Deck 18: Electric Current and Circuits

Question 1

A $2.50 \mathrm{~A}$ current is carried by a copper wire of radius $1.0 \mathrm{~mm}$ . If the density of conduction electrons is $8.0 \times$ $1028 \mathrm{~m}^{-3}$ , what is the drift velocity of the conduction electrons?

A) $6.2 \times 10^{-5} \mathrm{~m} / \mathrm{s}$
B) $6.2 \times 10^{-4} \mathrm{~m} / \mathrm{s}$
C) $3.2 \times 10^{-4} \mathrm{~m} / \mathrm{s}$
D) $3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}$
E) $1.6 \times 10^{-5} \mathrm{~m} / \mathrm{s}$

Answer 1

$6.2 \times 10^{-5} \mathrm{~m} / \mathrm{s}$

Question 2

Silver contains $5.8 \times 1028$ conduction electrons per $\mathrm{m} 3$ . How many conduction electrons are in a $1.0 \mathrm{~m}$ length of silver wire of diameter $2.6 \mathrm{~mm}$ ?

A) $3.1 \times 1023$
B) $4.7 \times 10^{4}$
C) $1.9 \times 105$
D) $6.0 \times 1023$
E) $1.2 \times 10^{24}$

Answer 2

$3.1 \times 1023$

Question 3

Aluminum has a resistivity of $2.65 \times 10^{-8} \Omega \times \mathrm{m}$ . What is the resistance of $15 \mathrm{~m}$ of aluminum wire with cross-sectional area $1.0 \mathrm{~mm}^{2}$ ?

A) $56 \Omega$
B) $0.13 \Omega$
C) $1.3 \times 102 \Omega$
D) $0.40 \Omega$
E) $1.6 \Omega$

Answer 3

$0.40 \Omega$

Question 4

One hundred meters of a certain type of wire has a resistance of $7.2 \Omega$ . What is the resistance of $2.5 \mathrm{~m}$ of this wire?

A) $1.8 \Omega$
B) $0.18 \Omega$
C) $18 \Omega$
D) $0.30 \Omega$
E) $3.0 \Omega$

Question 5

One hundred meters of $2.00 \mathrm{~mm}$ diameter wire has a resistance of $0.532 \Omega$ . What is the resistivity of the material from which the wire is made?

A) $1.67 \times 10^{-8} \Omega \cdot \mathrm{m}$
B) $5.40 \times 10^{-8} \Omega \cdot \mathrm{m}$
C) $2.35 \times 10^{-8} \Omega \cdot \mathrm{m}$
D) $2.65 \times 10-8 \Omega \cdot \mathrm{m}$
E) $1.59 \times 10^{-8} \Omega \cdot \mathrm{m}$

Question 6

The resistance of a wire increases by $3.9 \%$ when the temperature of the wire is raised $100^{\circ} \mathrm{C}$ . What is the temperature coefficient of resistivity of the wire material?

A) $0.00039^{\circ} \mathrm{C}^{-1}$
B) $0.039^{\circ} \mathrm{C}^{-1}$
C) $3.9^{\circ} \mathrm{C}^{-1}$
D) $0.0039^{\circ} \mathrm{C}^{-1}$
E) $0.39^{\circ} \mathrm{C}^{-1}$

Question 7

A $1.56-\mathrm{V}$ battery has an internal resistance of $0.120 \Omega$ . What is the maximum current that can be drawn from this battery?

A) $13.0 \mathrm{~A}$
B) $7.50 \mathrm{~A}$
C) infinite (or at least 1000s of amps)
D) $0.190 \mathrm{~A}$
E) $1.56 \mathrm{~A}$

Question 8

The potential difference of $12.4 \mathrm{~V}$ is placed across a $4.1 \Omega$ resistor. What is the current in the resistor?

A) $0.33 \mathrm{~A}$
B) $8.3 \mathrm{~A}$
C) $3.0 \mathrm{~A}$
D) $51 \mathrm{~A}$
E) $16 \mathrm{~A}$

Question 9

A $12.0 \mathrm{~V}$ battery is connected across a $4.00 \Omega$ resistor. If the current through the resistor is $2.80 \mathrm{~A}$ , what is the terminal voltage of the battery?

A) $11.2 \mathrm{~V}$
B) $11.6 \mathrm{~V}$
C) $9.6 \mathrm{~V}$
D) $12.0 \mathrm{~V}$
E) $12.8 \mathrm{~V}$

Question 10

A $12.0 \mathrm{~V}$ battery has an internal resistance of $0.080 \Omega$ . If the battery supplies $100 \mathrm{~A}$ when connected to a starter motor, what is the resistance of the motor?

