Question

calculate the resistivity of the material of a wire of length 1 m,radius 0.01 cm and of resistance 20 ohms

Answer 1

As we know,

R = ρ L/A

r = 0.01 cm = 1×10⁻⁴ m
A = πr² = 3.14×(1×10⁻⁴ )m² = 3.14×10⁻⁸ m²

now, ρ = RA/L 
           =(20×3.14×10⁻⁸ )/1
           =6.28×10⁻⁷ ohm-m

Answer 2

Given :

Length of the wire (L) = 1 m

Radius (R) = 0.01 cm = 10

Resistance (R) = 20 ohm

To Find :

Resistivity of the material of a wire

Solution :

We know, Resistance (R) = Resistivity (ρ) × $\frac{Length (L)}{Area (A)}$

∴ Resistivity (ρ) = $\frac{Resistance (R) * Area (A)}{Length (L)}$

                         = $\frac{20 * \pi * (10^-^4)^2}{1}$

                         = 20 × 3.14 × 10⁻⁸

                         = 62.8 × 10⁻⁸

                         = 6.28 × 10⁻⁷ Ohm. m

Therefore, the resistivity of the material of the wire of length 1 m and radius 0.01 cm is found to be 6.28 × 10⁻⁷ Ohm. m