Question

Calculate the resistivity of a material of a wire 1 m long, 0.4 mm in diameter and having a resistance of 2 ohm.

Answer 1

Answer:

length of wire, l = 1m

diameter of cross sectional area of wire , d = 0.4mm = 4 × 10^-4 m

so, cross sectional area of wire, A = πd²/4 = π(4 × 10^-4)²/4 = 4π × 10^-8 m²

resistance of wire, R = 2ohm.

we know,

where is resistivity or specific resistance of material of the wire.

or, 2 = × 1/{4π × 10^-8}

or, 2 × 4π × 10^-8 = .

or, = 8π × 10^-8 ohm.m

= 25.12 × 10^-8 ohm.m

= 2.512 × 10^-7 ohm.m

hence, resistivity of material is 2.512 × 10^-7 ohm.m