A) $0.080 \Omega$
B) $0.0012 \Omega$
C) $0.20 \Omega$
D) $0.040 \Omega$
E) $0.012 \Omega$

Question 11

The potential differences around a loop $A B C A$ in a circuit (starting at $A$ and going around the loop back to A) are $\mathrm{V}_{\mathrm{AB}}=10 \mathrm{~V}, \mathrm{~V}_{\mathrm{BC}}=6.0 \mathrm{~V}$ , and $\mathrm{V}_{\mathrm{CA}}$ . What is $\mathrm{V}_{\mathrm{CA}}$ ?

A) $16 \mathrm{~V}$
B) $4.0 \mathrm{~V}$
C) $-16 \mathrm{~V}$
D) $-12 \mathrm{~V}$
E) $-4.0 \mathrm{~V}$

Question 12

A $6.0 \Omega$ resistor and a $3.0 \Omega$ resistor are connected in parallel to a $1.5 \mathrm{~V}$ battery of negligible internal resistance. What is the current in the $3.0 \Omega$ resistor?

A) $0.75 \mathrm{~A}$
B) $0.25 \mathrm{~A}$
C) $2.0 \mathrm{~A}$
D) $0.17 \mathrm{~A}$
E) $0.50 \mathrm{~A}$

Question 13

What is the resistance of this combination of resistors?

A) $15 \Omega$
B) $4.0 \Omega$
C) $13 \Omega$
D) $14 \Omega$
E) $12 \Omega$

Question 14

Two capacitors of values $6.0 \mathrm{mF}$ and $9.0 \mathrm{mF}$ are connected in series. What is the capacitance of the combination?

A) $3.0 \mathrm{mF}$
B) $15 \mathrm{mF}$
C) $3.6 \mathrm{mF}$
D) $7.5 \mathrm{mF}$
E) $54 \mathrm{mF}$

Question 15

Two capacitors of values $6.00 \mathrm{mF}$ and $9.00 \mathrm{mF}$ are connected in series to a $30.0 \mathrm{~V}$ power supply. What is the resulting charge on the $6.00 \mathrm{mF}$ capacitor?

A) $180 \mathrm{mC}$
B) $200 \mathrm{mC}$
C) $108 \mathrm{mC}$
D) $270 \mathrm{mC}$
E) $90.0 \mathrm{mC}$

Question 16

Capacitors of values $1.0 \mathrm{~F}, 2.0 \mathrm{~F}, 3.0 \mathrm{~F}$ , and $6.0 \mathrm{~F}$ are connected in series across a $12 \mathrm{~V}$ power supply. Which capacitor has the greatest potential difference across it?

A) the $6.0 \mathrm{~F}$ capacitor
B) the $2.0 \mathrm{~F}$ capacitor
C) the $1.0 \mathrm{~F}$ capacitor
D) the $3.0 \mathrm{~F}$ capacitor
E) they all are equal

Question 17

Capacitors of values $1.0 \mathrm{~F}, 2.0 \mathrm{~F}, 3.0 \mathrm{~F}$ , and $6.0 \mathrm{~F}$ are connected in series across a $12 \mathrm{~V}$ power supply. Which capacitor has the greatest charge on it?

A) the $2.0 \mathrm{~F}$ capacitor
B) the $6.0 \mathrm{~F}$ capacitor
C) the $1.0 \mathrm{~F}$ capacitor
D) the $3.0 \mathrm{~F}$ capacitor
E) they are all equal

Question 18

The arrangement shown is composed of four $6.0 \mathrm{mF}$ capacitors. What is the capacitance of the combination?

A) $24.0 \mathrm{mF}$
B) $8.0 \mathrm{mF}$
C) $9.0 \mathrm{mF}$
D) $4.5 \mathrm{mF}$
E) $12.5 \mathrm{mF}$

Question 19

If $\mathrm{R}_{1}=6 \Omega, \mathrm{R}_{2}=8 \Omega, \mathrm{R}_{3}=2 \Omega, \varepsilon_{1}=4 \mathrm{~V}$ , and $\varepsilon_{2}=14 \mathrm{~V}$ , what is the current in $\mathrm{R}_{2}$ ?

A) 1 A down
B) $2.5 \mathrm{~A}$ up
C) 2.5 A down
D) 5 A down
E) $1 \mathrm{~A}$ up

Question 20

If $\mathrm{R}_{1}=6.0 \Omega, \mathrm{R}_{2}=8.0 \Omega, \mathrm{R}_{3}=2.0 \Omega, \varepsilon_{1}=4.0 \mathrm{~V}$ , and $\varepsilon_{2}=14 \mathrm{~V}$ , what is the power supplied to the circuit by $\varepsilon_{1}$ ?

