Question 1

The resistivity of the material of a wire is 1.76 × 10^-8 Ω ∙ m. If the diameter of the wire is 2.00 mm and its length is 2.00 m, what is its resistance? A)112 Ω B)11.2 Ω C)1.12 Ω D)0.112 Ω E)0.0112 Ω

Accepted Answer

The answer of The resistivity of the material of a...

Question 2

Calculate the current through a 10.0-m long 22-gauge nichrome wire with a radius of 0.321 mm if it is connected across a 12.0-V battery. The resistivity of the nichrome is 1.00 × 10^-6 Ω ∙ m. A)30.9 A B)61.8 A C)0.388 A D)0.776 A

Accepted Answer

First, calculate the resistance of the wire using the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area. The area $A$ of the wire can be found using the formula for the area of a circle, $A = \pi r^2$, where $r$ is the radius of the wire. Given that the radius $r = 0.321 \times 10^{-3}$ m (since 1 mm = $10^{-3}$ m), the area $A = \pi (0.321 \times 10^{-3})^2$ m$^2$.$$A = \pi (0.321 \times 10^{-3})^2 = 3.23 \times 10^{-7} \text{ m}^2$$Given that the resistivity $\rho = 1.00 \times 10^{-6} \Omega \cdot m$ and the length $L = 10.0$ m, the resistance $R$ can be calculated as:$$R = 1.00 \times 10^{-6} \Omega \cdot m \times \frac{10.0 m}{3.23 \times 10^{-7} m^2} = 31.0 \Omega$$Using Ohm's law $V = IR$, where $V$ is the voltage and $I$ is the current, we can solve for $I$:$$I = \frac{V}{R} = \frac{12.0 V}{31.0 \Omega} = 0.387 \text{ A}$$Rounding to three significant figures, the current $I$ is approximately 0.388 A.

Question 3

A metal bar is 20 cm long and has a rectangular cross-section measuring 1.0 cm × 2.0 cm. What is the voltage drop along its length when it carries a 4000-A current? The resistivity of the metal is 1.68 × 10^-8 Ω ∙ m. A)0.67 V B)0.34 V C)0.067 V D)0.034 V

Accepted Answer

The answer of A metal bar is 20 cm long...

Question 4

When a thin copper wire that is 178 m long is connected between a 1.2-V potential difference, a current of 2.0 amps flows through the wire. What is the diameter of this wire? The resistivity of copper is 1.72 × 10^-8? ? m.

Accepted Answer

The answer of When a thin copper wire that is...

Question 5

A light bulb operating at 110 V draws 1.40 A of current. What is its resistance?
A)12.7 Ω
B)78.6 Ω
C)109 Ω
D)154 Ω

Accepted Answer

We can use Ohm's Law:

Resistance = Voltage / Current

Resistance = 110 V / 1.40 A

Resistance = 78.6 Ω

Therefore, the correct answer is B) 78.6 Ω.

Question 6

A certain metal wire has a cross-sectional area of 1.0 cm² and a resistivity of 1.7 × 10^-8 Ω ∙ m. How long would it have to be to have a resistance of 1.0 Ω? A)5.9 × 10⁶ m B)5.9 m C)5.9 × 10⁴ m D)590 m E)5.9 km

Accepted Answer

The formula for resistance is:

R = ρ (L/A)

where R is the resistance, ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire.

Rearranging the formula to solve for L, we get:

L = (RA)/ρ

Substituting the given values, we get:

L = (1 Ω × 1.0 cm²) / (1.7 × 10⁻⁸ Ω ∙ m)
L = 5.88 × 10⁵ m

Converting meters to kilometers, we get:

L = 5.88 km

Therefore, the correct answer is E) 5.9 km.

