In metre-bridge experiment the balance point is obtained if the gaps are closed by 2 and 3 . A shunt of x is added to 3 resistor to shift the balance point by 22.5 cm . The value of x is

Step-by-step solution

The metre bridge operates on the Wheatstone bridge principle, with the balance condition R₁ R₂ = l 100 - l where l is the length from the R₁ side. With R₁ = 2 and R₂ = 3 , the initial balance point satisfies 2 3 = l 100 - l , yielding l = 40 cm. When a shunt resistance x is added in parallel to 3 , the equivalent resistance becomes R₂' = 3x x + 3 . The balance point shifts by 22.5 cm to l' = 62.5 cm. The new balance condition gives 2 3x x + 3 = 62.5 37.5 , which simplifies to 2(x + 3) 3x = 5 3 . Solving 2(x + 3) =