Question

What length of copper wire of resistivity 1.7*10^-8 ohm m and radius 1 mm is required so that it's resistance is 1 ohm ?

Answer 1

Answer:

184.7 m

Explanation:

Resistance of a wire is given by

R = ρ(L/A)

where,

R = resistance of wire

ρ = resistivity of wire

L = length of wire

A = cross sectional area of wire

From the question:

R = 1 Ω

ρ = 1.7 x 10⁻⁸ Ω m

r = 1 mm = 0.001 m

A = πr²

  = (22/7) x 0.001²

  = 3.14 x 10⁻⁶ m²

Substituting these values,

1 Ω= 1.7 x 10⁻⁸ Ω m x ( L/3.14 x 10⁻⁶ m² )

⇒ L = (1 x 3.14 x 10⁻⁶ m²) / 1.7 x 10⁻⁸ Ω m

      = 1.847 x 10² m

      = 184.7 m

Answer 2

we know the formula, $R=\rho\frac{l}{a}$

where R is resistance, $\rho$ is resistivity, l is length of wire and a is cross sectional area.

given, R = 1 ohm , $\rho$= 1.7 × 10^-8 ohm m, r = 1mm = 10^-3 m

so, cross sectional area of wire, a = πr²

= 3.14(10^-3)² = 3.14 × 10^-6 m²

now, from formula, 1 = (1.7 × 10^-8) × l/(3.14 × 10^-6)

l = 3.14 × 10^-6/1.7 × 10^-8

= 1.847 × 10²

= 184.7 m

hence, length of wire is 184.7 m