Three bulbs rated 40 W, 60 W, & 100 W are connected in series across a constant voltage source. Which one will be the brightest? Why?
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If the bulbs give their rated power when connected to voltage E, then their resistance R and power P are connected by
P =E^2/R
R = E^2/P
ie resistance is inversely proportional to power
Thus the bulbs have resistances in the ratio 10:6:4
When connected in series, the same current flows through each of them, and the voltage across each one is proportional to the resistance.
Therefore the greatest power is dissipated in the highest resistance; the 40W bulb is brightest.
P =E^2/R
R = E^2/P
ie resistance is inversely proportional to power
Thus the bulbs have resistances in the ratio 10:6:4
When connected in series, the same current flows through each of them, and the voltage across each one is proportional to the resistance.
Therefore the greatest power is dissipated in the highest resistance; the 40W bulb is brightest.
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You forgot an important part of the question.
The bulbs are all rated to used the same voltage.
Otherwise the answer is indeterminate.
You have been given the answer in terms of the resistance of the bulbs.
But if one is rated at 100 W 240 v
and one is 60 W 110 V
and one is 40 W at 12 V
then the resistances as shown are incorrect and you would get different results.
In the example I give the 100 W bulb has the highest resistance and would be the brightest in the circuit.
The bulbs are all rated to used the same voltage.
Otherwise the answer is indeterminate.
You have been given the answer in terms of the resistance of the bulbs.
But if one is rated at 100 W 240 v
and one is 60 W 110 V
and one is 40 W at 12 V
then the resistances as shown are incorrect and you would get different results.
In the example I give the 100 W bulb has the highest resistance and would be the brightest in the circuit.