Two identical cells each of emf 1.5 V are connected in series across a 10 $$\Omega$$ resistance. An ideal voltmeter connected across 10 $$\Omega$$ resistance reads 1.5 V. The internal resistance of each cell is _______ $$\Omega$$.

Two identical cells in series: Total EMF = $$2 \times 1.5 = 3$$ V, total internal resistance = $$2r$$.

The voltmeter reads 1.5 V across the 10 Ω resistance.

Current through the circuit:

$$I = \frac{V}{R} = \frac{1.5}{10} = 0.15 \text{ A}$$

Also, using Ohm's law for the full circuit:

$$I = \frac{\text{Total EMF}}{R + 2r} = \frac{3}{10 + 2r}$$

Equating: $$0.15 = \frac{3}{10 + 2r}$$

$$10 + 2r = 20$$

$$2r = 10$$

$$r = 5 \text{ Ω}$$