Comparison of EMF's of Two Cells using potentiometer

A battery of emf ε is connected the end terminal A and B of potentiometer wire with rheostat R_h, ammeter A₁ and key K in series. This is called an auxiliary circuit. Two cells of emf ε₁ and ε₂ are connected as shown in the figure. Positive terminals of the cells connected to A of potentiometer. Negative terminal connected to jockey as shown in figure.

  

Close the Key K and join the terminals 1 and 3 and find out the ε₁ when galvanometer shown no deflection. Suppose no deflection is at l₁ of potentiometer wire, then

ε₁ = Kl₁                                                                                     ……1

Similarly connect 2 and 3 terminal and find out ε₂ when there is no deflection in galvanometer. Suppose no deflection is at l₂ of potentiometer wire, then

ε₁ = Kl₂                                                                                     ...…2

Divide 1by 2 we get

ε₁/ ε₂ = l₁/l₂