In a meter bridge experiment, the balance point is found to be at 40 cm from the left end when an unknown resistance R is in the left gap and another unknown resistance S is in the right gap. When a 12 resistor is connected in parallel to S , the balance point shifts to 50 cm from the left end. The value of the resistance R is:

Step-by-step solution

Let the initial balance point be l₁ = 40 cm . According to the principle of the meter bridge: R S = l₁ 100 - l₁ = 40 60 = 2 3 S = 3 2 R When a 12 resistor is connected in parallel to S , the new resistance in the right gap becomes: S' = 12S 12 + S The new balance point is l₂ = 50 cm . The new balance condition is: R S' = 50 100 - 50 = 1 R = S' Substituting the expression for S' : R = 12S 12 + S Substitute S = 3 2 R into the equation: R = 12 ( 3 2 R ) 12 + 3 2 R R = 18R 12 + 1.5R Assuming R 0 , we can divide both si