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 A P is _ _ _ _ cm.

Step-by-step solution

In this potentiometer, for zero galvanometer reading, the potential at P must equal the potential at the junction between the 6Ω and 4Ω resistors. The voltage distribution across the resistors is V_ junction = E 6 6+4 = 0.6E from point A. Since the potentiometer wire is uniform with length 50 cm, the potential distribution is also uniform. Therefore, AP AB = 6 10 , giving AP = 50 0.6 = 30 cm.