Question

Resistance of a metal wire of length 1m is 26 ohm at room temperature. If diameter of wire is 0.3 mm, find the resistivity of the wire.

Answer 1

Step 1: Given data

Resistance , R = 26Ω
Length of wire, L = 1 m
Diameter of circular part of wire, d = 0.3 mm = 0.3 × 10⁻³m

Step 2: Formula used

Area (A) = πr²

Resistance, $R=\frac{\rho L}{A}$

Step 3: Finding the resistivity

We can write
The base area of the wire, A = πr² = $\frac{{\mathrm{\pi d}}^2}{4}\left[because,d=2r\right]$

Putting all the values

Area = $\frac{3.14\times (0.3\times 10⁻³)²}{4}$
After solving
​​​​​​
Area = 7.06 × 10⁻⁸ m²
Now, use the formula,
$R=\frac{\rho L}{A}$
Here, R is the resistance, ρ is the resistivity, L is the length of the wire and A is the base area of it.
So, $\rho =\frac{RA}{L}$

Putting all the values

ρ = 26Ω × 7.06 × 10⁻⁸m² 1
ρ = 26Ω × 7.06 × 10⁻⁸m²
ρ = 1.8356 × 10⁻⁶ Ωm
Hence, resistivity is 1.8356 × 10⁻⁶ Ωm at room temperature.