Deck 26: Direct Current Circuits

Question 1

During a physics demonstration,a fully charged 98-µF capacitor is discharged through a 125- $\varOmega$ resistor.What fraction of the capacitor's fully charged energy remains after 6.2 ms?

A)0.75
B)0.62
C)0.36
D)0.25
E)0.50

Answer 1

0.36

Question 2

A resistor and capacitor are connected in series in an open circuit.If a second identical resistor is connected in series in the circuit,the time constant for the circuit will

A)decrease.
B)increase.
C)stay the same.

Answer 2

increase.

Question 3

In the circuit shown,with the switch open the capacitors are completely uncharged.The switch is closed for a long time.The current through the circuit is 0.2 A.Determine the potential difference across the capacitor.

A)0.0 V
B)1.6 V
C)2.5 V
D)3.9 V

Answer 3

1.6 V

Question 4

In the circuit shown,with the switch open the capacitors are completely uncharged.The switch is closed for a long time.The current through the circuit is 0.2 A.Determine the potential difference across the 8.0 $\varOmega$ resistor.

A)0.0 V
B)1.6 V
C)2.5 V
D)3.9 V

Question 5

In the circuit shown,with the switch open the capacitor is completely uncharged.The switch is closed for a long time.The current through the circuit is 0.2 A.Determine the potential difference across the unknown resistor.

A)0.0 V
B)4.5 V
C)5.4 V
D)7.0 V

Question 6

An old 9.0-V battery produces a potential difference of 9.0 V when checked with a voltmeter.If the internal resistance is 14.3 Ω and a 100 Ω resistor is connected across the battery leads,what is the voltage across the battery's leads?

A)7.9 V
B)11 V
C)5.4 V
D)9.0 V
E)7.1 V

Question 7

A 9.0000-V battery is used to produce a current through two identical resistors in series,each having a resistance of 150.00 k $\varOmega$ .A handheld digital multimeter (DMM)is used to measure the potential difference across the first resistor by placing probe leads at each end of this resistor.Typical DMMs have an internal resistance of 10 M $\varOmega$ .What is the current in the circuit with the DMM connected?

A)30.22 $\mu$ A
B)30.00 $\mu$ A
C)29.78 $\mu$ A
D)30.33 $\mu$ A
E)30.14 $\mu$ A

Question 8

Lithium polymer batteries have revolutionized the battery field due to their light weight,high energy density (about four times greater than nickel-cadmium or nickel-metal-hydride cells)and low internal resistance.At 25 ^$\circ$ C a three cell lithium polymer battery has no load voltage of 11.1 V and an internal resistance of 300 m $\varOmega$ .If the battery is used to power a device that needs a minimum of 10.0 V,e.g.,it will not work if the applied voltage is below 10.0 V,what is the minimum resistance of that device?

A)1.35 $\varOmega$
B)2.43 $\varOmega$
C)2.73 $\varOmega$
D)3.03 $\varOmega$
E)4.62 $\varOmega$

Question 9

During a physics demonstration,a fully charged 98-µF capacitor is discharged through a 125- $\varOmega$ resistor.How long will it take for the capacitor to lose 75% of its initial energy?

A)4.3 ms
B)6.2 ms
C)8.5 ms
D)11 ms
E)24 ms

Question 10

Consider a triangle with a 150-Ω resistor along each edge.The resistors are connected at the corners of the triangle.A power supply applies a potential difference of 3.6 V to two corners of the resistor triangle.How much current does the power supply source?

A)0.0080 A
B)0.012 A
C)0.024 A
D)0.036 A
E)0.048 A

Question 11

A capacitor of capacitance C and a resistor of resistance R are connected in series.At time t = 0 the combination is connected across a battery of negligible internal resistance.When is the current through the resistor equal to half of its maximum value?

A)0.500 RC
B)0.693 RC
C)0.707 RC
D)0.721 RC

Question 12

The ammeter your physics instructor uses for in-class demonstrations has a resistance R_g and requires a current of 1.0 mA for full-scale deflection.The same ammeter can be used to measure currents of much greater values by wiring a shunt resistor of relatively small resistance,R_p ,in parallel with the ammeter.The shunt resistance needed to produce a full-scale current of 12 A is 3.5 m $\varOmega$ .What is the resistance of the ammeter,R_g?

A)75 $\varOmega$ .
B)35 $\varOmega$ .
C)42 $\varOmega$ .
D)28 $\varOmega$ .
E)60 $\varOmega$ .

Question 13

An old 9.0-V battery produces a potential difference of 9.0 V when checked with a voltmeter.A student is still suspicious of the battery and measures a voltage of 7.6 V when a 100-Ω resistor connects the battery leads.What is the internal resistance of this battery?

A)14.3 Ω
B)15.6 Ω
C)18.4 Ω
D)20.4 Ω
E)21.65 Ω

Question 14

A 9.0000-V battery is used to produce a current through two identical resistors in series,each having a resistance of 150.00 kΏ.A handheld digital multimeter (DMM)is used to measure the potential difference across the first resistor by placing probe leads at each end of this resistor.Typical DMMs have an internal resistance of 10 M $\varOmega$ .What is the potential difference that the DMM measures across the first resistor?

A)4.500 V
B)4.467 V
C)4.534 V
D)4.425 V
E)4.628 V

Question 15

In the circuit shown,with the switch open the capacitor is completely uncharged.The switch is closed for a long time.The current through the circuit is 0.2 A.Determine the value of the unknown resistor.

A)10 $\varOmega$
B)27 $\varOmega$
C)56 $\varOmega$
D)61 $\varOmega$

Question 16

When being used to measure current,an ammeter should be connected in

A)series with the circuit.
B)parallel with the circuit.
C)series with the voltmeter.
D)parallel with the voltmeter.

Question 17

A 9.0000-V battery is used to produce a current through two identical resistors in series,each having a resistance of 150.00 k $\varOmega$ .A handheld digital multimeter (DMM)is used to measure the potential difference across the first resistor by placing probe leads at each end of this resistor.Typical DMMs have an internal resistance of 10 M $\varOmega$ .What is the effective resistance of the circuit with the DMM connected?

A)296.85 k $\varOmega$
B)300.00 k $\varOmega$
C)297.78 k $\varOmega$
D)305.15 k $\varOmega$
E)302.22 k $\varOmega$

Question 18

The ammeter your physics instructor uses for in-class demonstrations has a resistance R_g = 60 $\varOmega$ and requires a current of 1.0 mA for full-scale deflection.The same ammeter can be used to measure currents of much greater values by wiring a shunt resistor of relatively small resistance,R_p ,in parallel with the ammeter.The value of the shunt resistance that allows the ammeter to be used to measure a current of 12 A at full-scale deflection is

A)5.0 m $\varOmega$ .
B)4.0 m $\varOmega$ .
C)3.5 m $\varOmega$ .
D)2.5 m $\varOmega$ .
E)1.7 m $\varOmega$ .

Question 19

A resistor and capacitor are connected in series in an open circuit.If a second identical resistor is connected in parallel in the circuit,the time constant for the circuit will

A)decrease.
B)increase.
C)stay the same.

Question 20

When being used to measure voltage,a voltmeter should be connected in

A)series with the circuit.
B)parallel with the circuit.
C)series with the ammeter.
D)parallel with the ammeter.

Question 21

In the movie Back to the Future,time travel is made possible by a flux capacitor,which generates 1.21 GW of power.Assuming that a 3.00-F capacitor is charged to full charge with a 12.0-V car battery and is discharged through a resistor,what is the resistance necessary to produce a peak power output of 1.21 * 10⁹ W in the resistor?

A)9.92 * 10^-9 ohm
B)8.72 * 10^-8 ohm
C)1.19 * 10^-7 ohm
D)1.79 * 10^-7 ohm
E)3.57 * 10^-7 ohm

Question 22

If the 2- $\mu$ F capacitor in the circuit shown initially had a potential difference of 10 V across its plates,how much charge is left on it after the switch has been closed for a duration equal to one half of the time constant?

A)12.1 µC
B)20 µC
C)7.9 µC
D)0.08 µC

Question 23

A 24-V battery is attached to a 3.0-mF capacitor and a 100-ohm resistor.If the capacitor is initially uncharged,how long will it take for the capacitor to reach a charge of 50 mC?

A)0.11 s
B)0.21 s
C)0.30 s
D)0.36 s
E)1.2 s

Question 24

A 24-V battery is attached to capacitor and a 100-ohm resistor.If 1.73 J of energy are dissipated by the resistor while the capacitor is charging,what is the capacitance of the capacitor?

A)6.0 mF
B)3.0 mF
C)8.3 mF
D)4.5 mF
E)7.2 mF

Question 25

In the circuit shown,R₁ = 5 $\varOmega$ ,R₂ = 10 $\varOmega$ ,and R₃ = 15 $\varOmega$ ,and $\varepsilon$ ₁ = 10 V,and $\varepsilon$ ₂ = 15 V.Using Kirchhoff's loop and junction laws,determine the currents I₁,I2,and I₃ flowing through R₁,R₂,and R₃,respectively,where the direction of each current is as indicated in the figure.

A)I₁ = 0.636 A,I₂ = 0.545 A,I₃ = 0.091 A
B)I₁ = 0.091 A,I₂ = 0.545 A,I₃ = 0.636 A
C)I₁ = 1.0 A,I₂ = -1.0 A,I₃ = 2.0 A
D)I₁ = 0.5 A,I₂ = 1.5 A,I₃ = 1.0 A

Question 26

A 24-V battery is attached to a 3.0-mF capacitor and a 100-ohm resistor.If the capacitor is initially uncharged,what is the charge on the capacitor 0.21 seconds after the circuit is connected to the battery?

A)61 mC
B)50 mC
C)21 mC
D)36 mC
E)43 mC

Question 27

A 24-V battery is attached to a 3.0-mF capacitor and a 100-ohm resistor.If the capacitor is initially uncharged,what is the voltage across the capacitor 0.16 seconds after the circuit is connected to the battery?

A)14 V
B)12 V
C)15 V
D)9.9 V
E)8.6 V

Question 28

In the figure shown,the time constant for the discharge of the capacitor is

A)10 sec.
B)20 sec.
C)30 sec.
D)40 sec.
E)50 sec.

Question 29

An RC circuit has a time constant of 2.10 s.At t = 0,the capacitor is fully charged.At what time will the voltage across the capacitor be half of its initial value?

A)0.728 s
B)1.35 s
C)1.46 s
D)1.83 s
E)2.58 s

Question 30

Beginning with an uncharged capacitor in an RC circuit,how long would it take,in multiples of time constant $\tau$ ,for the capacitor to be 98% charged?

A)9 $\tau$
B)0.9 $\tau$
C)90 $\tau$
D)4 $\tau$

Question 31

An RC circuit has a time constant of 2.10 s.At t = 0,the capacitor is fully charged.At what time will the energy stored in the capacitor be half of its initial value?

A)0.728 s
B)1.35 s
C)1.46 s
D)1.83 s
E)2.58 s

Question 32

A 24-V battery is attached to a 3.0-mF capacitor and a 100-ohm resistor.If the capacitor is initially uncharged,what is the voltage across the resistor 0.16 seconds after the circuit is connected to the battery?

A)12 V
B)14 V
C)9.9 V
D)15 V
E)8.6 V

Question 33

An RC circuit consisting of a 150 µF capacitor and a 1 M $\varOmega$ resistor is connected to a 100-V battery for a long time,and then the battery is shorted.After 30 s,a second identical resistor is placed in parallel with the original.What is the voltage across the capacitor 30 s after this?

A)0 V
B)54.9 V
C)75.6 V
D)84.3 V
E)100 V

Question 34

Assuming that a 1-F capacitor is charged to full charge with a 12-V car battery and is discharged through a resistor,what is the resistance necessary to produce a peak power output of 120 W in the resistor?

A)0.5 Ω
B)0.7 Ω
C)1.0 Ω
D)1.2 Ω
E)1.5 Ω

Question 35

Which of the following will reduce the decay time in an RC circuit?

A)increasing the dielectric constant of the capacitor
B)adding an additional 20 m of wiring between the capacitor and the resistor
C)increasing the voltage of the attached battery
D)adding an additional resistor in parallel with the resistor
E)None are correct.

Question 36

An ammeter must be placed in series with the circuit element whose current is to be measured.An ideal ammeter therefore has

A)zero resistance.
B)infinite resistance.
C)resistance equal to the circuit element.
D)None are correct.

Question 37

Consider an RC circuit with a capacitance of 150 $\mu$ 0F,a resistance of 1 MΩ and connected to a 200-V power source for a long time.The power supply is disconnected and shorted.How long should one wait before the voltage across the capacitor drops to below 50 V?

A)52 s
B)104 s
C)176 s
D)208 s
E)314 s

Question 38

In the circuit shown,determine the charge on each capacitor when switch S has been closed for a long time,where R₁ = 1 k $\varOmega$ ,R₂ = 2 k $\varOmega$ ,C₁ = 1 $\mu$ F,and C₂ = 2 $\mu$ F.

A)Q₁ = 3.33 µC and Q₂ = 6.66 µC
B)Q₁ = 3.33 µC and Q₂ = 13.3 µC
C)Q₁ = 13.3 µC and Q₂ = 3.33 µC
D)Q₁ = 6.66 µC and Q₂ = 13.3 µC

Question 39

A 24-V battery is attached to a 3.0-mF capacitor and a 100-ohm resistor.What is the energy dissipated as heat inside the resistor while the capacitor is charging.

A)0.036 J
B)0.30 J
C)0.86 J
D)1.7 J
E)5.76 J

Question 40

A 2-µF capacitor is connected in series with a 1.2-M $\varOmega$ resistor and a 5-V battery for a long time.What is the current in the resistor 1s after disconnecting the battery?

A)1.00 µA
B)1.25 µA
C)2.00 µA
D)2.50 µA
E)2.75 µA

Question 41

The circuit in the figure has 5 resistors and 2 ideal batteries.What is the magnitude of the current in the 4-ohm resistor?

A)1.2 A
B)1.5 A
C)1.8 A
D)2.6 A
E)4.5 A

Question 42

In the circuit shown,R₁ = 10 $\varOmega$ ,R₂ = 4 $\varOmega$ ,R₃ = 10 $\varOmega$ , $\varepsilon$ = 10 V,and capacitor has a capacitance C = 2 $\mu$ F and the switch S has been closed for a long time.After switch S is opened,how much total energy is dissipated through R₃?

A)3.27 mJ
B)1.02 mJ
C)4.84 µJ
D)1.41 µJ

Question 43

Which one of the equations is incorrect for the circuit below?

A)I₁ + I₂ - I₃ = 0
B)8I₁ - 2 I₂ = 7
C)2I₂ + 4I₃ = -12
D)I₃ - I₁ - I₂ = 0
E)All of the above are correct.

Question 44

A galvanometer reads I = 6 mA full scale and has an internal resistance r = 9.1 ohms.If you want to use it to read 7.1 volts full scale,what resistor,R,should you use in series with it?

A)1174 ohm
B)433 ohm
C)43.3 ohm
D)2.16 ohm
E)0.433 ohm

Question 45

Use Kirchhoff's rules to solve for i1 (in a)in the circuit shown above where i = 15.0 A,V = 14.0 V,and R = 6.00 $\varOmega$ .Note that this drawing represents a subset of a full circuit.

A)13.6
B)15.3
C)17.3
D)19.6
E)22.1

Question 46

How long does it take to charge a 50-µF capacitor to 90% of its maximum value through a 100-Ω resistor?

A)11.5 ms
B)87 s
C)2.3 µs
D)89 ns
E)1.2 s

Question 47

Two identical resistors are parallel to each other,and the combination is in series with a 5.0-nF capacitor,in a circuit with a switch open.If initially 15.0 V is across the capacitor,and 11 ns later the voltage across the resistor pair is 2.5 V,what is the resistance of each resistor?

A)2.5 $\varOmega$
B)1.2 $\varOmega$
C)0.12 $\varOmega$
D)0.24 $\varOmega$

Question 48

Two identical 2.5- $\varOmega$ resistors are parallel to each other,and the combination is in series with a 5.0-nF capacitor,in a circuit with a switch open.If initially 15.0 V is across the capacitor,how long after the switch is closed will the voltage across the resistor pair be 2.5 V?

A)1.1 ns
B)11 ns
C)4.4 ns
D)44 ns

Question 49

In the circuit shown the capacitor is initially uncharged and the switch is open.Determine how much charge would accumulate after switch S has been closed for 0.1 ms.

