Question

a wire is 20m long nd 0.3mm is diameter has resistance 10 ohm calculate resistivity​

Answer 1

Given :-

Length of the wire = 20 m

Diameter of the wire = 0.3 mm

Resistance of the wire = 10 Ω

To Find :-

The resistivity of the material.

Solution :-

We know that,

• R = Resistivity
• l = Length
• d = Diameter
• r = Radius
• a = Cross sectional area

Given that,

Length of the wire (l) = 20 m

Diameter of the wire (d) = 0.3 mm

Resistance of the wire = 10 Ω

Finding the radius of the wire,

$\underline{\boxed{\sf Radius \ of \ the \ wire=\dfrac{Diameter}{2} }}$

Substituting their values, we get

$\sf Radius=\dfrac{0.3}{2} =0.15$

First, finding the area of the wire

$\underline{\boxed{\sf A= \Pi r^{2}}}$

$\sf A= \Pi \bigg( \dfrac{d}{2} \bigg)^{2}$

Substituting their values, we get

$\sf A=3.14 \times 1.5 \times 10^{-4} \times 1.5 \times 10^{-4}$

$\sf A=7.065 \times 10^{-8} \ m^{2}$

Resistivity is given by the equation,

$\underline{\boxed{\sf \rho =R \ \dfrac{Cross \ sectional \ area \ of \ the \ wire}{Length \ of \ the \ wire} }}$

Substituting their values, we get

$\sf \rho =\dfrac{10 \times 7.065 \times 10^{-8}}{20}$

$\sf \rho =3.5325 \times 10^{-8} \ \Omega \ m$