Question

A 4.0Ω resistor is constructed using a wire diameter of 1.0 mm and a resistivity of 1.68×10

−8
Ω⋅m. The length of wire used to create the resistor is most nearly (A) 2340 m (B) 750 m (C) 240 m (D) 190 m (E) 60 m

Answer 1

To find the length of wire needed to create a 4.0Ω resistor with a given diameter and resistivity, use the resistance formula for a cylindrical conductor, and solve for the length, resulting in approximately 190 meters.

Step-by-step explanation:

The question involves finding the length of wire used to create a 4.0Ω resistor given the wire diameter (1.0 mm) and the resistivity (1.68×10⁻⁸ Ω·m). We use the formula for the resistance of a cylindrical conductor, R = ρL/A, where R is resistance, ρ is resistivity, L is length, and A is the cross-sectional area of the wire.

The area, A, can be calculated using the formula for the area of a circle, A = π(d/2)², where d is the diameter of the wire. Substituting the known values into the resistance formula and solving for L gives us the length of the wire that would create a 4.0Ω resistor.

Upon calculating using the given values, we find that the length of the wire is closest to option (D) 190 m.

Answer 2

To find the length of wire used to create the resistor, we can use the formula for resistance: R = ρ * (L/A). We are given the resistance (4.0Ω) and the wire diameter (1.0 mm). By plugging in these values and solving for L, we find that the length of wire used to create the resistor is approximately 240 m.

Step-by-step explanation:

To find the length of wire used to create the resistor, we can use the formula for resistance: R = ρ * (L/A), where R is the resistance, ρ is the resistivity, L is the length, and A is the cross-sectional area of the wire. We are given the resistance (4.0Ω) and the wire diameter (1.0 mm). We can use this information to find the cross-sectional area. The formula for the cross-sectional area of a wire is A = π * r^2, where r is the radius of the wire. Since we are given the diameter, we can divide it by 2 to find the radius. Plugging in the values, we have A = π * (0.5 mm)^2.

Now, we can rearrange the formula for resistance to solve for the length: L = R * (A/ρ). Plugging in the values, we have L = 4.0Ω * (π * (0.5 mm)^2 / (1.68×10^-8 Ω⋅m)). After calculating this expression, the length of wire used to create the resistor is most nearly 240 m (option C).