Question 1

A 24-Ω platinum wire at 25°C with a temperature coefficient of resistivity of 3.9 × 10−³ (°C)−¹ will have what resistance at 95°C?

Accepted Answer

Using the formula for temperature dependence of resistivity, we have:

ΔR/R = αΔT, where ΔR/R is the fractional change in resistance, α is the temperature coefficient of resistivity, and ΔT is the change in temperature.

ΔR/R = (3.9 × 10−3 (°C)−1) × (95°C − 25°C) = 0.273

Therefore, the increase in resistance is:

ΔR = (ΔR/R) × R = (0.273) × (24 Ω) = 6.552 Ω

So the final resistance at 95°C is:

Rf = R + ΔR = 24 Ω + 6.552 Ω = 30.552 Ω ≈ 31 Ω

Hence, the best choice is C.

Question 2

The temperature coefficient of resistivity is a quantity that is:

Accepted Answer

The temperature coefficient of resistivity can be negative for some materials, meaning that their resistance decreases as temperature increases. This is known as negative temperature coefficient (NTC) materials. Therefore, choice A and B are incorrect because the temperature coefficient of resistivity is not always positive or non-negative. Choice D is also incorrect because the symbol for the temperature coefficient of resistivity is usually represented by the Greek letter alpha (α), not sigma (σ).

Question 3

A resistor is made of a material that has a resistivity that is proportional to the current going through it.If the voltage across the resistor is doubled,what happens to the current through it?

Accepted Answer

The answer of A resistor is made of a material...

Question 4

A Nichrome wire has a radius of 0.9 mm and a resistivity of 1.5 × 10−⁶ Ω⋅m.What is the resistance per unit length of this wire?

Accepted Answer

The answer of A Nichrome wire has a radius of...

Question 5

Two cylindrical resistors are made of the same material and have the same resistance.The resistors,R₁ and R₂,have different radii,r₁ and r₂,and different lengths,L₁ and L₂.Which of the following relative values for radii and lengths would result in equal resistances?

Accepted Answer

The resistance of a cylindrical resistor is given by $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity of the material, $L$ is the length, and $A$ is the cross-sectional area. For a cylinder, $A = \pi r^2$. If two resistors have the same resistance, their $\frac{L}{A}$ ratios must be equal. Doubling the radius quadruples the area ($A \propto r^2$), so to keep the resistance the same, the length must also be quadrupled ($L \propto A$), maintaining the $\frac{L}{A}$ ratio constant.

Question 6

The resistivity of a material is doubled when heated a certain amount.What happens to the resistance of a resistor made of this material when heated the same amount?

Accepted Answer

The resistance of a resistor is directly proportional to the resistivity of the material it is made of. Therefore, if the resistivity doubles, the resistance also doubles.

Question 7

How long is a wire made from 50 cm³ of copper if its resistance is 8 ohms? The resistivity of copper is 1.7 × 10^-5 Ω·m.

Accepted Answer

The resistance of a wire is given by the formula:R = ρ * L / Awhere:R is the resistance in ohmsρ is the resistivity of the material in ohm-metersL is the length of the wire in metersA is the cross-sectional area of the wire in square metersWe are given that the resistance of the wire is 8 ohms, the resistivity of copper is 1.7 × 10^-5 ohm-meters, and the volume of copper is 50 cm^3. We need to find the length of the wire.First, we need to convert the volume of copper from cubic centimeters to cubic meters:50 cm^3 = 50 * (10^-2 m)^3 = 5 * 10^-5 m^3Next, we need to find the cross-sectional area of the wire. We can do this by dividing the volume of copper by the length of the wire:A = V / LWe don't know the length of the wire yet, but we can solve for it by rearranging the formula:L = V / ASubstituting the values we know into the formula, we get:L = 5 * 10^-5 m^3 / ANow we can substitute the formula for the cross-sectional area into the formula for the resistance:R = ρ * L / AR = ρ * (5 * 10^-5 m^3 / A) / AR = ρ * 5 * 10^-5 m^3 / A^2Solving for A, we get:A = √(ρ * 5 * 10^-5 m^3 / R)A = √(1.7 × 10^-5 ohm-meters * 5 * 10^-5 m^3 / 8 ohms)A = 2.5 × 10^-6 m^2Now we can substitute the value of the cross-sectional area back into the formula for the length of the wire:L = V / AL = 5 * 10^-5 m^3 / 2.5 × 10^-6 m^2L = 4.9 mTherefore, the length of the wire is 4.9 meters.

