As illustrated in the figure, the potentiometer wire AB has a total length of 50 cm . If the galvanometer shows zero deflection at AD = 30 cm , calculate the value of R .

Step-by-step solution

In a balanced meter bridge, the Wheatstone bridge principle is applicable as the galvanometer shows zero deflection. The ratio of the resistances is equal to the ratio of the corresponding balancing lengths of the wire. Given: Total length of the wire AB = 50 cm Balancing length AD = 30 cm Length DB = 50 - 30 = 20 cm Left resistance = 6 Right resistance = R Applying the balanced Wheatstone bridge condition: 6 R = AD DB 6 R = 30 20 6 R = 3 2 R = 6 2 3 = 4