Question

A wire of given material having length L and area of cross section a has resistance of 8 ohm . What what would be the resistance of another wire of the same material having length 1/2 area of cross section 2a.

Answer 1

Given :

• L is the length of wire
• A is the area of wire
• Resistance of wire is 8 ohm

To Find :

• Resistance of 2nd wire

Solution :

we know that

$\sf R= \rho \frac{l}{A} \\ \\\sf \therefore \rho \frac{l}{A} = 8\Omega$

In second case

Length of the wire becomes half and Area becomes 2 times.

$\sf R = \rho \frac{l}{A} \\ \\\sf R = \rho \bigg( \frac{l}{2} \bigg ) \times \frac{1}{2A} \\ \\\sf R= \rho \frac{l}{A} \times \frac{1}{4} \\ \\\sf R = 8 \times \frac{1}{4} \\ \\\sf R= 2\Omega$

Resistance of another wire is 2 ohm