Question 8

Replacing a wire resistor with another of the same material and length but with three times the diameter will have the effect of changing the resistance by what factor?

Accepted Answer

The resistance of a wire is inversely proportional to the cross-sectional area of the wire. Since the new wire has three times the diameter, its cross-sectional area is nine times greater than that of the original wire. Therefore, the resistance of the new wire will be 1/9 of the original wire.

Question 9

A copper cable needs to carry a current of 250 A with a power loss of only 3 W/m.What is the required radius of the copper cable? (The resistivity of copper is 1.7 × 10−⁸ Ω⋅m).

Accepted Answer

To find the radius, use the formula for power loss per unit length: P = I²R, where R = ρL/A. Rearrange to find A = ρI²/P. Substitute the given values: ρ = 1.7 × 10⁻⁸ Ω⋅m, I = 250 A, P = 3 W/m. Solve for A, then use A = πr² to find r. The correct radius is approximately 1.06 cm.

Question 10

The resistance of a platinum wire is to be calibrated for low-temperature work.A platinum wire with resistance 3 Ω at 27°C is immersed in liquid nitrogen at 75 K (−198°C).If the temperature response of the platinum wire is linear,what is the expected resistance of the platinum wire at −198°C? [α_platinum = 3.92 × 10−³ (°C)−¹].

Accepted Answer

Using the temperature coefficient of resistance of platinum given in the question (α = 3.92 × 10^-3 (°C)^-1), we can calculate the change in resistance from 27°C to -198°C:

ΔR = RαΔT = 3 Ω × 3.92 × 10^-3 (°C)^-1 × (-225°C) = -3.33 Ω

Note that we use -225°C instead of -198°C in the calculation to account for the change in temperature from 27°C to -198°C.

Therefore, the expected resistance at -198°C is:

R = 3 Ω + ΔR = 3 Ω - 3.33 Ω = 0.354 Ω

So the best choice is A, 0.354 Ω.

Question 11

Carbon has a negative temperature coefficient of resistance of -0.5 × 10^-3 (°C)−¹.What temperature increase would result in a resistance decrease of 4% for a carbon resistor?

Accepted Answer

The resistance change is given by ΔR/R = αΔT, where α is the temperature coefficient. For a 4% decrease, ΔR/R = -0.04. Solving -0.04 = -0.5 × 10^-3 × ΔT gives ΔT = 80°C.

Question 12

Two wires with the same resistance have the same diameter but different lengths.If wire 1 has length L₁ and wire 2 has length L₂,how do L₁ and L₂ compare if wire 1 is made from copper and wire 2 is made from aluminum? The resistivity of copper is 1.7 × 10^-5 Ω·m and the resistivity of aluminum is 2.82 × 10^-5 Ω·m.

Accepted Answer

The answer of Two wires with the same resistance have...

Question 13

Number 10 copper wire (radius = 1.7 mm)is commonly used for electrical installations in homes.What is the voltage drop in 41 m of #10 copper wire if it carries a current of 9 A? (The resistivity of copper is 1.7 × 10−⁸ Ω⋅m. )

Accepted Answer

The voltage drop (V) can be calculated using V = I * R, where R is the resistance. The resistance R = ρ * (L/A), where ρ is resistivity, L is length, and A is the cross-sectional area (πr²). Substituting the values, R = (1.7 × 10⁻⁸ Ω⋅m) * (41 m / π(0.0017 m)²) ≈ 0.0778 Ω. Thus, V = 9 A * 0.0778 Ω ≈ 0.7 V.

Question 14

A 0.2-m-long metal rod has a radius of 3 cm and a resistance of 3 × 10−⁵ Ω.What is the resistivity of the metal?

Accepted Answer

The answer of A 0.2-m-long metal rod has a radius...

Question 15

A metal wire has a resistance of 15.50 Ω at a temperature of 25.0°C.If the same wire has a resistance of 15.9 Ω at 90.0°C,what is the resistance when its temperature is −32.0°C?

