Question

3. A wire of given material having length I and area of cross section A has a 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 that,

A wire of having length L and area of cross section A has a Resistance of 4 Ω

We know,

⇒ R₁ = ρL / A

⇒ 4 = ρL / A ...(1)

Now, we need to find the resistance of another wire of the same material having length L/2 and area of cross section 2A, Resistivity would be same because they are made from same material.

⇒ R₂ = ( ρL/2 ) / 2A

⇒ R₂ = ρL / 4A ...(2)

Now, Ratio of (1) and (2),

⇒ 4 / R₂ = ( ρL / A ) / (ρL / 4A)

⇒ 4 / R₂ = 4

⇒ R₂ = 1 Ω

Hence, The resistance of the other wire will be 1 Ω.

Some Information :-

☛ Resistance of a conductor depends on the area of cross section, length, material, temperature.

Where, Resistance is

• directly proportional to the length of the conductor. Which means, On increasing the length of conductor the Resistance would also increase.
• inversely proportional to the area of cross section. Which means on reducing the area of cross section the resistance will increase.