In a meter bridge experiment, an unknown resistance X is connected in the left gap and a standard resistance of 30 is connected in the right gap. The meter bridge wire has a uniform resistance of r / cm . When this wire is replaced by another uniform wire of the same length but having a resistance of 2r / cm , the balancing length from the left end is found to be 40 cm . The value of the unknown resistance X is:

Step-by-step solution

The balancing condition for a meter bridge is given by: X R = l 100 - l where l is the balancing length from the left end. The resistance per unit length of the meter bridge wire cancels out in the ratio, meaning the balancing length is independent of the uniform resistance per unit length of the wire. Since the new balancing length is 40 cm with the 2r / cm wire, the balancing length with the original wire would also have been 40 cm . Using the balancing condition: X 30 = 40 100 - 40 X 30 = 40 60 X 30 = 2 3 X = 30