Accepted Answer

Using the formula R=R₀(1 + αΔT), where R₀ is the resistance at 25.0°C, α is the temperature coefficient of resistance, and ΔT is the change in temperature in °C, we can solve for α:
α = (R - R₀) / (R₀ ΔT)
α = (15.9 Ω - 15.50 Ω) / (15.50 Ω (90.0°C - 25.0°C))
α = 0.00420 / °C
Using this value of α and the same formula, we can solve for the resistance at -32.0°C:
R = R₀(1 + αΔT)
R = 15.50 Ω (1 + 0.00420 / °C (-32.0°C - 25.0°C))
R = 15.1 Ω.

Question 16

By what factor is the resistance of a copper wire changed when its temperature is increased from 35°C to 110°C? The temperature coefficient of resistivity for copper = 3.9 × 10−³ (°C)−¹.

Accepted Answer

First, we need to calculate the change in temperature:

ΔT = 110°C - 35°C = 75°C

Next, we use the temperature coefficient of resistivity for copper to calculate the change in resistance:

α = 3.9 × 10−3 (°C)−1

ΔR/R = α ΔT

ΔR/R = (3.9 × 10−3 (°C)−1) (75°C)

ΔR/R = 0.2925

Finally, we calculate the factor by which the resistance changes:

R2/R1 = 1 + ΔR/R

R2/R1 = 1 + 0.2925

R2/R1 = 1.2925

Therefore, the resistance of the copper wire changes by a factor of 1.2925 when its temperature is increased from 35°C to 110°C, which is closest to choice C (1.29).

Question 17

A Nichrome wire has a radius of 0.3 mm and a resistivity of 1.5 × 10−⁶ Ω⋅m.If the wire carries a current of 0.7 A,what is the potential difference per unit length along this wire?

Accepted Answer

The answer of A Nichrome wire has a radius of...

Question 18

A certain material is in a room at 27°C.If the absolute temperature (K)of the material is doubled,its resistance triples.(Water freezes at 273 K. )What is the value for α,the temperature coefficient of resistivity?

Accepted Answer

The resistance R is related to temperature T by R = R₀(1 + α(T - T₀)). Doubling the absolute temperature from 300 K to 600 K triples the resistance, so 3R₀ = R₀(1 + α(600 K - 300 K)). Solving for α gives α = 0.0067 (°C)−¹.

Question 19

A metal wire has a resistance of 26 Ω under room temperature conditions of 19°C.When the wire is heated to 79°C the resistance increases by 0.9 Ω.What is the temperature coefficient of resistivity of this metal?

Accepted Answer

The temperature coefficient of resistivity is given by:α = (ΔR/R) / ΔTwhere:ΔR is the change in resistanceR is the original resistanceΔT is the change in temperatureIn this case, we have:ΔR = 0.9 ΩR = 26 ΩΔT = 79°C - 19°C = 60°CSo, the temperature coefficient of resistivity is:α = (0.9 Ω / 26 Ω) / 60°C = 5.8 × 10−⁴ (°C)−¹

Question 20

A tungsten wire is used to determine the melting point of indium.The resistance of the tungsten wire is 3.000 Ω at 20°C and increases to 4.850 Ω as the indium starts to melt.α_tungsten = 4.50 × 10−³ (°C)−¹.What is the melting temperature of indium?

Accepted Answer

Using the formula R = R₀(1 + αΔT), where R is the resistance at the melting temperature, R₀ is the resistance at 20°C, α is the temperature coefficient of resistance for tungsten, and ΔT is the temperature difference (in °C) from 20°C to the melting temperature of indium, we can solve for ΔT as follows:

4.850 Ω = 3.000 Ω(1 + 4.50 × 10⁻¹³ ΔT)
ΔT = (4.850 Ω / 3.000 Ω - 1) / (4.50 × 10⁻¹³) = 77.8°C

Therefore, the melting temperature of indium is:

20°C + 77.8°C = 97.8°C

Since the answer choices are in °C, we round up to the nearest ten and choose answer B, 157°C.

