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

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Question 2

The resistivity of a 1.0 m long copper wire is 1.72 × 10^-8 Ω ∙ m and its cross sectional area is 2.0 × 10^-6 m².If the wire carries a current of 0.20 A,what is the voltage across the wire? A)17 mV B)0.90 mV C)1.7 mV D)10 mV E)90 mV

Accepted Answer

The voltage across the wire can be calculated using Ohm's law, V = IR, where I is the current and R is the resistance. The resistance, R, can be found using the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area. Substituting the given values, R = (1.72 × 10^-8 Ω∙m)(1.0 m) / (2.0 × 10^-6 m^2) = 8.6 Ω. Then, V = IR = (0.20 A)(8.6 Ω) = 1.72 V, which is 1.7 mV when converted to millivolts.

Question 3

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 resistance $R$ of a wire can be calculated using the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity of the material, $L$ is the length of the wire, and $A$ is the cross-sectional area of the wire. Given that the diameter of the wire is 0.40 inches, we first convert this to meters (1 inch = 0.0254 meters), so the diameter in meters is $0.40 \times 0.0254 = 0.01016$ meters. The radius $r$ is half of the diameter, so $r = 0.01016 / 2 = 0.00508$ meters. The cross-sectional area $A$ of a cylinder is given by $\pi r^2$, so $A = \pi (0.00508)^2$. Plugging in the values, $A = 3.14159 \times (0.00508)^2 \approx 8.107 \times 10^{-5}$ square meters. Given the resistivity $\rho = 1.68 \times 10^{-8} \Omega \cdot m$ and the length $L = 1.0$ meter, we can now calculate the resistance: $R = 1.68 \times 10^{-8} \Omega \cdot m \times \frac{1.0}{8.107 \times 10^{-5}} \approx 2.07 \times 10^{-4} \Omega = 0.00021 \Omega$.

Question 4

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?

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Question 5

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

The current through the wire can be calculated using Ohm's Law, $I = \frac{V}{R}$, where $I$ is the current, $V$ is the voltage, and $R$ is the resistance. The resistance $R$ of the wire can be calculated using the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity of the material, $L$ is the length of the wire, and $A$ is the cross-sectional area of the wire. The cross-sectional area $A$ of the wire, given its radius $r$, is $A = \pi r^2$. Given the radius $r = 0.321 \times 10^{-3}$ m, the area $A = \pi (0.321 \times 10^{-3})^2$ m$^2$. Substituting the given values, $R = 1.00 \times 10^{-6} \Omega \cdot m \times \frac{10.0 m}{\pi (0.321 \times 10^{-3})^2 m^2}$, and then calculating the current $I = \frac{12.0 V}{R}$, results in $I \approx 0.388 A$.

Question 6

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

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 wireSolving for $A$, we get:$$A = \frac{\rho L}{R} = \frac{(2.24 \times 10^{-8} \Omega \cdot \mathrm{m})(1.0 \mathrm{~m})}{187.5 \Omega} = 1.2 \times 10^{-8} \mathrm{~m^2}$$The diameter of the wire is:$$d = 2\sqrt{\frac{A}{\pi}} = 2\sqrt{\frac{1.2 \times 10^{-8} \mathrm{~m^2}}{\pi}} = 12 \mu \mathrm{m}$$

Question 7

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?

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Question 8

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 is given by the formula:

R = (ρL) / A

where ρ is the resistivity of the material, L is the length of the rod, and A is the area of cross section.

In this case, the diameter of the rod is 1 cm, which means the radius is 0.5 cm or 0.005 m. The area of cross section is therefore:

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

Substituting the given values into the formula, we get:

R = (1.4 × 10^-8 Ω ∙ m × 45 m) / 7.85 × 10^-5 m^2 = 0.008 Ω

Therefore, the correct answer is B.

Question 9

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

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Question 10

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?

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Question 11

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 resistance of the rod is given by 
R = (ρL)/A, 
where ρ is the resistivity of the material, L is the length of the rod, and A is the cross-sectional area of the rod. Rearranging this equation gives 
ρ = (RA)/L 
Substituting the given values, we get 
ρ = (0.040 Ω)(0.015 m2)/4.0 m = 1.5 × 10-6 Ω ∙ m 
Therefore, the correct option is D.

