Question

A Nichrome wire of resistivity ( rho = 1.5 × 10⁻⁶ ) Ω.m, length 38.5 m, and radius 0.32 mm. Find its resistance.

a. 7.58 Ω
b. 15.16 Ω
c. 30.32 Ω
d. 60.64 Ω

Answer 1

The resistance of a Nichrome wire with a resistivity of 1.5 × 10⁻⁶ Ω.m, length of 38.5 m, and radius of 0.32 mm is approximately 7.58 Ω. Therefore, the correct answer is option a. 7.58 Ω.

Step-by-step explanation:

The student is asking about finding the resistance of a Nichrome wire with given resistivity, length and radius. The formula to calculate resistance R is given by R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area of the wire.

Using the formula for the area of a circle (A = πr²) and converting the radius from millimeters to meters, we can determine the resistance of the wire.

First, convert the radius from millimeters to meters: 0.32 mm = 0.32 × 10⁻³ m.

Next, calculate the cross-sectional area A: A = π × (0.32 × 10⁻³ m)².

Now calculate the resistance using the given length and resistivity: R = (1.5 × 10⁻⁶ Ω.m × 38.5 m) / A.

When you do the necessary computations, the resistance comes out to be approximately 7.58 Ω, which corresponds to option a.

Therefore, the correct answer is option a. 7.58 Ω.