Two identical cells, when connected either in parallel or in series gives same current in an external resistance 5 Ω. The internal resistance of each cell will be ___________ Ω.

Solution

Physics sir · 3 steps

Write the current for both connections, set them equal, and the internal resistance falls right out.

1. Series connection. The EMFs add to 2E and the internal resistances add to 2r. So the current is Iₛ = 2E/(R + 2r).
2. Parallel connection. Identical cells in parallel keep the EMF at E, and the internal resistance becomes r/2. So the current is Iₚ = E/(R + r/2) = 2E/(2R + r).

   2E/(R + 2r) = 2E/(2R + r) ⇒ R + 2r = 2R + r ⇒ r = R

3. So. With R = 5 Ω, the internal resistance of each cell is r = 5 Ω.

The idea to keep. Two identical cells give the same current in series and in parallel only when r = R. Remember that parallel identical cells keep EMF E but halve the internal resistance.

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