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

Question

G1 Physics · Accepted Answer

At the balance point P, the potential of P on the potentiometer wire equals the potential of the junction of the 6 Ω and 4 Ω resistors. The 6 Ω and 4 Ω resistors form a potential divider across A and B. Therefore the resistance ratio of the two parts of the potentiometer wire must satisfy R(AP)/R(PB) = 6/4 = 3/2. Because the potentiometer wire is uniform, resistance is proportional to length: AP/PB = 3/2. Also, AP + PB = 50 cm. Thus, AP = [3/(3 + 2)] × 50 = 30 cm. Correct option: B.