Question

A cylindrical conductor of length $‘l’$ and uniform area of cross-section $‘A’$ has resistance $‘R’$. The area of cross-section of another conductor of the same material and same resistance but of length $‘2l’$ is

• A. $\frac{A}{2}$
• B. $\frac{3A}{2}$
• C. $2A$
• D. $3A$

Answer 1

The correct option is C

$2A$

Step 1: Given Data

Length of the first conductor $l_1=l$

Length of the second conductor $l_2=2l$

Resistance of both the conductors $=R$

Let the resistivity of both the conductors be $\rho$.

Area of the first conductor $A_1=A$

Let the area of the second conductor be $A_2$.

Step 2: Formula Used

We know that resistance is given as,

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

Step 3: Calculate the required Area

$$\begin{gathered} \therefore R=\rho \frac{l_1}{A_1}=\rho \frac{l_2}{A_2} \\ \Rightarrow \frac{l_1}{A_1}=\frac{l_2}{A_2} \end{gathered}$$

Upon substituting the values we get,

$$\begin{gathered} \frac{l}{A}=\frac{2l}{A_2} \\ \Rightarrow A_2=2A \end{gathered}$$

Hence, the correct answer is option (C).