Question

In the shown arrangement of the experiment of the meter bridge if $AC$ corresponding to null deflection of galvanometer is $x$, what would be its value if the radius of the wire $AB$ is doubled?

• A. $x$
• B. $x/4$
• C. $4x$
• D. $2x$

Answer 1

Answer: (A)

$x$

Resistance of wire between A and C $R_{AB}=\rho \frac{x}{A}$ where A is the radius of the wire and x is the length of wire in cm between A and C.

Resistance of wire between B and C $R_{BC}=\rho \frac{100-x}{A}$

Using $\frac{R_1}{R_{AB}}=\frac{R_2}{R_{BC}}$

$\therefore$ $\frac{R_1}{\rho \frac{x}{A}}=\frac{R_2}{\rho \frac{100-x}{A}}$ $⟹\frac{R_1}{x}=\frac{R_2}{100-x}$

Thus position of balance point does not depend on the radius of wire.