I stumbled upon these sentences while studying and this seems to be horribly confusing.
resistance is proportional to the inverse of the power of the bulb in series connection and so the bulb with the lowest wattage(power) will have maximum resistance and it will glow the brightest.
But what i don't seem to understand is that the brightness of the bulb should depend on the power or heat dissipated(in case of an incandescent light bulb) then why is it that in this case the bulb with the lowest power or the highest resistance glows the brightest.
Moreover in the next paragraph, which is for bulbs in parallel connection, it is said that
As the resistance of the highest wattage (power) bulb is minimum, it will glow the brightest.
Another question that arises at this point is that why are the two paragraphs contradicting?
From both the paragraphs it is clear that the relationship used is
resistance is proportional to the inverse of the power $$P ∝ \frac{1}{R}$$
but then why wasn't the other two formulas used
$$P= VI = {I^2}R$$
according to
$$P= {I^2}R$$
resistance is directly proportional to the electric power so shouldn't the power increase with increase in resistance or vice-versa.
One thing that is to be kept in mind is that the bulbs were manufactured for working of the same voltage.
Best Answer
When the book says:
What it is referring to is the power rating of the bulb. This power rating assumes the bulb has a potential difference across it of 120 V (in North America at least - maybe 220 V in India). So, if you compare a bulb rated at 60 watts and a bulb rated at 100 watts the 100 watt bulb will have a lower resistance and draw more current when they are connected in parallel (they way they are designed to used).
If, on the other hand, you connect the bulbs in series, then what is constant is the current not the voltage. The bulb with the highest power rating, which has the lowest resistance, will thus have the smaller voltage drop across it and thus will dissipate the smaller amount of power.