Question 7

A 1.0-mm diameter extension cord is made of metal having a resistivity of 1.68 × 10^-8 Ω ∙ m. When it carries a current of 15 A, what is the potential difference between two points in the cord that are 100 m apart? A)12 V B)23 V C)32 V D)41 V

Accepted Answer

We can use the formula for the resistance of a wire: R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area.
The cross-sectional area of the cord is A = πr^2 = π(0.0005 m)^2 = 7.85 × 10^-7 m^2.
The resistance of the cord is then: R = (1.68 × 10^-8 Ω ∙ m)(100 m)/(7.85 × 10^-7 m^2) = 2.15 Ω
The potential difference between the two points can be found using Ohm's Law: V = IR = (15 A)(2.15 Ω) = 32.25 V.
Therefore, the answer is choice C.

Question 8

When a 1.0-m length of metal wire is connected to a $1.5 - \mathrm { V }$ battery, a current of $8.0 \mathrm {~mA}$ flows through it. What is the diameter of the wire? The resistivity of the metal is 2.24 × 10^-8 ? ? m. A)12 ?m B)6.0 ?m C)24 ?m D)2.2 ?m

Accepted Answer

The resistance of the wire is:$$R = \frac{V}{I} = \frac{1.5 \mathrm{~V}}{8.0 \times 10^{-3} \mathrm{~A}} = 187.5 \Omega$$The resistance of a wire is given by:$$R = \frac{\rho L}{A}$$where:* $\rho$ is the resistivity of the metal* $L$ is the length of the wire* $A$ is the cross-sectional area of the wireWe can rearrange this equation to solve for the cross-sectional area:$$A = \frac{\rho L}{R}$$Substituting in the given values, we get:$$A = \frac{(2.24 \times 10^{-8} \Omega \cdot \mathrm{m})(1.0 \mathrm{~m})}{187.5 \Omega} = 1.20 \times 10^{-8} \mathrm{~m^2}$$The diameter of the wire is:$$d = 2\sqrt{\frac{A}{\pi}} = 2\sqrt{\frac{1.20 \times 10^{-8} \mathrm{~m^2}}{\pi}} = 12 \mu \mathrm{m}$$Therefore, the correct answer is A) 12 ?m.

Question 9

A rod is 4.0 m long and has a square cross-section that is 1.5 cm on each side. An ohmmeter measures 0.040 Ω across its ends. What is the resistivity of the material from which this rod is made? A)0.023 Ω ∙ m B)0.015 Ω ∙ m C)1.5 × 10^-4 Ω ∙ m D)2.3 × 10^-6 Ω ∙ m

Accepted Answer

The resistivity (ρ) of the material can be calculated using the following formula:

ρ = RA/l

where R is the resistance measured by the ohmmeter, A is the cross-sectional area of the rod, and l is the length of the rod.

First, we need to convert the dimensions of the rod to meters:

Side of square cross-section = 1.5 cm = 0.015 m
Length of rod = 4.0 m

The cross-sectional area (A) of the rod is:

A = (side of square cross-section)² = (0.015 m)² = 2.25 × 10^-4 m²

Now we can plug in the values and solve for ρ:

ρ = RA/l = (0.040 Ω)(2.25 × 10^-4 m²)/4.0 m = 2.25 × 10^-6 Ω ∙ m

Therefore, the answer is D) 2.3 × 10^-6 Ω ∙ m, which is the closest value to our calculated value.

Question 10

A 12-V battery is connected across a 100-Ω resistor. How many electrons flow through the wire in 1.0 min? (e = 1.60 × 10^-¹⁹ C A)1.5 × 10¹⁹ B)2.5 × 10¹⁹ C)3.5 × 10¹⁹ D)4.5 × 10¹⁹

Accepted Answer

The answer of A 12-V battery is connected across a...

Question 11

How much current will be flowing through a $57.0 - \mathrm { m }$ length of copper wire with radius $0.0 \mathrm {~mm}$ if it is connected to a source supplying $62.0 \mathrm {~V} ?$ The resistivity of the metal is 1.68 × 10^-8 ? ? m. A)0 A B)0 × 10⁸ A C)0 nA D)0 A.

Accepted Answer

The answer of How much current will be flowing through...

Question 12

The graph shown in the figure shows the results of measurements of the dc current through a circuit device for various potential differences across it. Assume that all the numbers shown are accurate to two significant figures. What is the resistance of this device?

