Figure shows a potentiometer wire AB having resistance of 5 and length 10 m. An e.m.f. is 0.4 V of battery, the balancing length AP is (internal resistance is negligible)

Step-by-step solution

Current in the primary circuit is given by: I = V R + R_ AB I = 5 45 + 5 = 5 50 = 0.1 A Potential difference across the potentiometer wire AB is: V_ AB = I R_ AB = 0.1 5 = 0.5 V Potential gradient (potential drop per unit length) of the wire AB is: k = V_ AB L = 0.5 10 = 0.05 V/m For balancing an e.m.f. E = 0.4 V , the balancing length l is given by: E = k l 0.4 = 0.05 l l = 0.4 0.05 = 8 m Answer: 8 m