A uniform wire AB of length 120 cm is connected across a battery. Two resistors, an unknown resistor R and a 15 resistor, are connected in series across AB such that R is connected to end A and the 15 resistor is connected to end B . A galvanometer connects the junction of the two resistors to a point P on the wire AB . If the galvanometer shows zero deflection when the distance of point P from A is 80 cm , the value

Step-by-step solution

For the galvanometer to show zero deflection, the circuit acts as a balanced Wheatstone bridge. The ratio of the resistances must be equal to the ratio of the corresponding lengths of the uniform wire. Given the total length L = 120 cm and the balancing length from A is l₁ = 80 cm . The remaining length of the wire is l₂ = 120 - 80 = 40 cm . Applying the balance condition: R 15 = l₁ l₂ R 15 = 80 40 R 15 = 2 R = 30 Answer: 30