Question

If the resistance of a certain copper wire is 1 Ω, then the resistance of a similar nichrome wire will be about ______.

Options

• 25 Ω

• 30 Ω

• 60 Ω

• 45 Ω

Answer 1

If the resistance of a certain copper wire is 1 Ω, then the resistance of a similar nichrome wire will be about 60 Ω.

Explanation:

The resistance (R) of a wire is given by the formula:

R = `rho l/A`

Since the nichrome wire is described as similar, its length (l) and area (A) are identical to those of the copper wire. This means its resistance depends entirely on its resistivity (ρ).

Resistivity of copper = 1.68 × 10⁻⁸ Ω m

Resistivity of nichrome = 1.10 × 10⁻⁶ Ω m

The resistivity of nichrome is roughly 60 times greater than that of copper.

Consequently, its resistance will also be 60 times greater:

Resistance of nichrome wire = 60 × 1 Ω

Resistance of nichrome wire = 60 Ω