2 electric bulbs of 50w and 100w are given. Which one will be brighter when they are connected 1) in series 2) in parallel and why?

For a given rated voltage bulb,

The resistance of 50W rated bulb is much more than that of the 100W bulb.resistance is given by:

     R=V²/P

and the total current in the circuit in series is given by:

        I=V/R_s

where R_s=R_A +R_B

as same current passes through each bulb when connected in series,50W bulb will glow brighter as power , P=I²R, is more in case of 50 W bulb.

 

similarly , when the bulbs are connected in parallel, 100W bulb will be much brighter as power ,P=V²/R ,is more in case of 100 W bulb.