In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36 cm length of wire. This cell is now replaced by another cell of emf 1.80 V. The difference in balancing length of potentiometer wire in above conditions will be ___________ cm.

Solution

Physics sir · 3 steps

Balancing length is proportional to emf, so 1.5 times the emf needs 1.5 times the length.

1. Why length tracks emf. The driver cell sends a steady current through the wire, so every centimetre has the same potential drop k. At balance no current flows through the cell, so its emf equals the drop across the balancing length: E = kl.

   E₂/E₁ = l₂/l₁

2. Find the new length. l₂ = 36 × 1.80/1.20 = 36 × 1.5 = 54 cm.
3. So. The difference is 54 - 36 = 18 cm.

The common slip: 54. Reporting the new balancing length instead of the difference gives 54, not 18.

The idea to keep. In a potentiometer, emf is proportional to balancing length as long as the driver circuit is unchanged. Set up the ratio, and read the question for whether it wants the new length or the change.

Answer from the NTA final answer key. Solution by PrepWiser.