A) $4.0 \mathrm{~W}$
B) $16 \mathrm{~W}$
C) $20 \mathrm{~W}$
D) $8.0 \mathrm{~W}$
E) $12 \mathrm{~W}$

Question 21

Three resistors, $\mathrm{R}_{1}=4.0 \Omega, \mathrm{R}_{2}=3.0 \Omega$ , and $\mathrm{R}_{3}=2.0 \Omega$ , are connected in series to a $9.0 \mathrm{~V}$ battery. What is the total power dissipated by the circuit?

A) $2.0 \mathrm{~W}$
B) $20 \mathrm{~W}$
C) $4.0 \mathrm{~W}$
D) $5.1 \mathrm{~W}$
E) $9.0 \mathrm{~W}$

Question 22

Three resistors, $\mathrm{R}_{1}=4 \Omega, \mathrm{R}_{2}=3.0 \Omega$ , and $\mathrm{R}_{3}=2.0 \Omega$ , are connected in series to a $9.0 \mathrm{~V}$ battery. What is the power dissipated by $\mathrm{R}_{1}$ ?

A) $9.0 \mathrm{~W}$
B) $2.3 \mathrm{~W}$
C) $5.1 \mathrm{~W}$
D) $2.0 \mathrm{~W}$
E) $4.0 \mathrm{~W}$

Question 23

Three resistors, $\mathrm{R}_{1}=9.0 \Omega, \mathrm{R}_{2}=3.0 \Omega$ , and $\mathrm{R}_{3}=1.0 \Omega$ , are connected in parallel to a $9.0 \mathrm{~V}$ battery. What is the power dissipated by $\mathrm{R}_{2}$ ?

A) $81 \mathrm{~W}$
B) $9.0 \mathrm{~W}$
C) $27 \mathrm{~W}$
D) $2.0 \mathrm{~W}$
E) $3.0 \mathrm{~W}$

Question 24

Three resistors, $\mathrm{R}_{1}=9.00 \Omega, \mathrm{R}_{2}=3.00 \Omega$ , and $\mathrm{R}_{3}=1.00 \Omega$ , are connected in parallel to a $9.00 \mathrm{~V}$ battery. What is the total power dissipated in the circuit?

A) $117 \mathrm{~W}$
B) $80.1 \mathrm{~W}$
C) $99.0 \mathrm{~W}$
D) $180 \mathrm{~W}$
E) $18.0 \mathrm{~W}$

Question 25

The watt, $\mathrm{W}$ , is equivalent to which of the following?

A) $\mathrm{C} / \mathrm{J}$
B) $\mathrm{A} \cdot \mathrm{V}$
C) $\mathrm{A} / \mathrm{V}$
D) $\mathrm{C} \cdot \mathrm{J}$
E) $\mathrm{V} 2 / \mathrm{A}$

Question 26

A $2.0 \Omega$ resistor is connected across a $6.0 \mathrm{~V}$ power supply. An ammeter with internal resistance of $1.0 \Omega$ is used to measure the current in this circuit. What is the ammeter reading?

A) $1.0 \mathrm{~A}$
B) $2.0 \mathrm{~A}$
C) $3.0 \mathrm{~A}$
D) $4.0 \mathrm{~A}$
E) an ammeter with less resistance than the rest of the circuit will not produce a reading

Question 27

A series circuit consists of a $12.0 \mathrm{~V}$ source of emf, a $2.00 \mathrm{mF}$ capacitor, a $1000 \Omega$ resistor, and a switch. What is the time constant for this circuit?

A) $0.0825 \mathrm{~s}$
B) $1.00 \mathrm{~ms}$
C) $10.0 \mathrm{~s}$
D) $2.00 \mathrm{~s}$
E) $0.693 \mathrm{~s}$

Question 28

Copper has $8.5 \times 1028$ current-carrying electrons per $\mathrm{m} 3$ . A copper wire of radius $0.15 \mathrm{~mm}$ carries a current of $17 \mathrm{~mA}$ . What is the average drift velocity for the electrons?

A) $2.7 \times 10^{-9} \mathrm{~m} / \mathrm{s}$
B) $18 \times 10^{-6} \mathrm{~m} / \mathrm{s}$
C) $56 \times 10^{-6} \mathrm{~m} / \mathrm{s}$
D) more information is needed for this calculation

Question 29

A wire of radius $0.15 \mathrm{~mm}$ is made of an unknown metal and carries a current of $8.4 \mathrm{~mA}$ . The drift velocity for electrons in the wire is measured to be $36 \times 10^{-6} \mathrm{~m} / \mathrm{s}$ . What is the charge carrier density of the metal from which the wire is made?

