Question

Statement-1: In the meter bridge experiment shown in figure, the balance length AC corresponding to null deflection of the galvanometer is x. If the radius of the wire AB is doubled, the balance length becomes 4x.

Statement-2: The resistance of a wire is inversely proportional to the square of its radius.

Answer 1

Statement-1 is false. Statement-2 is true.

Answer 2

Statement-2 is correct because the resistance of a wire is given by $R = \rho_m \frac{L}{A}$, where $A = \pi r^2$. Thus, $R \propto \frac{1}{r^2}$. In a meter bridge, the balance condition is $\frac{R_1}{R_2} = \frac{R_{AC}}{R_{CB}}$. If the resistance per unit length of the wire AB is $\rho$, then $R_{AC} = \rho x$ and $R_{CB} = \rho (L-x)$, where $L$ is the total length of the wire. This gives $\frac{R_1}{R_2} = \frac{x}{L-x}$. When the radius of the wire AB is doubled, its resistance per unit length becomes $\rho/4$. Let the new balance length be $x'$. The balance condition becomes $\frac{R_1}{R_2} = \frac{(\rho/4) x'}{(\rho/4) (L-x')} = \frac{x'}{L-x'}$. Since $R_1$, $R_2$, and $L$ remain unchanged, the balance length $x'$ must be equal to $x$. Therefore, Statement-1 is false.