Deck 21: Current and Direct Current Circuits

Question 1

To increase the current density in a wire of length $\ell$ and diameter D,you can

A)decrease the potential difference between the two ends of the wire.
B)increase the potential difference between the two ends of the wire.
C)decrease the magnitude of the electric field in the wire.
D)heat the wire to a higher temperature.
E)combine both (b)and (d).

Answer 1

increase the potential difference between the two ends of the wire.

Question 2

A nichrome wire and an aluminum wire,each with the same initial resistance,have the same change in resistance when heated separately.( $\rho$ _Al = 2.82 *10 ^{- 8} $\Omega$ .m; $\alpha$ _Al = 3.9 *10 ^{- 3} / $\degree$ C; $\rho$ _nichrome = 1.50* 10 ^{- 6} $\Omega$ .m; $\alpha$ _nichrome = 0.40 * 10 ^{- 3} / $\degree$ C. )The ratio of the temperature change of the nichrome wire to the temperature change of the aluminum wire is

A)0.019.
B)0.10.
C)0.18.
D)9.8.
E)53.

Answer 2

9.8.

Question 3

In the Drude model of electrical conduction,the current density is directly proportional to

A)the average time interval between successive collisions.
B)the number of charge carriers per unit volume.
C)the square of the electron charge.
D)the electric field present in the wire.
E)the product of all four quantities listed above.

Answer 3

the product of all four quantities listed above.

Question 4

Jadeen says that you can increase the resistance of a copper wire by hammering the wire to make it narrower and longer.Arnell says that you can increase its resistance by heating the wire.Which one,if either,is correct,and why?

A)Arnell,because the conductivity of the wire increases when it is heated.
B)Arnell,because the conductivity of the wire decreases when it is heated.
C)Jadeen,because the conductivity of a wire is directly proportional to its area and inversely proportional to its length.
D)Jadeen,because the conductivity of a copper wire does not increase when it is hammered.
E)Both are correct because (b)and (d)are both correct.

Question 5

Light bulb A is rated at 60 W and light bulb B is rated at 100 W.Both are designed to operate at 110 V.Which statement is correct?

A)The 60 W bulb has a greater resistance and greater current than the 100 W bulb.
B)The 60 W bulb has a greater resistance and smaller current than the 100 W bulb.
C)The 60 W bulb has a smaller resistance and smaller current than the 100 W bulb.
D)The 60 W bulb has a smaller resistance and greater current than the 100 W bulb.
E)We need to know the resistivities of the filaments to answer this question.

Question 6

The electron density in copper is 8.49 *10²⁸ electrons/m³.The electron charge is e = -1.60 *10 ^{- 19} C.When a 1.00 A current is present in a copper wire with a 0.40 cm² cross-section,the electron drift velocity,in m/s,with direction defined relative to the current density,is

A)-1.84 *10 ^{- 6}.
B)+1.84 * 10 ^{- 6}.
C)-1.84.
D)-5.43 * 10 ^- .
E)+5.43 * 10 ^- .

Question 7

Most telephone cables are made of copper wire of either 24 or 26 gauge.If the resistance of 24-gauge wire is 137 $\Omega$ /mile and the resistance of 26-gauge wire is 220 $\Omega$ /mile,what is the ratio of the diameter of 24-gauge wire to that of 26-gauge wire?

A)1.6
B)1.3
C)0.62
D)0.79
E)0.88

Question 8

A rod (length = 80 cm)with a rectangular cross section (1.5 mm * 2.0 mm)has a resistance of 0.20 $\Omega$ .What is the resistivity of the material used to make the rod?

A)6.0 *10 ^{- 7} $\Omega$ . m
B)3.8 *10 ^{- 7} $\Omega$ . m
C)7.5 *10^{- 7} $\Omega$ .m
D)3.0 *10 ^{- 7} $\Omega$ . m
E)4.8 *10 ^{- 7} $\Omega$ .m

Question 9

The diagram shown represents a portion of a wire in a circuit.A current is flowing in the wire in the direction shown.Under the convention that it is positive charge that flows the electric field points in the direction of the current.How can the electric field change direction where the wire bends?

