A meter bridge has unknown end corrections and at the left and right ends, respectively. When two resistors R₁ and R₂ are placed in the left and right gaps respectively, such that R₁ R₂ = 1 2 , the balance point is found at 33 cm from the left end. When the resistors are interchanged, the new balance point is found at 68 cm from the left end. The value of the right end correction is ______ cm .

Step-by-step solution

Let the total length of the meter bridge wire be 100 cm . Taking end corrections into account, the balanced Wheatstone bridge condition is: R_ left R_ right = l + 100 - l + For the first case: 1 2 = 33 + 100 - 33 + = 33 + 67 + 67 + = 66 + 2 2 - = 1 (1) For the second case, the resistors are interchanged, so the ratio becomes 2 1 : 2 1 = 68 + 100 - 68 + = 68 + 32 + 64 + 2 = 68 + - 2 = -4 (2) Multiplying equation (2) by 2 , we get: 2 - 4 = -8 (3) Subtracting equation (3) from equation (1): (2 - ) - (2 - 4 ) = 1 - (-8