Meter Bridge

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.