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Two identical cells of the same e.m.f. and same internal resistance give the same current through an external resistance 2 Ω, regardless of whether they are connected in series or parallel. The internal resistance of the cell is
  • a)
    1 Ω
  • b)
    2 Ω
  • c)
    3 Ω
  • d)
    4 Ω
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Two identical cells of the same e.m.f. and same internal resistance gi...
Given information:

- Two identical cells have the same e.m.f. and the same internal resistance.
- The external resistance is 2 Ω.
- The current through the external resistance is the same whether the cells are connected in series or parallel.

To find: The internal resistance of the cell.

Solution:

Let the e.m.f. of each cell be E and the internal resistance of each cell be r.

Case 1: Cells are connected in series

In this case, the total e.m.f. is 2E and the total internal resistance is 2r. The current through the external resistance is given by:

I = (2E) / (2r + 2Ω)

Simplifying the above equation:

I = E / (r + 1Ω)

Case 2: Cells are connected in parallel

In this case, the total e.m.f. is E and the total internal resistance is r/2. The current through each cell is:

I1 = E / (r/2 + 2Ω)
I2 = E / (r/2 + 2Ω)

The total current through the external resistance is:

I = I1 + I2

Simplifying the above equation:

I = 2E / (r + 4Ω)

As per the given information, the current through the external resistance is the same in both cases. Therefore, equating the above two expressions for I:

E / (r + 1Ω) = 2E / (r + 4Ω)

Simplifying the above equation:

r = 2Ω

Therefore, the internal resistance of the cell is 2 Ω.

Answer: Option B.
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Two identical cells of the same e.m.f. and same internal resistance give the same current through an external resistance 2 Ω, regardless of whether they are connected in series or parallel. The internal resistance of the cell isa)1 Ωb)2 Ωc)3 Ωd)4 ΩCorrect answer is option 'B'. Can you explain this answer?
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