A)There is an excess of negative charge in the center of the wire.
B)There is an excess of positive charge at the bottom end of the wire.
C)There is an excess of negative charge at the right end of the upper portion of the wire.
D)There is an accumulation of positive charge on the surface,particularly at the bend,such that the sum of electric fields gives the new electric field.
E)There is an accumulation of electrical potential as the current traverses the wire: The higher potential in the lower half is the source of the field.

Question 10

The temperature coefficient of resistivity of iron is 5.0 *10 ^{- 3} / $\degree$ C;that of carbon is-0.50 *10 ^{- 3} / $\degree$ C.When an iron wire and a carbon rod,each having the same 10 $\Omega$ resistance at 20 $\degree$ C,are cooled from that temperature to -80 $\degree$ C,the new ratio of the resistance of the carbon rod to the resistance of the iron wire at the lower temperature is

A)-0.10.
B)+1.9.
C)+2.1.
D)-10.
E)+10.

Question 11

A high-resistance material is used as an insulator between the conductors of a length of coaxial cable.The resistance material,which forms a hollow tube,has an inner radius a and an outer radius b,and the insulator provides a resistance R between the conductors.If a second insulator,made of the same material and having the same length,is made with double both the inner radius and the outer radius of the first,what resistance would it provide between the conductors?

A)R
B)2 R
C)4 R
D)(ln2)R
E)R/(ln2)

Question 12

A wire (length = 2.0 m,diameter = 1.0 mm)has a resistance of 0.45 $\Omega$ .What is the resistivity of the material used to make the wire?

A)5.6*10^{- 7} $\Omega$ . m
B)1.2 *10 ^{- 7} $\Omega$ . m
C)1.8*10 ^{- 7} $\Omega$ . m
D)2.3 *10^{- 7} $\Omega$ . m
E)7.1* 10 ^{- 7} $\Omega$ . m

Question 13

If a mile of 24-gauge copper wire has a resistance of 0.14 k $\Omega$ and the resistivity of copper is 1.7 *10 ^{- 8} $\Omega$ . m,what is the diameter of the wire? (1 mile = 1.6 km)

A)0.40 mm
B)0.50 mm
C)0.63 mm
D)0.80 mm
E)0.25 mm

Question 14

In the Drude model of electrical conduction,the current density is NOT directly proportional to

A)the average time interval between successive collisions.
B)the number of charge carriers per unit volume.
C)the square of the electron charge.
D)the electric field present in the wire.
E)the resistivity of the wire.

Question 15

An electric device,which heats water by immersing a resistance wire in the water,generates 50 cal of heat per second when an electric potential difference of 12 V is placed across its leads.What is the resistance of the heater wire? (Note: 1 cal = 4.186 J)

A)0.94 $\Omega$
B)0.81 $\Omega$
C)0.58 $\Omega$
D)0.69 $\Omega$
E)1.5 $\Omega$

Question 16

A conductor of radius r,length $\ell$ and resistivity $\rho$ has resistance R.What is the new resistance if it is stretched to 4 times its original length?

A) $\frac { 1 } { 16 }$ R
B) $\frac { 1 } { 4 }$ R
C)R
D)4R
E)16R

Question 17

What is the resistance of a wire made of a material with a resistivity of 3.2*10 ^{- 8} $\Omega$ . m if its length is 2.5 m and its diameter is 0.50 mm?

A)0.16 $\Omega$
B)0.10 $\Omega$
C)1.28 $\Omega$
D)0.41 $\Omega$
E)0.81 $\Omega$

Question 18

If 480 C pass through a 4.0- $\Omega$ resistor in 10 min,what is the potential difference across the resistor?

A)3.6 V
B)2.8 V
C)2.4 V
D)3.2 V
E)5.0 V

Question 19

A rod of 2.0-m length and a square (2.0 mm *2.0 mm)cross section is made of a material with a resistivity of 6.0 *10 ^{- 8} $\Omega$ . m.If a potential difference of 0.50 V is placed across the ends of the rod,at what rate is heat generated in the rod?

A)3.0 W
B)5.3 W
C)8.3 W
D)1.3 W
E)17 W

Question 20

How many electrons pass through a 20- $\Omega$ resistor in 10 min if there is a potential drop of 30 volts across it?

A)5.6*10²¹
B)7.5 *10²¹
C)9.4 * 10²¹
D)1.1* 10²¹
E)3.8* 10²¹

Question 21

What is the equivalent resistance between points a and b when R = 13 $\Omega$ ?

A)29 $\Omega$
B)23 $\Omega$
C)26 $\Omega$
D)20 $\Omega$
E)4.6 $\Omega$

Question 22

A battery has an internal resistance of 4.0 $\Omega$ .Which of the following load resistors would have the most power delivered to it when connected across the battery?

A)1.4 $\Omega$
B)2.0 $\Omega$
C)4.0 $\Omega$
D)8.0 $\Omega$
E)16 $\Omega$

Question 23

The circuit below contains three 100-W light bulbs and a capacitor.The emf $\varepsilon$ = 110V.At the instant the switch S is closed,which light bulb is brightest?

A)A
B)B
C)C
D)A and B
E)All three are equally bright.

Question 24

What maximum power can be generated from an 18-V emf using any combination of a 6.0- $\Omega$ resistor and a 9.0- $\Omega$ resistor?

A)54 W
B)71 W
C)90 W
D)80 W
E)22 W

Question 25

The circuit below contains three 100-watt light bulbs.The emf $\varepsilon$ = 110 V.Which light bulb(s)is(are)the brightest?

A)A
B)B
C)C
D)B and C
E)All three are equally bright.

Question 26

What is the equivalent resistance between points A and B in the figure when R = 20 $\Omega$ ?

A)77 $\Omega$
B)63 $\Omega$
C)70 $\Omega$
D)84 $\Omega$
E)140 $\Omega$

Question 27

An electric heater is constructed by applying a potential difference of 110 V across a wire with a resistance of 5.0 $\Omega$ .What is the power rating of the heater?

A)2.0 kW
B)2.4 kW
C)1.7 kW
D)1.5 kW
E)60 kW

Question 28

What is the equivalent resistance between points a and b when R = 12 $\Omega$ ?

A)20 $\Omega$
B)16 $\Omega$
C)24 $\Omega$
D)28 $\Omega$
E)6.0 $\Omega$

Question 29

What is the equivalent resistance between points a and b when R = 30 $\Omega$ ?

A)27 $\Omega$
B)21 $\Omega$
C)24 $\Omega$
D)18 $\Omega$
E)7.5 $\Omega$

Question 30

A small bulb is rated at 7.50 W when operated at 125 V.The tungsten filament has a temperature coefficient of resistivity $\alpha$ = 4.50*10 ^{- 3} / $\degree$ C.When the filament is hot and glowing,its temperature is seven times room temperature (20 $\degree$ C).What is the resistance of the filament (in ohms)at room temperature?

A)234
B)1 350
C)2 080
D)4 530
E)5 630

Question 31

The algebraic sum of the changes of potential around any closed circuit loop is

A)zero.
B)maximum.
C)zero only if there are no sources of emf in the loop.
D)maximum if there are no sources of emf in the loop.
E)equal to the sum of the currents in the branches of the loop.

Question 32

What is the equivalent resistance between points a and b?

A)14 $\Omega$
B)8.0 $\Omega$
C)6.0 $\Omega$
D)25 $\Omega$
E)40 $\Omega$

Question 33

What is the equivalent resistance between points A and B in the figure when R = 10 $\Omega$ ?

