Question

A wire of given material having length L and area of cross section A has resistance of 4ohm.what would be the resistance of another wire of the same material having length 1/2 and area of cross section 2A?

Answer 1

Given:

Wire A has length L , Area of cross-section as A , and net resistance of 4 ohms.

To find:

Net resistance of another wire B , having length as L/2 and area of cross-section as 2A.

Calculation:

Since the question has mentionedthat both the wires are of the same given material we can say that the resistivity factor for both the wires will be same.

For wire A :

$\therefore \: 4 = \rho \times \bigg( \dfrac{L}{A} \bigg)$

For wire B , let resistance be x

$\therefore \: x = \rho \times \bigg( \dfrac{ \frac{L}{2}}{2A} \bigg)$

$= > \: x = \dfrac{1}{4} \bigg \{ \rho \times \bigg( \dfrac{ L}{A} \bigg) \bigg \}$

Putting available values , we get :

$= > \: x = \dfrac{1}{4} \bigg \{ 4 \bigg \}$

$= > \: x = 1 \: ohm$

So resistance of wire B is 1 ohm.