Accepted Answer

The answer of The graph shown in the figure shows...

Question 13

What is the resistance of 1.0 m of a solid cylindrical metal cable having a diameter of 0.40 inches and a resistivity of 1.68 × 10^-8 Ω ∙ m? A)0.00012 Ω B)0.00021 Ω C)0.0012 Ω D)0.0021 Ω

Accepted Answer

The answer of What is the resistance of 1.0 m...

Question 14

A 1.0-m length of nichrome wire has a radius of 0.50 mm and a resistivity of 1.0 × 10^-6 Ω ∙ m. When this wire carries a current of 0.50 A, what is the voltage across its ends? A)0.0030 V B)0.32 V C)0.64 V D)1.6 V

Accepted Answer

The answer of A 1.0-m length of nichrome wire has...

Question 15

A certain metal has a resistivity of 1.68 × 10^-8 Ω ∙ m. You have a long spool of wire made from this metal. If this wire has a diameter of 0.15 mm, how long should you cut a segment so its resistance will be 15 Ω? A)16 mm B)16 cm C)1.6 m D)16 m

Accepted Answer

The answer of A certain metal has a resistivity of...

Question 16

A 25-m wire of diameter 0.30 mm draws 0.499 A when connected across a 3.0-V potential difference.
(a)What is the resistance of the wire?
(b)What is the resistivity of the material from which the wire is made?

Accepted Answer

The answer of A 25-m wire of diameter 0.30 mm...

Question 17

The graph shown in the figure shows the results of measurements of the dc current through a circuit device for various potential differences across it. Assume that all the numbers shown are accurate to two significant figures. What is the resistance of this device?

Accepted Answer

The answer of The graph shown in the figure shows...

Question 18

What is the resistance of a cylindrical metal rod 1.0 cm in diameter and 45 m long, if the resistivity of the metal is 1.4 × 10^-8 Ω ∙ m? A)0.0063 Ω B)0.0080 Ω C)0.80 Ω D)6.3 Ω

Accepted Answer

The resistance of a cylindrical rod can be calculated using the formula:

R = (ρ × L) / A

where, 
R = resistance 
ρ = resistivity of the material 
L = length of the cylinder 
A = cross-sectional area of the cylinder

In this case, 
diameter = 1.0 cm 
radius (r) = 0.5 cm = 0.005 m 
length (L) = 45 m 
resistivity (ρ) = 1.4 × 10^-8 Ω ∙ m

The cross-sectional area (A) of the cylinder can be calculated using the formula:

A = π × r^2

Substituting the values,

A = π × (0.005 m)^2 = 7.85 × 10^-5 m^2

Now, substituting all the values in the formula for resistance, we get:

R = (1.4 × 10^-8 Ω ∙ m × 45 m) / (7.85 × 10^-5 m^2)

R = 0.008 Ω

Therefore, the answer is B) 0.0080Ω

Question 19

The resistance of a 100-cm wire of cross sectional area 2 × $10 ^ { - 6 }$ $m ^ { 2 }$ is 400 ?. What is the resistivity of the material from which this wire is made?
A)0.80 × $10 ^ { - 4 }$ ? ? m
B)8.0 × $10 ^ { - 4 }$ ? ? m
C)0.80 × $10 ^ { - 5 }$ ? ? m
D)0.80 × $10 ^ { - 6 }$ ? ? m
E)8.0 × $10 ^ { - 6 }$ ?v

Accepted Answer

The resistivity ($\rho$) is calculated using the formula $\rho = R \times \frac{A}{L}$, where $R$ is resistance, $A$ is cross-sectional area, and $L$ is length. Substituting the given values: $\rho = 400 \times \frac{2 \times 10^{-6}}{1} = 8.0 \times 10^{-4}$ ? ? m.

Question 20

A 120-m long metal wire having a resistivity of 1.68 × 10^-8 Ω ∙ m has a resistance of 6.0 Ω. What is the diameter of the wire? A)0.065 mm B)0.65 mm C)0.65 cm D)0.65 m

Accepted Answer

We can use the formula for resistance of a wire:
R = (ρL)/A
where R is the resistance, ρ is the resistivity, L is the length, and A is the cross-sectional area.

