The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of 2 $$\Omega$$. The value of internal resistance of each cell is

Two identical cells provide the same current through $$R = 2\,\Omega$$ whether connected in series or parallel. Find the internal resistance of each cell.

EMF = $$2E$$, internal resistance = $$2r$$:

$$I_s = \frac{2E}{R + 2r} = \frac{2E}{2 + 2r}$$

EMF = $$E$$, internal resistance = $$r/2$$:

$$I_p = \frac{E}{R + r/2} = \frac{E}{2 + r/2}$$

$$\frac{2E}{2 + 2r} = \frac{E}{2 + r/2}$$

$$\frac{2}{2 + 2r} = \frac{1}{2 + r/2}$$

$$2(2 + r/2) = 2 + 2r$$

$$4 + r = 2 + 2r$$

$$r = 2\,\Omega$$

Hence, the correct answer is Option A: 2 $$\Omega$$.