JEE Main 2022 · 29 June · evening · Single correct · +4 / −1
The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of 2Ω. The value of internal resistance of each cell is
- (a) 2Ω
- (b) 4Ω
- (c) 6Ω
- (d) 8Ω
Answer and solution
Answer (a) 2Ω
Solution
Physics sir · 3 steps
Write the current for series and for parallel, set them equal, and r drops out as equal to R.
- Series. In series the EMFs add to 2E and the internal resistances add to 2r. The current through R is Iₛ = 2E/(2r + R).
- Parallel. In parallel the EMF stays E and the internal resistance becomes r/2. The current is Iₚ = E/(r/2 + R) = 2E/(r + 2R).
2E/(2r + R) = 2E/(r + 2R) ⇒ 2r + R = r + 2R ⇒ r = R
- So. With R = 2 Ω, each cell has r = 2 Ω. Check: both currents come out to E/3. The answer is (a).
The idea to keep. Two identical cells give the same current in series and in parallel only when each cell's internal resistance equals the external resistance. Remember r = R.
Answer from the NTA final answer key. Solution by PrepWiser.