Question 1

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

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Question 2

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^-19C) A)1.5 × 10¹⁹ B)2.5 × 10¹⁹ C)3.5 × 10¹⁹ D)4.5 × 10¹⁹

Accepted Answer

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Question 3

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

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Question 4

A jeweler needs to electroplate gold,having an atomic mass of 196.97 g/mol,onto a bracelet.He knows that the charge carriers in the ionic solution are singly-ionized gold ions,Au⁺,and has calculated that he must deposit Of gold to reach the necessary thickness.How much current does he need to plate the bracelet in 3.0 hours? (e = 1.60 × 10^-19 C,N_A = 6.02 × 10²³ atoms/mol) A)9.1 mA B)540 mA C)33 A D)1,800 mA

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Question 5

A 4000-Ω resistor is connected across a 220-V power source.What current will flow through the resistor?
A)0.055 A
B)1.8 A
C)5.5 A
D)18 A

Accepted Answer

According to Ohm's Law, the current flowing through a resistor is directly proportional to the voltage across it and inversely proportional to its resistance. Therefore,

I = V/R

Substituting the given values, we get

I = 220 V / 4000 Ω

I = 0.055 A

Hence, the correct answer is choice A) 0.055 A.

Question 6

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 7

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

To find the length of the wire, use the formula for resistance: R = ρ(L/A), where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area. First, calculate the area A = π(d/2)^2, where d = 0.15 mm = 0.00015 m. Then solve for L: L = RA/ρ. Substituting the values, L = (15 Ω)(π(0.00015 m/2)^2)/(1.68 × 10^-8 Ω ∙ m) ≈ 16 m.

Question 8

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 cylindrical conductor is given by the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area. First, convert the diameter from inches to meters (0.40 inches = 0.01016 meters). The radius is half of the diameter, so r = 0.00508 meters. The cross-sectional area A = πr² = π(0.00508)². Then, calculate the resistance: R = (1.68 × 10⁻⁸ Ω ∙ m)(1.0 m) / (π(0.00508 m)²) ≈ 0.00021 Ω.

Question 9

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 10

The resistance of a 100-cm wire of cross sectional area 2 ×

Is 400 Ω.What is the resistivity of the material from which this wire is made?
A)0.80 ×  Ω ∙ m
B)8.0 ×  Ω ∙ m
C)0.80 ×  Ω ∙ m
D)0.80 ×  Ω ∙ m
E)8.0 ×  Ωv

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Question 11

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 12

How much current will be flowing through a 57.0mm. Length of copper wire with radius 0.0mm If it is connected to a source supplying 62.0V? The resistivity of the metal is 1.68 × 10^-8 Ω ∙ m. A)0 A B)0 × 10⁸ A C)0 nA D)0.. A

Accepted Answer

The radius of the wire is given as 0.0 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 cross-sectional area for the current to flow through (i.e., an infinitely thin wire), no current can flow. Hence, the correct answer is 0 A.

Question 13

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 14

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 15

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

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Question 16

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 ($\rho$) of a material is given by the formula $\rho = R \frac{A}{L}$, where $R$ is the resistance, $A$ is the cross-sectional area, and $L$ is the length of the material. Here, $R = 0.040 \Omega$, $A = (1.5 \times 10^{-2} m)^2 = 2.25 \times 10^{-4} m^2$, and $L = 4.0 m$. Plugging these values into the formula gives $\rho = 0.040 \Omega \times \frac{2.25 \times 10^{-4} m^2}{4.0 m} = 2.25 \times 10^{-6} \Omega \cdot m$, which is closest to option D, $2.3 \times 10^{-6} \Omega \cdot m$.

Question 17

What is the voltage drop across a 5.0-Ω resistor if the current through it is 5.0 A?
A)100 V
B)25 V
C)4.0 V
D)1.0 V

Accepted Answer

The voltage drop across a resistor can be calculated using Ohm's Law, V = IR, where V is the voltage, I is the current, and R is the resistance. Substituting the given values, V = 5.0 A * 5.0 Ω = 25 V.

Question 18

When a 1.0-m length of metal wire is connected to a Battery,a current of Flows 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

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Question 19

What potential difference is required to cause 4.00 A to flow through a resistance of 330 Ω?
A)12.1 V
B)82.5 V
C)334 V
D)1320 V

Accepted Answer

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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:

R = (ρL)/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.

We can rearrange this formula to solve for A:

A = (ρL)/R

Substituting the given values:

A = (1.68 × 10^-8 Ω ∙ m)(120 m)/(6.0 Ω)
A = 3.36 × 10^-7 m^2

We can calculate the diameter using the formula:

A = π/4 × d^2

Where d is the diameter.

Rearranging and substituting:

d = √(4A/π)
d = √(4(3.36 × 10^-7 m^2)/π)
d = 0.0654 m or 65.4 mm

So the answer is B, 0.65 mm (rounded to two significant figures).

Quiz 21: Electric Current and Direct-Current Circuits

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

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 4000-Ω resistor is connected across a 220-V power source.What current will flow through the resistor?

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 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 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.

The resistance of a 100-cm wire of cross sectional area 2 × Is 400 Ω.What is the resistivity of the material from which this wire is made?

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?

How much current will be flowing through a 57.0mm. Length of copper wire with radius 0.0mm If it is connected to a source supplying 62.0V? The resistivity of the metal is 1.68 × 10-8 Ω ∙ m.

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

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 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 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?

What is the voltage drop across a 5.0-Ω resistor if the current through it is 5.0 A?

When a 1.0-m length of metal wire is connected to a Battery,a current of Flows through it.What is the diameter of the wire? The resistivity of the metal is 2.24 × 10-8 Ω ∙ m.

What potential difference is required to cause 4.00 A to flow through a resistance of 330 Ω?

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 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 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^-19C)

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 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 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 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.

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?

How much current will be flowing through a 57.0mm. Length of copper wire with radius 0.0mm If it is connected to a source supplying 62.0V? The resistivity of the metal is 1.68 × 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?

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?

When a 1.0-m length of metal wire is connected to a Battery,a current of Flows through it.What is the diameter of the wire? The resistivity of the metal is 2.24 × 10^-8 Ω ∙ m.

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?