A)1.47 nC
B)14.7 nC
C)67.8 nC
D)67.8 pC

Question 50

What is the current in the 4.0 $\varOmega$ resistor in the circuit shown in the figure?

A)1.1 A
B)1.3 A
C)1.7 A
D)2.8 A
E)4.0 A

Question 51

Two identical light bulbs are connected to a battery.Will the light bulbs be brighter if they are connected to the battery in series or in parallel?

A)in series
B)in parallel
C)The brightness will be the same in series and in parallel.
D)There is not enough information to determine an answer.

Question 52

A voltmeter must be placed in parallel with the circuit element whose voltage is to be measured.An ideal voltmeter therefore has

A)zero resistance.
B)infinite resistance.
C)resistance equal to the circuit element.
D)None are correct.

Question 53

In the circuit shown,R₁ = 10 $\varOmega$ ,R₂ = 4 $\varOmega$ ,R₃ = 10 $\varOmega$ , $\varepsilon$ = 10 V,and capacitor has a capacitance C = 2 $\mu$ F.Determine the energy stored in the capacitor when switch S has been closed for a long time.

A)3.27 µJ
B)1.02 mJ
C)4.94 µJ
D)3.55 mJ

Question 54

A galvanometer reads I = 6 mA full scale and has an internal resistance r = 9.1 ohms.If a resistor,R = 425 $\varOmega$ is connected in series with the galvanometer,what is the full scale voltage of the device?

A)4.23 V
B)7.10 V
C)2.55 V
D)2.60 V
E)7.15 V

Question 55

A direct current power supply is connected to a circuit containing one resistor,and 1.5 A is drawn.If a second identical resistor is connected to the power supply in series with the first,how much current is drawn from the battery?

A)3.0 A
B)0.75 A
C)1.5 A
D)6.0 A

Question 56

A direct current power supply is connected to a circuit containing one resistor,and 1.5 A is drawn.If a second identical resistor is connected to the power supply in parallel with the first,how much current is drawn from the battery?

A)3.0 A
B)0.75 A
C)1.5 A
D)6.0 A

Question 57

The circuit in the figure has 5 resistors and 2 ideal batteries.What is the magnitude of the current in the 3-ohm resistor?

A)1.2 A
B)1.5 A
C)1.8 A
D)2.6 A
E)4.5 A

Question 58

Two parallel plate capacitors,C₁ and C₂ are connected in series to a 60-V battery,a switch S,and a 200-K $\varOmega$ resistor as shown in the figure.Both capacitors are air gap capacitors and have plates with an area of 2.0 cm² and a separation of 0.10 mm.The capacitors are initially uncharged and switch S is open.After switch S is closed,how long will it take for the capacitors to charge to 50% of their maximum value?

A)8.9 * 10^-7 s
B)1.2 * 10^-6 s
C)1.8 * 10^-6 s
D)2.5 * 10^-6 s
E)4.9 * 10^-6 s

Question 59

A capacitor stores energy of 1.25 J.If when it is connected by means of a switch to a 15- $\varOmega$ resistor it discharges to half this value in 15 s,how much charge flowed off the capacitor in this time?

A)0.34 C
B)0.79 C
C)0.95 C
D)1.9 C

Question 60

In the circuit shown in the figure,the switches S1 and S2 are initially open and the 20-mF capacitor has a charge of 100 mC.About how long will it take after switch S1 is closed (switch S2 remains open)for the charge on the capacitor to drop to 5 mC?

A)3.0 s
B)6.0 s
C)9.0 s
D)12 s
E)18 s

Question 61

You have an RC circuit with the switch initially open.When the switch is closed which of the voltage as a function of time plots most accurately represents the charging of the capacitor?

A)(A)
B)(B)
C)(C)
D)(D)
E)(E)

Question 62

A 0.20-mF capacitor discharges through a resistor with R = 61 k $\varOmega$ .How long will it take for the capacitor to reach 85% of its initial charge?

A)0.5 s
B)4.2 s
C)0.25 s
D)1.98 s
E)33.2 s

Question 63

You have an RC circuit with the switch initially open.When the switch is closed which of the voltage as a function of time plots most accurately represents the charging of the capacitor?

A)(A)
B)(B)
C)(C)
D)(D)
E)(E)