Q. For the two cells having same EMF E and internal resistance r, the current passing through the external resistor 6Ω is same when both the cells are connected either in parallel or in series.

The value of internal resistance r is _____ Ω.

(A) 3

(B) 6

(C) 4

(D) 9

Correct Answer: 6

Explanation

When two identical cells each of EMF E and internal resistance r are connected in series, the equivalent EMF becomes 2E and equivalent internal resistance becomes 2r.

Current in series combination,
I_s = 2E / (6 + 2r)

When the same two cells are connected in parallel, the equivalent EMF remains E and equivalent internal resistance becomes r/2.

Current in parallel combination,
I_p = E / (6 + r/2)

Given that the current through the external resistor is same in both cases:

2E / (6 + 2r) = E / (6 + r/2)

Cancelling E from both sides and solving:

2(6 + r/2) = 6 + 2r

12 + r = 6 + 2r

r = 6 Ω

Hence, the value of internal resistance is:

6 Ω

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