Question

A cylindrical conductor of length $l$ and uniform area of the cross-section $A$has resistance$R$. Another conductor of length $2l$ and resistance $R$of the same material has an area of cross-section

• 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 cylindrical conductor $=l$

Area of the cross-section of the cylindrical conductor $=A$

Resistance of the cylindrical conductor $=R_c$

Length of conductor “X", $l_x=2l$

Resistance of conductor “X” $=R_x$

Resistance of both the conductors is the same, $R_c=R_x$

Area of the cross-section of conductor “X”, $A_x=?$

Resistivity of the cylindrical conductor and conductor “X” $=\rho$

Step 2: Formula used

$R_c=\rho \frac{l}{A}$ ……………………..(a)

$R_x=\rho \frac{l_x}{A_x}$…………………….(b)

Step 3: Calculation of the area of cross-section of conductor X

Substituting the given value of length in equation (b), we get

$R_x=\rho \frac{2l}{A_x}$ …………………(c)

Since the resistance of both the conductors is the same, therefore on comparing equations (a) and (c) we get

$$\begin{gathered} \rho \frac{l}{A}=\rho \frac{2l}{A_x} \\ {A}_x=2A \end{gathered}$$

Hence, option (C) is correct.