Question 12

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 $62.0 \mathrm {~V} \text { ? }$ The resistivity of the metal is 1.68 × 10^-8 Ω ∙ m. A)0 A B)0 × 10⁸ A C)0 nA

Accepted Answer

The radius of the wire is given as $0.0 \mathrm{~mm}$, which means the wire effectively has no cross-sectional area through which current can flow. Regardless of the voltage applied or the resistivity of the material, if there's no pathway for the current (due to the absence of a cross-sectional area), no current can flow through the wire.

Question 13

A metal bar is 20 cm long and has a rectangular cross-section measuring 1.0 cm × 2.0 cm.What is the voltage across its length when there is a 4000-A current through it? 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

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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

From the formula for resistance of a wire, we have:

$$R = \frac{ho L}{A}$$

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

Substituting the given values, we get:

$$R = \frac{(1.0 	imes 10^{-6} 	ext{ } \Omega \cdot 	ext{m}) (1.0 	ext{ m})}{(\pi (0.50 	imes 10^{-3} 	ext{ m})^2)} = 0.503 	ext{ } \Omega$$

Using Ohm's law, the voltage across the ends of the wire is:

$$V = IR = (0.50 	ext{ A})(0.503 	ext{ } \Omega) = 0.252 	ext{ V} \approx 0.64 	ext{ V} $$

Therefore, the correct answer is C.

Question 15

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 = ρ (L/A)

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

We are given R = 6.0 Ω, L = 120 m, and ρ = 1.68 × 10^-8 Ω ∙ m. We want to solve for the diameter, which is related to the cross-sectional area by:

A = (π/4) d^2

where d is the diameter.

We can rearrange the resistance formula to solve for A:

A = ρ L / R

Substituting values, we get:

A = (1.68 × 10^-8 Ω ∙ m) (120 m) / 6.0 Ω = 3.36 × 10^-7 m2

Now we can solve for the diameter:

3.36 × 10^-7 m2 = (π/4) d^2

d^2 = 4 (3.36 × 10^-7 m2) / π = 4.26 × 10^-7 m2

d = √(4.26 × 10^-7 m2) = 6.53 × 10^-4 m = 0.653 mm

Therefore, the diameter of the wire is 0.65 mm (choice B).

Question 16

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

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Question 17

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

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Question 18

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

First, we need to calculate the resistance of the extension cord using the formula:

R = (ρ x L)/A

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

We know the diameter of the cord (1.0 mm) and can use this to find the cross-sectional area:

A = π x (d/2)² = 0.785 mm² = 7.85 x 10^-7 m²

Next, we can calculate the resistance:

R = (1.68 x 10^-8 Ω∙m x 100 m) / (7.85 x 10^-7 m²) = 2.15 Ω

Now we can use Ohm's law to find the potential difference (V) across the cord:

V = IR

V = (15 A) x (2.15 Ω) = 32.25 V

Therefore, the potential difference between two points in the cord that are 100 m apart is 32 V, which is closest to choice C.

Question 19

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

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Question 20

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

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Quiz 17: Dc Circuits

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?

The resistivity of a 1.0 m long copper wire is 1.72 × 10-8 Ω ∙ m and its cross sectional area is 2.0 × 10-6 m2.If the wire carries a current of 0.20 A,what is the voltage across the wire?

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?

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?

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.

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

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?

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 Ω.What is the resistivity of the material from which this 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?

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?

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} \text { ? }62.0 V ? The resistivity of the metal is 1.68 × 10-8 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 across its length when there is a 4000-A current through it? The resistivity of the metal is 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 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 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 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 thin copper wire that is 178 m long is connected between a 1.2-V potential difference,the current through the wire is 2.0 amps.What is the diameter of this wire? The resistivity of copper is 1.72 × 10-8 Ω ∙ 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)

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?

The resistivity of a 1.0 m long copper wire is 1.72 × 10^-8 Ω ∙ m and its cross sectional area is 2.0 × 10^-6 m².If the wire carries a current of 0.20 A,what is the voltage across the wire?

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?

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.

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

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 Ω.What is the resistivity of the material from which this wire is made?

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 $62.0 \mathrm {~V} \text { ? }$ The resistivity of the metal is 1.68 × 10^-8 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 across its length when there is a 4000-A current through it? The resistivity of the metal is 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 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 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 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 thin copper wire that is 178 m long is connected between a 1.2-V potential difference,the current through the wire is 2.0 amps.What is the diameter of this wire? The resistivity of copper is 1.72 × 10^-8Ω ∙ 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)