R₂)
D) ε²/R₂
E)

Question 44

In the figure, voltmeter V₁ reads 600 V, voltmeter V₂ reads 580 V, and ammeter A reads 100 A. The power wasted in the transmission line connecting the power house to the consumer is:

A) 1 kW
B) 2 kW
C) 58 kW
D) 59 kW
E) 60 kW

Question 45

A certain voltmeter has an internal resistance of 10,000 $\Omega$ and a range from 0 to 12 V. To extend its range to 120 V, use a series resistance of:

A) 1,111 $\Omega$
B) 90,000 $\Omega$
C) 100,000 $\Omega$
D) 108,000 $\Omega$
E) 120,000 $\Omega$

Question 46

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

Question 47

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

Question 48

In the diagrams, all light bulbs are identical and all emf devices are identical. In which circuit (I, II, III, IV, V) will the bulbs be dimmest?

A) I
B) II
C) III
D) IV
E) V

Question 49

When switch S is open, the ammeter in the circuit shown reads 2.0 A. When S is closed, the ammeter reading:

A) increases slightly
B) remains the same
C) decreases slightly
D) doubles
E) halves

Question 50

By using only two resistors, R₁ and R₂ a student is able to obtain resistances of 3 $\Omega$ , 4 $\Omega$ , 12 $\Omega$ , and 16 $\Omega$ . The values of R₁ and R₂ (in ohms) are:

A) 3, 4
B) 2, 12
C) 3, 16
D) 4, 12
E) 4, 16

Question 51

A 3- $\Omega$ and a 1.5- $\Omega$ resistor are wired in parallel and the combination is wired in series to a 4- $\Omega$ resistor and a 10-V emf device. The potential difference across the 3- $\Omega$ resistor is:

A) 2.0 V
B) 6.0 V
C) 8.0 V
D) 10 V
E) 12 V

Question 52

A 3- $\Omega$ and a 1.5- $\Omega$ resistor are wired in parallel and the combination is wired in series to a 4- $\Omega$ resistor and a 10-V emf device. The current in the 3- $\Omega$ resistor is:

A) 0.33 A
B) 0.67 A
C) 2.0 A
D) 3.3 A
E) 6.7 A

Question 53

In an antique automobile, a 6-V battery supplies a total of 48 W 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

Question 54

A 120-V power line is protected by a 15-A fuse. What is the maximum number of "120 V, 500 W" light bulbs that can be operated at full brightness from this line?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 55

A certain ammeter has an internal resistance of 1 $\Omega$ and a range from 0 to 50 mA. To make its range from 0 to 5 A, use:

A) a series resistance of 99 $\Omega$
B) an extremely large (say 10⁶ $\Omega$ ) series resistance
C) a resistance of 99 $\Omega$ in parallel
D) a resistance of 1/99 $\Omega$ in parallel
E) a resistance of 1/1000 $\Omega$ in parallel

Question 56

A total resistance of 3.0 $\Omega$ is to be produced by combining an unknown resistor R with a 12 $\Omega$ resistor. What is the value of R and how is it to be connected to the 12 $\Omega$ resistor?

A) 4.0 $\Omega$ , parallel
B) 4.0 $\Omega$ , series
C) 2.4 $\Omega$ , parallel
D) 2.4 $\Omega$ , series
E) 9.0 $\Omega$ , series

Question 57

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 $\varepsilon$ , resistance and R, and capacitance C for each for the circuits are 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

Question 58

A certain galvanometer has a resistance of 100 $\Omega$ and requires 1 mA for full scale deflection. To make this into a voltmeter reading 1 V full scale, connect a resistance of:

A) 1000 $\Omega$ in parallel
B) 900 $\Omega$ in series
C) 1000 $\Omega$ in series
D) 10 $\Omega$ in parallel
E) 0.1 $\Omega$ in series

Question 59

Resistor 1 has twice the resistance of resistor 2. They are connected in parallel to a battery. The ratio of the thermal energy dissipation by 1 to that by 2 is:

A) 1:4
B) 1:2
C) 1:1
D) 2:1
E) 4:1

Question 60

In the diagrams, all light bulbs are identical and all emf devices are identical. In which circuit (I, II, III, IV, V) will the bulbs glow with the same brightness as in circuit X?

A) I
B) II
C) III
D) IV
E) V

Question 61

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 $\tau$ _a Conversely, suppose S is initially open. When it is then closed, the circuit has a time constant $\tau$ _b The ratio $\tau$ _a/ $\tau$ _b is:

A) 1
B) 2
C) 0.5
D) 0.667
E) 1.5

Question 62

A certain capacitor, in series with a 720- $\Omega$ resistor, is being charged. At the end of 10 ms its charge is half the final value. The capacitance is about:

A) 9.6 $\mu$ F
B) 14 $\mu$ F
C) 20 $\mu$ F
D) 7.2 F
E) 10 F

Question 63

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

Question 64

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?

A) I
B) II
C) III
D) IV
E) V

Question 65

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

Question 66

An initially uncharged capacitor C is connected in series with resistor R. This combination is then connected to a battery of emf V₀. Sufficient 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 energy dissipated by R is independent of R
D) The total energy dissipated by R is independent of V₀
E) The initial current (just after the battery was connected) is independent of C

Question 67

A certain capacitor, in series with a resistor, is being charged. At the end of 10 ms its charge is half the final value. The time constant for the process is about:

A) 0.43 ms
B) 2.3 ms
C) 6.9 ms
D) 10 ms
E) 14 ms

Question 68

The time constant RC has units of:

A) second/farad
B) second/ohm
C) 1/second
D) second/watt
E) none of these

Question 69

In the circuit shown, the capacitor is initially uncharged. At time t = 0, switch S is closed. If $\tau$ denotes the time constant, the approximate current through the 3 $\Omega$ resistor when t = $\tau$ /10 is:

A) 0.38 A
B) 0.50 A
C) 0.75 A
D) 1.0 A
E) 1.5 A

Question 70

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 $\varepsilon$ , resistance R, and the capacitance C for each of the circuits are 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, 2, 4
D) 4, 2, 1, 3
E) 3, 1, 2, 4