We know R = 6.0 Ω, L = 120 m, and ρ = 1.68 × 10-8 Ω ∙ m. We need to find A.

Rearranging the equation, we get:
A = (ρL)/R

Substituting the values we have:
A = (1.68 × 10-8 Ω ∙ m) × (120 m) / 6.0 Ω
A = 3.36 × 10-7 m2

The formula for the area of a circle is:
A = πr2

Solving for r, we get:
r = √(A/π)
r = √(3.36 × 10-7 m2 / π)
r = 0.000326 m

The diameter is twice the radius, so:
d = 2r
d = 2 × 0.000326 m
d = 0.000652 m

Converting to millimeters, we get:
d = 0.652 mm

Therefore, the answer is B.

Quiz 22: Current and Resistance

The resistivity of the material of a wire is 1.76 × 10-8 Ω ∙ m. If the diameter of the wire is 2.00 mm and its length is 2.00 m, what is its resistance?

Calculate the current through a 10.0-m long 22-gauge nichrome wire with a radius of 0.321 mm if it is connected across a 12.0-V battery. The resistivity of the nichrome is 1.00 × 10-6 Ω ∙ m.

A metal bar is 20 cm long and has a rectangular cross-section measuring 1.0 cm × 2.0 cm. What is the voltage drop along its length when it carries a 4000-A current? The resistivity of the metal is 1.68 × 10-8 Ω ∙ m.

When a thin copper wire that is 178 m long is connected between a 1.2-V potential difference, a current of 2.0 amps flows through the wire. What is the diameter of this wire? The resistivity of copper is 1.72 × 10-8 ? ? m.

A light bulb operating at 110 V draws 1.40 A of current. What is its resistance?

A certain metal wire has a cross-sectional area of 1.0 cm2 and a resistivity of 1.7 × 10-8 Ω ∙ m. How long would it have to be to have a resistance of 1.0 Ω?

A 1.0-mm diameter extension cord is made of metal having a resistivity of 1.68 × 10-8 Ω ∙ m. When it carries a current of 15 A, what is the potential difference between two points in the cord that are 100 m apart?

When a 1.0-m length of metal wire is connected to a 1.5−V1.5 - \mathrm { V }1.5−V battery, a current of 8.0 mA8.0 \mathrm {~mA}8.0 mA flows through it. What is the diameter of the wire? The resistivity of the metal is 2.24 × 10-8 ? ? m.

A rod is 4.0 m long and has a square cross-section that is 1.5 cm on each side. An ohmmeter measures 0.040 Ω across its ends. What is the resistivity of the material from which this rod is made?

A 12-V battery is connected across a 100-Ω resistor. How many electrons flow through the wire in 1.0 min? (e = 1.60 × 10-19 C

How much current will be flowing through a 57.0−m57.0 - \mathrm { m }57.0−m length of copper wire with radius 0.0 mm0.0 \mathrm {~mm}0.0 mm if it is connected to a source supplying 62.0 V?62.0 \mathrm {~V} ?62.0 V? The resistivity of the metal is 1.68 × 10-8 ? ? m.

The graph shown in the figure shows the results of measurements of the dc current through a circuit device for various potential differences across it. Assume that all the numbers shown are accurate to two significant figures. What is the resistance of this device?

What is the resistance of 1.0 m of a solid cylindrical metal cable having a diameter of 0.40 inches and a resistivity of 1.68 × 10-8 Ω ∙ m?

A 1.0-m length of nichrome wire has a radius of 0.50 mm and a resistivity of 1.0 × 10-6 Ω ∙ m. When this wire carries a current of 0.50 A, what is the voltage across its ends?

A certain metal has a resistivity of 1.68 × 10-8 Ω ∙ m. You have a long spool of wire made from this metal. If this wire has a diameter of 0.15 mm, how long should you cut a segment so its resistance will be 15 Ω?

