Question 1

A copper cable is to be designed to carry a current of 300 A with a power loss of only 2.0 watts per meter. What is the required radius of the copper cable? (The resistivity of copper is 1.7 × 10−⁸ Ω ⋅ m.)

Accepted Answer

The answer of A copper cable is to be designed...

Question 2

In the Drude model of electrical conduction, the current density is NOT directly proportional to

Accepted Answer

The current density is inversely proportional to the resistivity of the wire, not directly proportional.

Question 3

To increase the current density in a wire of length  and diameter D, you can

Accepted Answer

The current density in a wire is directly proportional to the potential difference between its two ends. Hence, increasing the potential difference will increase the current density.

Question 4

The heating coil of a hot water heater has a resistance of 20 ohms and operates at 210 V. If electrical energy costs 5.5 cents per kW-hr, what does it cost to raise the 200 kg of water in the tank from 15°C to 80°C? (The specific heat of water is 4 186 J/kg°C)

Accepted Answer

The answer of The heating coil of a hot water...

Question 5

Light bulb A is rated at 60 W and light bulb B is rated at 100 W. Both are designed to operate at 110 V. Which statement is correct?

Accepted Answer

The power of the bulb is given by P=V^2/R, where P is power, V is voltage and R is resistance. As both bulbs are designed to operate at the same voltage, the bulb with a higher power rating (100 W) must have a lower resistance than the bulb with a lower power rating (60 W). Therefore, option B is correct as it states that the 60 W bulb has a greater resistance and smaller current than the 100 W bulb. Option A and D are incorrect because they suggest that the 60 W bulb has a greater current, which is not possible as the higher power 100 W bulb would draw more current. Option C and E are also incorrect as they do not take into account the power rating of the bulbs.

Question 6

A conductor of radius r, length  and resistivity ρ has resistance R. It is melted down and formed into a new conductor, also cylindrical, with one fourth the length of the original conductor. The resistance of the new conductor is

Accepted Answer

The answer of A conductor of radius r, length ...

Question 7

An aluminum wire of cross-sectional area 4.0 mm² is carrying a current of 8.0 A. The density of aluminum is 2.7 g/cm³, and its molar mass is 27 g. Assuming one free electron per aluminum atom, what is the drift speed of the electrons in this wire?

Accepted Answer

The answer of An aluminum wire of cross-sectional area 4.0...

Question 8

Jadeen says that you can increase the resistance of a copper wire by hammering the wire to make it narrower and longer. Arnell says that you can increase its resistance by heating the wire. Which one, if either, is correct, and why?

Accepted Answer

Both Jadeen and Arnell are correct. Jadeen's method increases resistance by making the wire longer and narrower, which increases resistance due to a longer path for electrons and a smaller cross-sectional area for current flow. Arnell's method increases resistance by heating the wire, which increases the atomic vibrations within the copper, making it harder for electrons to pass through, thus decreasing its conductivity.

Question 9

Jadeen says that you can increase the resistance of a copper wire by hammering the wire to make it narrower and longer. Arnell says that you can increase its resistance by heating the wire. Which one, if either, is correct, and why?

Accepted Answer

Both Jadeen and Arnell are correct. Jadeen's method increases resistance by making the wire longer and narrower, which increases its resistance due to the physical dimensions affecting the resistance (resistance is directly proportional to length and inversely proportional to cross-sectional area). Arnell's method increases resistance by heating the wire, which increases its resistivity because the atomic lattice vibrates more at higher temperatures, making it harder for electrons to pass through, thus increasing resistance.

Question 10

What is the resistance of 1 000 m of 4-mm diameter copper wire? (ρ_Cu = 1.7 × 10^-8 Ω ⋅ m)

Accepted Answer

The answer of What is the resistance of 1 000...

Question 11

In the Drude model of electrical conduction, the current density is directly proportional to

Accepted Answer

The answer of In the Drude model of electrical conduction,...

Question 12

A high-voltage transmission line carries 1 000 A at 700 kV for a distance of 100 miles. If the resistance per length in the wire is 0.5 Ω/mile, what is the power loss due to resistive losses?

