Question

the resistance of wire of length 1m is 22 ohm at 20°c the diameter is 0.4 m find its resistivity

Answer 1

Given :

• Resistance = 22 Ω
• Length = 1 m
• Diameter = 0.4 m
• Temperature = 20 °C

To find :

• Resistivity or specific resistance

Solution :

The formula for resistivity $(\rho)$ is given by :

$\boxed{\huge{\tt{\rho = R \dfrac{A}{l}}}}$

For finding resistivity , we have to find the area of cross section first :

Diameter = 0.4 m

$\therefore$ radius = 0.4/2 = 0.2 m

Area of cross section of wire = πr²

$= \tt \dfrac{22}{7} \times 0.2 \times 0.2 \\ \\ \tt = \frac{22}{7} \times \frac{2}{10} \times \frac{2}{10} \\ \\ \tt = \frac{88}{7 \times 100} \\ \\ \tt = \frac{12.57}{100} \\ \\ \tt = 0.1257 \: {m}^{2} \\ \\ \tt \: = 0.12 \: {m}^{2}$

Using this in the formula of resistance :

$\tt \rho = \dfrac{22 \times 0.12}{1} \\ \\ \tt \rho = \frac{22 \times 12}{100} \\ \\ \tt \rho = \frac{264}{100}$

$\tt \rho = 2.64 \Omega\ m$