A)20 $\Omega$
B)10 $\Omega$
C)25 $\Omega$
D)15 $\Omega$
E)3.2 $\Omega$

Question 34

A conductor of radius r,length $\ell$ and resistivity $\rho$ has resistance R.It is melted down and formed into a new conductor,also cylindrical,with one fourth the length of the original conductor.The resistance of the new conductor is

A) $\frac { 1 } { 16 }$ R
B) $\frac { 1 } { 4 }$ R
C)R
D)4R
E)16R

Question 35

The circuit below contains three 100-W light bulbs.The emf $\varepsilon$ = 110 V.Which light bulb(s)is(are)brightest?

A)A
B)B
C)C
D)B and C
E)All three are equally bright.

Question 36

A cook plugs a 500 W crockpot and a 1 000 W kettle into a 240 V power supply,all operating on direct current.When we compare the two,we find that

A)I_crockpot < I_kettle and R_crockpot < R_kettle.
B)I_crockpot < I_kettle and R_crockpot > R_kettle.
C)I_crockpot = I_kettle and R_crockpot = R_kettle.
D)I_crockpot > I_kettle and R_crockpot < R_kettle.
E)I_crockpot > I_kettle and R_crockpot > R_kettle.

Question 37

The circuit below contains three 100-watt light bulbs and a capacitor.The emf $\varepsilon$ = 110V.The capacitor is fully charged.Which light bulb(s)is(are)dimmest?

A)A
B)B
C)C
D)A and B
E)All three are equally bright (or dim).

Question 38

A light bulb is rated at 30 W when operated at 120 V.How much charge enters (and leaves)the light bulb in 1.0 min?

A)17 C
B)15 C
C)14 C
D)13 C
E)60 C

Question 39

How much energy is dissipated as heat during a two-minute time interval by a 1.5-k $\Omega$ resistor which has a constant 20-V potential difference across its leads?

A)58 J
B)46 J
C)32 J
D)72 J
E)16 J

Question 40

What is the equivalent resistance between points A and B in the figure when R = 18 $\Omega$ ?

A)48 $\Omega$
B)64 $\Omega$
C)80 $\Omega$
D)96 $\Omega$
E)110 $\Omega$

Question 41

Determine the potential difference V_a - V_b shown in the circuit below.

A)-5.0 V
B)+5.0 V
C)-10 V
D)+10 V
E)0 V

Question 42

Which of the identical light bulb(s)is(are)brightest when the capacitor has half its maximum charge?

A)A
B)B
C)C
D)A and B
E)All three are equally bright.

Question 43

When a 20-V emf is placed across two resistors in series,a current of 2.0 A is present in each of the resistors.When the same emf is placed across the same two resistors in parallel,the current through the emf is 10 A.What is the magnitude of the greater of the two resistances?

A)7.2 $\Omega$
B)7.6 $\Omega$
C)6.9 $\Omega$
D)8.0 $\Omega$
E)2.8 $\Omega$

Question 44

What is the magnitude of the potential difference across the 20- $\Omega$ resistor?

A)3.2 V
B)7.8 V
C)11 V
D)5.0 V
E)8.6 V

Question 45

At what rate is thermal energy being generated in the 2R-resistor when $\varepsilon$ = 12 V and R = 3.0 $\Omega$ ?

A)12 W
B)24 W
C)6.0 W
D)3.0 W
E)1.5 W

Question 46

At what rate is thermal energy generated in the 5- $\Omega$ resistor when $\varepsilon$ = 24 V?

A)13 W
B)3.2 W
C)23 W
D)39 W
E)51 W

Question 47

Determine the current in the 10-V emf.

A)2.3 A
B)2.7 A
C)1.3 A
D)0.30 A
E)2.5 A

Question 48

The circuit below contains 4 100-W light bulbs.The emf is 110 V.Which light bulb(s)is(are)brightest?

