A potentiometer of length L is used to compare emfs. If the balance lengths for cells of emf ε₁ and ε₂ are l₁ and l₂ respectively, then ε₁ / ε₂ equals

1. In a potentiometer, the emf being compared equals K × l, where K is potential gradient and l is balance length. 2. For emf ε₁, ε₁ = K × l₁; for emf ε₂, ε₂ = K × l₂. 3. Dividing the two equations, ε₁ / ε₂ = l₁ / l₂. 4. So the ratio of emfs equals the ratio of balance lengths (K cancels). _Source: syllabus Physics, Ch 3 "Current Electricity", §3 potentiometer_