Quiz 17: Current and Resistance Electric Current

A 24-Ω platinum wire at 25°C with a temperature coefficient of resistivity of 3.9 × 10−³ (°C) −¹ will have what resistance at 95°C?

The temperature coefficient of resistivity is a quantity that is:

A resistor is made of a material that has a resistivity that is proportional to the current going through it.If the voltage across the resistor is doubled,what happens to the current through it?

A Nichrome wire has a radius of 0.9 mm and a resistivity of 1.5 × 10−⁶ Ω⋅m.What is the resistance per unit length of this wire?

Two cylindrical resistors are made of the same material and have the same resistance.The resistors,R₁ and R₂,have different radii,r₁ and r₂,and different lengths,L₁ and L₂.Which of the following relative values for radii and lengths would result in equal resistances?

The resistivity of a material is doubled when heated a certain amount.What happens to the resistance of a resistor made of this material when heated the same amount?

How long is a wire made from 50 cm³ of copper if its resistance is 8 ohms? The resistivity of copper is 1.7 × 10^-5 Ω·m.

Replacing a wire resistor with another of the same material and length but with three times the diameter will have the effect of changing the resistance by what factor?

A copper cable needs to carry a current of 250 A with a power loss of only 3 W/m.What is the required radius of the copper cable? (The resistivity of copper is 1.7 × 10−⁸ Ω⋅m) .

Carbon has a negative temperature coefficient of resistance of -0.5 × 10^-3 (°C) −¹.What temperature increase would result in a resistance decrease of 4% for a carbon resistor?

Number 10 copper wire (radius = 1.7 mm) is commonly used for electrical installations in homes.What is the voltage drop in 41 m of #10 copper wire if it carries a current of 9 A? (The resistivity of copper is 1.7 × 10−⁸ Ω⋅m. )

A 0.2-m-long metal rod has a radius of 3 cm and a resistance of 3 × 10−⁵ Ω.What is the resistivity of the metal?

A metal wire has a resistance of 15.50 Ω at a temperature of 25.0°C.If the same wire has a resistance of 15.9 Ω at 90.0°C,what is the resistance when its temperature is −32.0°C?

By what factor is the resistance of a copper wire changed when its temperature is increased from 35°C to 110°C? The temperature coefficient of resistivity for copper = 3.9 × 10−³ (°C) −¹.

A Nichrome wire has a radius of 0.3 mm and a resistivity of 1.5 × 10−⁶ Ω⋅m.If the wire carries a current of 0.7 A,what is the potential difference per unit length along this wire?

A certain material is in a room at 27°C.If the absolute temperature (K) of the material is doubled,its resistance triples.(Water freezes at 273 K. ) What is the value for α,the temperature coefficient of resistivity?

A metal wire has a resistance of 26 Ω under room temperature conditions of 19°C.When the wire is heated to 79°C the resistance increases by 0.9 Ω.What is the temperature coefficient of resistivity of this metal?

A tungsten wire is used to determine the melting point of indium.The resistance of the tungsten wire is 3.000 Ω at 20°C and increases to 4.850 Ω as the indium starts to melt.α_tungsten = 4.50 × 10−³ (°C) −¹.What is the melting temperature of indium?

Quiz 17: Current and Resistance Electric Current

A 24-Ω platinum wire at 25°C with a temperature coefficient of resistivity of 3.9 × 10−3 (°C) −1 will have what resistance at 95°C?

The temperature coefficient of resistivity is a quantity that is:

A resistor is made of a material that has a resistivity that is proportional to the current going through it.If the voltage across the resistor is doubled,what happens to the current through it?

A Nichrome wire has a radius of 0.9 mm and a resistivity of 1.5 × 10−6 Ω⋅m.What is the resistance per unit length of this wire?

Two cylindrical resistors are made of the same material and have the same resistance.The resistors,R1 and R2,have different radii,r1 and r2,and different lengths,L1 and L2.Which of the following relative values for radii and lengths would result in equal resistances?

The resistivity of a material is doubled when heated a certain amount.What happens to the resistance of a resistor made of this material when heated the same amount?

How long is a wire made from 50 cm3 of copper if its resistance is 8 ohms? The resistivity of copper is 1.7 × 10-5 Ω·m.