A)A
B)B
C)C
D)D
E)C and D

Question 49

What is the current in the 15- $\Omega$ resistor when $\varepsilon$ = 9.0 V?

A)0.20 A
B)0.30 A
C)0.10 A
D)0.26 A
E)0.60 A

Question 50

A resistor of unknown resistance and a 15- $\Omega$ resistor are connected across a 20-V emf in such a way that a 2.0 A current is observed in the emf.What is the value of the unknown resistance?

A)75 $\Omega$
B)12 $\Omega$
C)7.5 $\Omega$
D)30 $\Omega$
E)5.0 $\Omega$

Question 51

What is the magnitude of the current in the 20- $\Omega$ resistor?

A)0.75 A
B)0.00 A
C)0.25 A
D)0.50 A
E)1.00 A

Question 52

Determine $\varepsilon$ when I = 0.50 A and R = 12 $\Omega$ .

A)12 V
B)24 V
C)30 V
D)15 V
E)6.0 V

Question 53

How much heat is produced in the 10- $\Omega$ resistor in 5.0 s when $\varepsilon$ = 18 V?

A)72 J
B)32 J
C)50 J
D)18 J
E)90 J

Question 54

At what rate is thermal energy generated in the 30- $\Omega$ resistor?

A)20 W
B)27 W
C)60 W
D)13 W
E)30 W

Question 55

At what rate is thermal energy generated in the 20- $\Omega$ resistor when $\varepsilon$ = 20 V?

A)6.5 W
B)1.6 W
C)15 W
D)26 W
E)5.7 W

Question 56

Determine R when I = 0.20 A and $\varepsilon$ = 18 V.

A)50 $\Omega$
B)8.0 $\Omega$
C)10 $\Omega$
D)20 $\Omega$
E)30 $\Omega$

Question 57

The circuit below contains 4 100-W light bulbs.The emf is 110 V.Which light bulb(s)is(are)brightest?

A)A
B)B
C)C
D)D
E)C and D

Question 58

The circuit below contains 3 100-W light bulbs and a capacitor.The emf is 110 V.Which light bulb(s)is(are)brightest? (Assume the capacitor is fully charged. )

A)A
B)B
C)C
D)A and B
E)All three are equally bright.

Question 59

What is the current in the 10- $\Omega$ resistor ?

A)0.60 A
B)3.0 A
C)1.2 A
D)2.4 A
E)0.30 A

Question 60

The circuit below contains 5 identical light bulbs.The emf is 110 V.Which light bulb(s)is(are)brightest?

A)A: The one closest to the positive terminal of the battery.
B)A and C: The bulbs closest to the positive terminal of the battery.
C)A and B: Because they are closest to the terminals of the battery.
D)C and D: Because they receive current from A and B and from E.
E)E: Because the potential difference across E is that of the battery.

Question 61

If I = 2.0 A in the circuit segment shown below,what is the potential difference V_B -V_A?

A)+10 V
B)-20 V
C)-10 V
D)+20 V
E)+30 V

Question 62

If the current in the 4.0- $\Omega$ resistor is 1.4 A,what is the magnitude of the potential difference,V_A - V_B?

A)69 V
B)55 V
C)62 V
D)48 V
E)31 V

Question 63

If R = 4.0 k $\Omega$ ,C = 3.0 mF, $\varepsilon$ = 15 V,Q = 12 mC,and I = 2.0 mA,what is the potential difference V_b- V_a?

A)+3.0 V
B)-19 V
C)-3.0 V
D)+27 V
E)+21 V

Question 64

If $\varepsilon$ = 8.0 V,at what rate is that emf providing energy to the circuit shown below?

A)8.4 W
B)7.6 W
C)5.6 W
D)11 W
E)2.0 W

Question 65

If Q = 350 $\mu$ C and I = 4.0 mA in the circuit segment shown below,determine the potential difference,V_A - V_B.

