Question

*PHYSICS*

A wire of a given material having length l and area of cross-section A has a resistance of

4Ω. What would be the resistance of another wire of the same material having length l/2 and

area of cross-section 2A.​

Answer 1

Given:

A wire of a given material having length l and area of cross-section A has a resistance of 4Ω.

To find:

Resistance of another wire of the same material having length l/2 and area of cross-section 2A?

Calculation:

Let initial resistance be R:

$\therefore \: R = \rho \times \dfrac{l}{A} = 4 \: \Omega$

Now, in the new wire, the length is l/2 and area is 2a:

$\therefore \: R2 = \rho \times \dfrac{ (\frac{l}{2}) }{2A}$

$\implies \: R2 = \rho \times \dfrac{ l }{4A}$

$\implies \: R2 = \dfrac{1}{4} \times \bigg( \rho \times \dfrac{ l }{A} \bigg)$

$\implies \: R2 = \dfrac{1}{4} \times 4 \: \Omega$

$\implies \: R2 = 1\: \Omega$

So, resistance of new wire is 1 ohm.