A 25-m wire of diameter 0.30 mm draws 0.499 A when connected across a 3.0-V potential difference. (a)What is the resistance of the wire? (b)What is the resistivity of the material from which the wire is made?

The graph shown in the figure shows the results of measurements of the dc current through a circuit device for various potential differences across it. Assume that all the numbers shown are accurate to two significant figures. What is the resistance of this device?

What is the resistance of a cylindrical metal rod 1.0 cm in diameter and 45 m long, if the resistivity of the metal is 1.4 × 10-8 Ω ∙ m?

The resistance of a 100-cm wire of cross sectional area 2 × 10−610 ^ { - 6 }10−6 m2m ^ { 2 }m2 is 400 ?. What is the resistivity of the material from which this wire is made?

A 120-m long metal wire having a resistivity of 1.68 × 10-8 Ω ∙ m has a resistance of 6.0 Ω. What is the diameter of the wire?

The resistivity of the material of a wire is 1.76 × 10^-8 Ω ∙ m. If the diameter of the wire is 2.00 mm and its length is 2.00 m, what is its resistance?

Calculate the current through a 10.0-m long 22-gauge nichrome wire with a radius of 0.321 mm if it is connected across a 12.0-V battery. The resistivity of the nichrome is 1.00 × 10^-6 Ω ∙ m.

A metal bar is 20 cm long and has a rectangular cross-section measuring 1.0 cm × 2.0 cm. What is the voltage drop along its length when it carries a 4000-A current? The resistivity of the metal is 1.68 × 10^-8 Ω ∙ m.

When a thin copper wire that is 178 m long is connected between a 1.2-V potential difference, a current of 2.0 amps flows through the wire. What is the diameter of this wire? The resistivity of copper is 1.72 × 10^-8? ? m.

A certain metal wire has a cross-sectional area of 1.0 cm² and a resistivity of 1.7 × 10^-8 Ω ∙ m. How long would it have to be to have a resistance of 1.0 Ω?

A 1.0-mm diameter extension cord is made of metal having a resistivity of 1.68 × 10^-8 Ω ∙ m. When it carries a current of 15 A, what is the potential difference between two points in the cord that are 100 m apart?

When a 1.0-m length of metal wire is connected to a $1.5 - \mathrm { V }$ battery, a current of $8.0 \mathrm {~mA}$ flows through it. What is the diameter of the wire? The resistivity of the metal is 2.24 × 10^-8 ? ? m.

A 12-V battery is connected across a 100-Ω resistor. How many electrons flow through the wire in 1.0 min? (e = 1.60 × 10^-¹⁹ C

How much current will be flowing through a $57.0 - \mathrm { m }$ length of copper wire with radius $0.0 \mathrm {~mm}$ if it is connected to a source supplying $62.0 \mathrm {~V} ?$ The resistivity of the metal is 1.68 × 10^-8 ? ? m.

What is the resistance of 1.0 m of a solid cylindrical metal cable having a diameter of 0.40 inches and a resistivity of 1.68 × 10^-8 Ω ∙ m?

A 1.0-m length of nichrome wire has a radius of 0.50 mm and a resistivity of 1.0 × 10^-6 Ω ∙ m. When this wire carries a current of 0.50 A, what is the voltage across its ends?

A certain metal has a resistivity of 1.68 × 10^-8 Ω ∙ m. You have a long spool of wire made from this metal. If this wire has a diameter of 0.15 mm, how long should you cut a segment so its resistance will be 15 Ω?

What is the resistance of a cylindrical metal rod 1.0 cm in diameter and 45 m long, if the resistivity of the metal is 1.4 × 10^-8 Ω ∙ m?

The resistance of a 100-cm wire of cross sectional area 2 × $10 ^ { - 6 }$ $m ^ { 2 }$ is 400 ?. What is the resistivity of the material from which this wire is made?

A 120-m long metal wire having a resistivity of 1.68 × 10^-8 Ω ∙ m has a resistance of 6.0 Ω. What is the diameter of the wire?