Question

The specific resistance of the wire is 1.1 m long and 0.4 mm diameter having a resistance of 4.2 ohm will be?

Answer 1

Use this general formula: R = ρ L / A

ρ = RA / L
= [4.2 Ω × π (0.4/2 × 10^-3 m)^2] / (1.1 m)
≈ 4.8 × 10^-7 Ω m

∴ Specific Resistance of wire is approximately 4.8 × 10^-7 Ω m

Answer 2

Given: Length of wire, l = 1.1m

           Diameter of wire, d = 0.4mm

           Resistance , R = 4.2 ohm

To Find: specific resistance, s.

Solution:

To calculate specific resistance formula used:

• Resistance = specific resistance x ( length/ area)
• R = s x ( l/A)

To calculate area(A) of wire, formula used:

• As the wire is in a circular shape, its area A = πr²

• r is the radius of wire, r = diameter/2

  r = d/2

     = 0.4/2

     = 0.2mm

Converting mm into meter (m):

1mm = 0.001 m

0.2mm = 0.2 x 0.001

            = 0.0002m

Applying specific resistance formula:

R = s x (l/A)

4.2 = s x ( 1.1 / πr²)

(4.2 x πr²) / 1.1 = s

s = 4.2 x 3.14x (0.0002)² / 1.1

 = 13.188 x (0.0002)² / 1.1

 = 13.188 x (4 x 10 ⁻⁸)/1.1

 = 11.98 x4 x 10 ⁻⁸

 = 47.9 x 10 ⁻⁸ohm.m

On round-off the value-

s  = 4.8 x 10⁻⁷ohm.m

Hence, specific resistance of wire is 4.8 x 10⁻⁷ohm.m