Length of a potentiometer wire is 200 cm when a 10 volt cell is used, its balancing length is 60 cm. Now the length of potentiometer wire is increased to 300 cm. In the case, what will be the balancing length of a 20 volt cell?

It λ be the resistance per unit length of the potentiometer wire, E0 be the emf of potentiometer driving cell, ε be the emf of cell used and l be its balancing length, then ε=(E0λL)(λl)⇒ε=E0lL∴ ε1=E0l1L1 and ε2=E0l2L2∴ ε2ε1=(l2l1)(L1L2)⇒2010=l260×200300⇒l2=180 cm