In a meter bridge experiment, the condition for null deflection in the galvanometer is given by:
where:
- and are the resistances in the two arms of the bridge,
- is the distance from point A to point D where the galvanometer shows null deflection, and
- is the total length of the wire AB (usually 1 meter).
Initially, the null deflection occurs at a distance . If the radius of the wire AB is doubled, its cross-sectional area becomes 4 times the original area ( ), since the area is proportional to the square of the radius ( ).
The resistance of a wire is given by , where is the resistivity. Since the resistivity and length of the wire remain constant, the resistance is inversely proportional to the area. Therefore, when the area becomes 4 times larger, the resistance of the wire becomes times the original resistance.
Let the initial resistance of wire AD be and the resistance of wire DB be . Then .
Now let be the distance corresponding to null deflection when the radius is doubled. Let be the new radius
Then
The resistance of the wire segment AD changes to , and the resistance of segment DB changes to
We have
Since the resistances connected to the gaps are not changed, we have
Therefore, .
The correct answer is (A) X.
