Question

The resistance of a wire of 0.01 cm radius and 1.0 cm length is 7 Ω. Calculate its resistivity.

Answer 1

Given: Radius (r) = 0.01 cm = 10⁻⁴ m

Length (l) = 1.0 cm = 0.01 m = 10⁻² m

Resistance (R) = 7 Ω

Area (A) = πr²

= 3.14 × (10⁻⁴)⁻²

= 3.14 × 10⁻⁸ m²

The resistance R is given by:

R = `rho l/A`

⇒ ρ = `(R * A)/l`

= `(7 xx 3.14 xx 10^-8)/10^-2`

= 21.98 × 10⁻⁸ × 10²

= 21.98 × 10⁻⁶ Ω m

= 2.198 × 10⁻⁵ Ω m

∴ The resistivity of the wire is 2.198 × 10⁻⁵ Ω m.