State the principle of potentiometer. Draw a circuit diagram used to compare the emf of two primary cells. Write the formula used. How can the sensitivity of a potentiometer be increased?

Principle of potentiometer: The potential drop along any length of the wire is directly proportional to that length. When a constant current flows through a wire of uniform cross-section and composition then,
                          V ∝ l 

Comparison of emfs of two primary cells: The circuit diagram is shown in the figure.


When the key K is closed, a constant current flows the potentiometer wire. By closing key K₁, the null point can be obtained for cell E_1. The jockey is moved along the wire and adjusted till galvanometer shows no deflection. 
Suppose AJ₁ = l₁ is the balancing length for cell E₁.
Then E₁ = k l₁
where, k is the potential gradient.
Now, the null point is obtained for cell E₂ by closing key K₂.
Let AJ₂ = l₂ be the balancing length in this case.
Then E₂ = kl_{2
                      $\therefore \boxed{\frac{{\mathrm{E}}_2}{{\mathrm{E}}_1} = \frac{{\mathrm{l}}_2}{{\mathrm{l}}_1}}$} 

Hence, by increasing the length of a potentiometer's wire the sensitivity of a potentiometer can be increased.