Resistivity: Nichrome wire, often used for heating elements, has resistivity of 1.0 × 10^-6 Ω ∙ m at room temperature. What length of wire of diameter 0.250 mm is needed to wind a resistor that has 50 ohms at room temperature?

Question

Quizplus · Accepted Answer

We can use the formula R = ρ (L/A) to solve for the length of the wire needed, 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.

First, we need to find the cross-sectional area of the wire. The diameter is given as 0.250 mm, so the radius is 0.125 mm or 0.000125 m. The cross-sectional area is then:

A = πr^2 = π(0.000125 m)^2 = 4.91 × 10^-8 m^2

Next, we can plug in the given values and solve for L:

50 Ω = (1.0 × 10^-6 Ω ∙ m) (L/4.91 × 10^-8 m^2)

L = (50 Ω) (4.91 × 10^-8 m^2) / (1.0 × 10^-6 Ω ∙ m) = 2.455 m

So the length of wire needed is 2.455 m, which is closest to option B (2.45 m).

Resistivity: Nichrome Wire, Often Used for Heating Elements, Has Resistivity