Accepted Answer

The answer of A high-voltage transmission line carries 1 000...

Question 13

A high-resistance material is used as an insulator between the conductors of a length of coaxial cable. The resistance material, which forms a hollow tube, has an inner radius a and an outer radius b, and the insulator provides a resistance R between the conductors. If a second insulator, made of the same material and having the same length, is made with double both the inner radius and the outer radius of the first, what resistance would it provide between the conductors?

Accepted Answer

The resistance of a cylindrical shell (like the insulator in a coaxial cable) is inversely proportional to the logarithm of the ratio of the outer radius to the inner radius. When both the inner and outer radii are doubled, the ratio of the outer radius to the inner radius remains the same, meaning the resistance provided by the insulator does not change.

Question 14

A cook plugs a 500 W crockpot and a 1 000 W kettle into a 240 V power supply, all operating on direct current. When we compare the two, we find that

Accepted Answer

The current (I) drawn by an appliance can be calculated using the formula $I = \frac{P}{V}$, where $P$ is the power in watts and $V$ is the voltage. For the crockpot, $I = \frac{500}{240}$ and for the kettle, $I = \frac{1000}{240}$. This shows that the kettle draws more current than the crockpot. The resistance (R) of an appliance can be calculated using the formula $R = \frac{V^2}{P}$. Therefore, the crockpot, with lower power, has higher resistance compared to the kettle with higher power.

Quiz 27: Current and Resistance

A copper cable is to be designed to carry a current of 300 A with a power loss of only 2.0 watts per meter. What is the required radius of the copper cable? (The resistivity of copper is 1.7 × 10−8 Ω ⋅ m.)

In the Drude model of electrical conduction, the current density is NOT directly proportional to

To increase the current density in a wire of length and diameter D, you can

The heating coil of a hot water heater has a resistance of 20 ohms and operates at 210 V. If electrical energy costs 5.5 cents per kW-hr, what does it cost to raise the 200 kg of water in the tank from 15°C to 80°C? (The specific heat of water is 4 186 J/kg°C)

Light bulb A is rated at 60 W and light bulb B is rated at 100 W. Both are designed to operate at 110 V. Which statement is correct?

A conductor of radius r, length and resistivity ρ has resistance R. It is melted down and formed into a new conductor, also cylindrical, with one fourth the length of the original conductor. The resistance of the new conductor is

An aluminum wire of cross-sectional area 4.0 mm2 is carrying a current of 8.0 A. The density of aluminum is 2.7 g/cm3, and its molar mass is 27 g. Assuming one free electron per aluminum atom, what is the drift speed of the electrons in this wire?

Jadeen says that you can increase the resistance of a copper wire by hammering the wire to make it narrower and longer. Arnell says that you can increase its resistance by heating the wire. Which one, if either, is correct, and why?

Jadeen says that you can increase the resistance of a copper wire by hammering the wire to make it narrower and longer. Arnell says that you can increase its resistance by heating the wire. Which one, if either, is correct, and why?

What is the resistance of 1 000 m of 4-mm diameter copper wire? (ρCu = 1.7 × 10-8 Ω ⋅ m)

In the Drude model of electrical conduction, the current density is directly proportional to

A high-voltage transmission line carries 1 000 A at 700 kV for a distance of 100 miles. If the resistance per length in the wire is 0.5 Ω/mile, what is the power loss due to resistive losses?

A cook plugs a 500 W crockpot and a 1 000 W kettle into a 240 V power supply, all operating on direct current. When we compare the two, we find that

A copper cable is to be designed to carry a current of 300 A with a power loss of only 2.0 watts per meter. What is the required radius of the copper cable? (The resistivity of copper is 1.7 × 10−⁸ Ω ⋅ m.)

An aluminum wire of cross-sectional area 4.0 mm² is carrying a current of 8.0 A. The density of aluminum is 2.7 g/cm³, and its molar mass is 27 g. Assuming one free electron per aluminum atom, what is the drift speed of the electrons in this wire?

What is the resistance of 1 000 m of 4-mm diameter copper wire? (ρ_Cu = 1.7 × 10^-8 Ω ⋅ m)