A `100W` and a `500W` bulbs are joined in series and connected to the mains which bulb will glow brighter?

Explanation

Let `R_(1)` and `R_(2)` be the resistance of the two bulbs. If each bulb is connected separately to the mains of voltage V,
then `P_(1) =V^(2)/R_(1)` and `P_(2) =V^(2)/R_(2)`
`therefore P_(1)/P_(2) =R_(2)/R_(1)` (or ) `R_(1)/R_(2) =P_(2)/P_(1) =500/100=5`
If the two bulbs are in series with the mains, the same current .i. flows through each of them.
Let `P_(1)` and `P_(2)` bee the powers dissipated by two bulbs, turn
`P_(1)^(1) = i^(2)R_(1)` and `P_(2)^(1) =i^(2)R_(2)`
`therefore P_(1)^(1)/P_(2)^(1) =R_(1)/R_(2) =5` or `P_(1)^(1) =5P_(2)^(1)`
Since 100 watt bulb dissipates more power, it glows brighter.