A)-30 V
B)+80 V
C)+40 V
D)-40 V
E)+10 V

Question 66

If Q = 400 $\mu$ C and the potential difference V_A - V_B = -10 V in the circuit segment shown below,what is the current in the resistor?

A)1.0 mA right to left
B)1.0 mA left to right
C)3.5 mA right to left
D)3.5 mA left to right
E)None of the above

Question 67

If R = 3.0 k $\Omega$ ,C = 5.0 mF, $\varepsilon$ = 6.0 V,Q = 15 mC,and I = 4.0 mA,what is the potential difference V_b - V_a?

A)-3.0 V
B)+9.0 V
C)-15 V
D)+21 V
E)-6.0 V

Question 68

If R = 2.0 k $\Omega$ ,C = 4.0 mF, $\varepsilon$ = 8.0 V,Q = 20 mC,and I = 3.0 mA,what is the potential difference V_b - V_a?

A)+7.0 V
B)+19 V
C)+9.0 V
D)-3.0 V
E)-14 V

Question 69

If $\varepsilon$ ₁ = 4.0 V, $\varepsilon$ ₂ = 12.0 V,R₁ = 4 $\Omega$ ,R₂ = 12 $\Omega$ ,C = 3 $\mu$ F,Q = 18 $\mu$ C,and I = 2.5 A,what is the potential difference V_a -V_b?

A)-30 V
B)30 V
C)5.0 V
D)-5.0 V
E)-1.0 V

Question 70

What is the potential difference V_B - V_A when the I = 1.5 A in the circuit segment below?

A)+22 V
B)-22 V
C)-38 V
D)+38 V
E)+2.0 V

Question 71

Determine the potential difference,V_A - V_B,in the circuit segment shown below when I = 2.0 mA and Q = 50 $\mu$ C.

A)-40 V
B)+40 V
C)+20 V
D)-20 V
E)-10 V

Question 72

Determine the magnitude and sense (direction)of the current in the 500- $\Omega$ resistor when I = 30 mA.

A)56 mA left to right
B)56 mA right to left
C)48 mA left to right
D)48 mA right to left
E)26 mA left to right

Question 73

If R = 3.0 k $\Omega$ ,C = 6.0 nF, $\varepsilon$ ₁ = 10.0 V,Q = 18 nC, $\varepsilon$ ₂ = 6.0 V,and I = 5.0 mA,what is the potential difference V_b - V_a?

A)-13 V
B)+28 V
C)+13 V
D)-28 V
E)+2.0 V

Question 74

Determine the resistance R when I = 1.5 A.

A)40 $\Omega$
B)8.0 $\Omega$
C)85 $\Omega$
D)28 $\Omega$
E)32 $\Omega$

Question 75

At what rate is power supplied by the 10-V emf shown below?

A)-10 W
B)+10 W
C)zero
D)+20 W
E)-20 W

Question 76

Determine the magnitude and sense (direction)of the current in the 10- $\Omega$ resistor when I = 1.8 A.

A)1.6 A right to left
B)1.6 A left to right
C)1.2 A right to left
D)1.2 A left to right
E)1.8 A left to right

Question 77

What is the potential difference V_B - V_A when I = 0.50 A in the circuit segment shown below?

A)+28 V
B)+2.0 V
C)-28 V
D)-2.0 V
E)+18 V

Question 78

If I = 0.40 A in the circuit segment shown below,what is the potential difference V_a -V_b?

A)31 V
B)28 V
C)25 V
D)34 V
E)10 V

Question 79

If R₁ = 10 $\Omega$ ,R₂ = 15 $\Omega$ ,R₃ = 20 $\Omega$ ,and I = 0.50 A,at what rate is heat being generated in these resistors?

A)29 W
B)16 W
C)22 W
D)11 W
E)1.1 W

Question 80

What is the potential difference V_b - V_a shown in the circuit below.

A)-8.0 V
B)+8.0 V
C)-18 V
D)+18 V
E)-12 V