If two bulbs, one of 200 W and the other of 100 W are connected in series with a 100 V battery, then which bulb will have more brightness?

100 W bulb will have more brightness.

Electric power is the rate at which the electric energy is dissipated or consumed.

$R=\frac{V^2}{P}$

$R \alpha \frac{1}{P}$

The resistance of the bulb is inversely proportional to the power of the bulb.

So, the bulb which has more power will have low resistance(i.e. 200 W bulb will have low resistance)

The heat dissipated by the bulb:

$\mathrm{H}={\mathrm{I}}^2\mathrm{R}$

Heat dissipated will be more in the bulb with more resistance.

Heat dissipation of 100 W bulb will be more, so 100 W bulb will have more brightness. Because the brightness of the bulb depends on the heat dissipation by the bulb.