Question

A wire of length 2 cm and area of cross-section 2 cm2 has a resistance of 4 ohm. Calculate the specific resistance of the wire.​

Answer 1

Answer:

The specific resistance of the wire = 0.04 Ohm-m

Explanation:

Given :

• Length of the wire = 2 cm
• Area of cross section = 2 cm²
• Resistance of the wire = 4 Ω

To find :

the specific resistance of the wire

Solution :

Resistance of the wire is given by,

   $\lonrightarrow \sf R=\dfrac{\rho L}{A}$

where

➙ ρ denotes specific resistance

➙ L denotes length of the wire

➙ A denotes cross sectional area of the wire

Substitute

➙ R = 4 Ω

➙ L = 2 cm

➙ A = 2 cm²

  $\sf 4 \Omega =\dfrac{\rho \times 2cm}{2 cm^2} \\\\ \sf 4\Omega=\dfrac{\rho}{1 \ cm} \\\\ \sf \rho =4 \Omega \times 1 \ cm \\\\ \sf \rho=4\Omega \times 0.01 m \\\\ \sf \rho=0.04 \ \Omega - m$

Therefore,

specific resistance of the wire = 0.04 Ohm-m