Question 1

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 2

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 3

A high-voltage transmission line carries 1000 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 1000 A...

Question 4

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 5

A cook plugs a 500-W crock-pot and a 1000-W kettle into a 240-V power supply, all operating on direct current. When we compare the two, we find that

Accepted Answer

Power (P) = Voltage (V) x Current (I)
For the crock-pot, P = 500W and V = 240V, therefore I = 2.08A
For the kettle, P = 1000W and V = 240V, therefore I = 4.17A

Resistance (R) = Voltage (V) / Current (I)
Therefore, for the crock-pot, R = 240V / 2.08A = 115.4 ohms
For the kettle, R = 240V / 4.17A = 57.6 ohms

So, we can see that Icrock-pot < Ikettle and Rcrock-pot > Rkettle, which is the option B. The kettle has a higher power rating and therefore draws more current, and its resistance is lower as well.

Question 6

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 7

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 8

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 rating of a bulb is given by P=V^2/R, where P is power, V is voltage, and R is resistance. Since both bulbs operate at the same voltage of 110 V, the bulb with the larger power rating (100 W) must have a smaller resistance than the bulb with the smaller power rating (60 W). Thus, choice B is correct - the 60-W bulb has a greater resistance and smaller current than the 100-W bulb.

Question 9

What is the resistance of 1000 m of 4-mm diameter copper wire? (ρCu = 1.7 × 10⁻⁸ Ω ⋅ m)

Accepted Answer

The answer of What is the resistance of 1000 m...

Question 10

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 11

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

Accepted Answer

According to Ohm's law, current density is directly proportional to the potential difference (V) and inversely proportional to the cross-sectional area of the wire (A). Therefore, increasing the potential difference will increase the current density. Heat may increase the resistance of the wire, so option E is not the best choice. Options A and C are incorrect because they describe ways to decrease the current density.

Question 12

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.

Quiz 28: Current and Resistance

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

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?

A high-voltage transmission line carries 1000 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?

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?

A cook plugs a 500-W crock-pot and a 1000-W kettle into a 240-V power supply, all operating on direct current. When we compare the two, we find that

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?

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?

What is the resistance of 1000 m of 4-mm diameter copper wire? (ρCu = 1.7 × 10−8 Ω ⋅ m)

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.)

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

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 1000 m of 4-mm diameter copper wire? (ρCu = 1.7 × 10⁻⁸ Ω ⋅ m)

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.)