Question

In a potentiometer experiment the following circuit arrangement is used. AB is the potentiometer wire.

When the key K₁ is closed (K₂ open), the balancing length is found to be l . When the key K₂ is closed (K₁ open), the balancing length is found to be 2l . The value of r, in terms of R₁ and R₂ , is

(1) \(\frac{R_1R_2}{R_2-R_1}\)

(2) \(\frac{2R_1R_2}{R_2-R_1}\)

(3) \(\frac{R_1R_2}{R_2-2R_1}\)

(4) \(\frac{2R_1R_2}{R_2-2R_1}\)

Answer 1

 (3) \(\frac{R_1R_2}{R_2-2R_1}\)

Let V₁ be the terminal voltage when K₁ is closed, that is ,when R₁ is connected across the cell of emf E and internal resistance r.

Let V₂ be the terminal voltage when K₂ is closed.

Dividing (1) by (2), we get: