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 (a)A/2 (b) 3A/2 (c) 2A (d) 3A​

Answer 1

Explanation:

a)A/2 because Area is inversly proportional to the length

Answer 2

The new cross sectional area is 2A.

Explanation:

The resistance of a conductor is given by :

$R=\rho\dfrac{l}{A}$ ......(1)

l is length of the cylindrical conductor

A is area of cross section

Let R' is the resistance of another conductor of length 2l and area A'. Its resistance is R. So,

$R=\rho \dfrac{2l}{A'}$ ........(2)

Dividing equation (1) and (2) we get :

$\dfrac{R}{R}=\dfrac{\rho l/A}{\rho 2l/A'}\\\\1=\dfrac{l}{A}\times \dfrac{A'}{2l}\\\\1=\dfrac{A'}{2A}\\\\A'=2A$

So, the new cross sectional area is 2A.

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