A) $2.1 \times 10^{28} \mathrm{~m}^{-3}$
B) $4.2 \times 10^{30} \mathrm{~m}^{-3}$
C) $1.3 \times 10^{29} \mathrm{~m}^{-3}$
D) need more information to do this calculation.

Question 30

Copper has $8.5 \times 10^{28}$ current carrying electrons per $\mathrm{m}^{3}$ . A copper wire carries a current of $17 \mathrm{~mA}$ , and the drift velocity of the electrons is measured to be $18 \times 10^{-6} \mathrm{~m} / \mathrm{s}$ . What is the wire's radius?

A) $1.5 \mathrm{~mm}$
B) $0.15 \mathrm{~mm}$
C) $2.7 \mathrm{~mm}$
D) $0.27 \mathrm{~mm}$

Question 31

A carbon resistor is made of a cylinder of carbon, of length $1.5 \mathrm{~cm}$ . If the resistivity of carbon is $3.5 \times 10^{-5}$ $\Omega \cdot \mathrm{m}$ , and a potential difference of $0.15 \mathrm{~V}$ causes a current of $12 \mathrm{~A}$ to flow through the resistor, what is the radius of the cylinder?

A) $12 \mathrm{~mm}$
B) $1.2 \mathrm{~mm}$
C) $3.7 \mathrm{~mm}$
D) $6.5 \mathrm{~mm}$

Question 32

A carbon resistor is made of a cylinder of carbon, of diameter $7.4 \mathrm{~mm}$ . If the resistivity of carbon is $3.5 \times 10$ $-5 \mathrm{~W} \cdot \mathrm{m}$ , and a potential difference of $0.15 \mathrm{~V}$ causes a current of $12 \mathrm{~A}$ to flow through the resistor, what is the length of the cylinder?

A) $1.5 \mathrm{~cm}$
B) $0.5 \mathrm{~cm}$
C) $6.1 \mathrm{~cm}$
D) $0.15 \mathrm{~cm}$

Question 33

A circuit joins points $A, B, C$ and $D$ into a single square loop. The voltage drops from $A$ to $B, B$ to $C$ , and $C$ to $\mathrm{D}$ , are $-5.2 \mathrm{~V}, 2.1 \mathrm{~V}$ , and $1.0 \mathrm{~V}$ , respectively. If one were to measure the voltage drop from $\mathrm{C}$ to $\mathrm{B}$ , one would obtain:

A) $-6.1 \mathrm{~V}$
B) $2.1 \mathrm{~V}$
C) $-2.1 \mathrm{~V}$
D) $-4.1 \mathrm{~V}$
E) $4.1 \mathrm{~V}$
F) $6.1 \mathrm{~V}$

Question 34

Two identical circuits have a capacitor in series with a resistor and a switch. In circuit $A$ , the resistor has resistance $\mathrm{R}$ , while in circuit $\mathrm{B}$ , its resistance is $4 \mathrm{R}$ . The capacitors are identical. Each capacitor begins fully charged, and each circuit is open. When each circuit is completed (i.e., the switch in them is closed), the capacitor will begin to discharge. If a time $t$ is required for circuit A's capacitor to fully discharge (say, by $99 \%$ ), what time will be required for circuit B's capacitor to do the same?

A) $2 \mathrm{t}$
B) $0.25 \mathrm{t}$
C) $\mathrm{t}$
D) $4 \mathrm{t}$
E) $0.5 \mathrm{t}$

Question 35

What is the ratio of the time it takes for the capacitor in a series RC circuit to reach $90 \%$ of maximum charge from an uncharged state, to the time required for the capacitor to discharge from a fully charged state to $90 \%$ ?

A) Answer depends on the particular values of $\mathrm{R}$ and $\mathrm{C}$ .
B) 9 times as long
C) The same time is required.
D) $1 / 9$ as long
E) 22 times as long
F) $1 / 22$ times as long

Question 36

Two ceramic cylinders have the following properties. Cylinder $\mathrm{A}$ has radius $\mathrm{R}$ and height $2 \mathrm{H}$ , while Cylinder $B$ has radius $3 R$ and height $H / 4$ . Their resistances are measured, and it is found that $R_{A} / R_{B}=2$ . What is the ratio of the resistivities $\rho_{\mathrm{A}} / \rho_{\mathrm{B}}$ of the ceramics from which the cylinders are made?

A) $1 / 36$
B) $16 / 9$
C) $9 / 8$
D) $9 / 4$
E) 36
F) $1 / 18$