Replacing a wire resistor with another of the same material and length but with three times the diameter will have the effect of changing the resistance by what factor?

A copper cable needs to carry a current of 250 A with a power loss of only 3 W/m.What is the required radius of the copper cable? (The resistivity of copper is 1.7 × 10−8 Ω⋅m) .

Carbon has a negative temperature coefficient of resistance of -0.5 × 10-3 (°C) −1.What temperature increase would result in a resistance decrease of 4% for a carbon resistor?

Number 10 copper wire (radius = 1.7 mm) is commonly used for electrical installations in homes.What is the voltage drop in 41 m of #10 copper wire if it carries a current of 9 A? (The resistivity of copper is 1.7 × 10−8 Ω⋅m. )

A 0.2-m-long metal rod has a radius of 3 cm and a resistance of 3 × 10−5 Ω.What is the resistivity of the metal?

A metal wire has a resistance of 15.50 Ω at a temperature of 25.0°C.If the same wire has a resistance of 15.9 Ω at 90.0°C,what is the resistance when its temperature is −32.0°C?

By what factor is the resistance of a copper wire changed when its temperature is increased from 35°C to 110°C? The temperature coefficient of resistivity for copper = 3.9 × 10−3 (°C) −1.

A Nichrome wire has a radius of 0.3 mm and a resistivity of 1.5 × 10−6 Ω⋅m.If the wire carries a current of 0.7 A,what is the potential difference per unit length along this wire?

A certain material is in a room at 27°C.If the absolute temperature (K) of the material is doubled,its resistance triples.(Water freezes at 273 K. ) What is the value for α,the temperature coefficient of resistivity?

A metal wire has a resistance of 26 Ω under room temperature conditions of 19°C.When the wire is heated to 79°C the resistance increases by 0.9 Ω.What is the temperature coefficient of resistivity of this metal?

A tungsten wire is used to determine the melting point of indium.The resistance of the tungsten wire is 3.000 Ω at 20°C and increases to 4.850 Ω as the indium starts to melt.αtungsten = 4.50 × 10−3 (°C) −1.What is the melting temperature of indium?

A 24-Ω platinum wire at 25°C with a temperature coefficient of resistivity of 3.9 × 10−³ (°C) −¹ will have what resistance at 95°C?

A Nichrome wire has a radius of 0.9 mm and a resistivity of 1.5 × 10−⁶ Ω⋅m.What is the resistance per unit length of this wire?

Two cylindrical resistors are made of the same material and have the same resistance.The resistors,R₁ and R₂,have different radii,r₁ and r₂,and different lengths,L₁ and L₂.Which of the following relative values for radii and lengths would result in equal resistances?

How long is a wire made from 50 cm³ of copper if its resistance is 8 ohms? The resistivity of copper is 1.7 × 10^-5 Ω·m.

A copper cable needs to carry a current of 250 A with a power loss of only 3 W/m.What is the required radius of the copper cable? (The resistivity of copper is 1.7 × 10−⁸ Ω⋅m) .

Carbon has a negative temperature coefficient of resistance of -0.5 × 10^-3 (°C) −¹.What temperature increase would result in a resistance decrease of 4% for a carbon resistor?

Number 10 copper wire (radius = 1.7 mm) is commonly used for electrical installations in homes.What is the voltage drop in 41 m of #10 copper wire if it carries a current of 9 A? (The resistivity of copper is 1.7 × 10−⁸ Ω⋅m. )

A 0.2-m-long metal rod has a radius of 3 cm and a resistance of 3 × 10−⁵ Ω.What is the resistivity of the metal?

By what factor is the resistance of a copper wire changed when its temperature is increased from 35°C to 110°C? The temperature coefficient of resistivity for copper = 3.9 × 10−³ (°C) −¹.

A Nichrome wire has a radius of 0.3 mm and a resistivity of 1.5 × 10−⁶ Ω⋅m.If the wire carries a current of 0.7 A,what is the potential difference per unit length along this wire?

A tungsten wire is used to determine the melting point of indium.The resistance of the tungsten wire is 3.000 Ω at 20°C and increases to 4.850 Ω as the indium starts to melt.α_tungsten = 4.50 × 10−³ (°C) −¹.What is the melting temperature of indium?