In a meter bridge experiment, a resistance of 20 is connected in the left gap and a resistance of 30 is connected in the right gap. To shift the balance point to exactly the center of the bridge wire ( 50 cm from the left end), an unknown resistance X is connected in parallel with the 30 resistance. The value of X is ______ .

Step-by-step solution

For the balance point to be at 50 cm , the effective resistance in the left gap must be equal to the effective resistance in the right gap. Let the effective resistance in the right gap be R_ eff . 20 R_ eff = 50 100 - 50 = 1 R_ eff = 20 Since X is connected in parallel with the 30 resistance, we have: 1 R_ eff = 1 30 + 1 X 1 20 = 1 30 + 1 X 1 X = 1 20 - 1 30 = 3 - 2 60 = 1 60 X = 60 Answer: 60