Question

In the shown arrangement of a 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

The correct option is A $x$

From the arrangement in the figure, it is clear that the ratio of potential difference across the resistances $=\frac{V_{AC}}{V_{CB}}$

Now $V\propto I\times \rho \frac{l}{A}$

If $l_0$ is the length of wire AB, ratio of potential differences across the

resistances $=\frac{x}{l_0-x}$

Now if the radius of the wire AB is doubled, resistances of both the wires segments get one-fourth, hence current in the wire increases. Still the potential difference across the whole wire is same. Thus the same potential is there across the wire AB. Thus the same ratio of potentials is observed at segments of same length. Hence x does not change.