Question

Resistance of a metal wire of length 1 m is 26 Ohm at 20'C.If the diameter of the wire is 0.3 mm.What will be the resistivity of the metal at that temperature.

Answer 1

Resistance = 26 ohm

Diameter of wire =0.3 mm =0.03 cm

Radius will be = 0.03/2 = 0.015 cm

Now,

Temperature is constant that he 20 degree Celsius.

Now

We know the formula for Resistivity :-

R = Resistivity *l/A

Where

L is the length of wire and A is the area of the cross section of wire.

Now,

Area of cross section is :-

$\pi {r}^{2} = \frac{22}{7} \times 0.015 \times 0.015 \\ \\ = \frac{22}{7} \times 0.000225 \\ \\ = 0.000707 = 0.00071 \: {cm}^{2}$

Now,

Resistivity = Resistance * Area /length

$= \frac{26 \times 0.00071}{10} \\ \\ \\ = 0.000184 \: ohm \: cm \\ \\ =$

=1.84 *10¯⁴ ohm centimeter

Answer 2

According to the Question

Resistance , R = 26Ω

Length of wire = 1m

Diameter of circular part of wire = 0.3mm

= 0.3 × 10⁻³m

Area of wire ,

A = πr²

= πd²/4 [d = 2r]

= 3.14 × (0.3 × 10⁻³)² ÷ 4m²

= 3.14 × 9 × 10⁻⁸ ÷ 4 m²

= 28.26 ÷ 4 × 10⁻⁸ m²

= 7.06 × 10⁻⁸ m²

Now, use formula,

R = ρL/A

ρ = RA ÷ L

= 26Ω × 7.06 × 10⁻⁸m² ÷ 1m

ρ = 1.8356 × 10⁻⁶ Ωm

Resistivity = 1.8356 × 10⁻⁶ Ωm at 20°C