Question

a cylindrical conductor of length l and uniform area of cross section A has resistance R. another conductor of length 2l and resistance R of the same material has area of cross section -----?

Answer 1

R = ρL/A

R₁/R₂ = (L₁/L₂) × (A₂/A₁)

A₂ = (R₁/R₂) × (L₂/L₁) × A₁

A₂ = (R/R) × (2L/L) × A

A₂ = 2A

Cross section area of another conductor is 2A

Answer 2

The area of another conductor is 2A .

Given:

Length $= l_1 = l$

Area of cross section $= a_1 = A$

Resistance $= R_1 = R$

Length of another conductor $= l_2 = 2l$

Resistance of another conductor $= R_2 = R$

To find:

Area of cross section of another conductor $= a_2 = x = ?$

Solution:

The formula of resistivity is given below:

$\rho=R \frac{A}{l}$

Case 1:

$\rho=R \frac{A}{l}$

Case 2:

$\rho=R \frac{x}{2 l}$

Since, both the cases are of same material, we can equate the resistivity,

Thus,

$\Rightarrow R \frac{A}{l}=R \frac{x}{2 l}$

On solving, we get,

$\therefore x=2 A$.