The total length of potentiometer wire AB is 50 cm in the arrangement as shown in the figure. If P is the point where the galvanometer shows zero reading then the length AP is ________ cm.

Solution

Physics sir · 4 steps

Zero deflection means the top junction and P sit at the same potential, so the wire splits like 6 to 4.

1. Spot the bridge. The 6 Ω and 4 Ω resistors in series and the wire AB are both connected across the same battery. With the galvanometer between their middle points, this is a Wheatstone bridge, just like a metre bridge.
2. Balance condition. At null, no current flows through G. So the potential drop across 6 Ω equals the drop across AP, and the drop across 4 Ω equals the drop across PB. For a uniform wire, resistance is proportional to length.

   6/4 = AP/PB = AP/(50 - AP)

3. Solve. 6(50 - AP) = 4 AP, so 300 = 10 AP and AP = 30 cm. Check: PB = 20 cm, and 30 : 20 = 6 : 4.
4. So. The null point P is 30 cm from A, which is option (b).

The idea to keep. At a null point, match each resistor to the wire segment on the same side of the galvanometer. Then the lengths divide in the same ratio as the resistances.

Answer from the NTA final answer key. Solution by PrepWiser.