The resistance of the bulb is defined as R =V2/P So the resistance of 50W bulb is double than the resistance of 100W bulb. When they are connected in series the current through both bulbs is same. Hence 50-watt bulb will be brighter because P=I2R. In parallel, the voltage will be same in both bulbs. So, the 100-watt bulb will be brighter because of P=V2/R.
