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Question

if a bulb is connected in series with two bulbs parallels to each other which formula should I useto find which is more bright? why can't I use heat directly proportional to power and the relation of power in series and parallel? How do I know which relation to use in a question because heat is directly proportional to resistance in one formula and inversely proportional to it in other?


Solution

The power dissipated by a bulb is given by
P = V2/R    (1),
where V is the voltage on the light bulb and R is the electrical resistance.
First, we simplify the circuit where the light bulbs are in series.
The total resistance of the series circuit is
Rseries = R + R = 2R.
Secondly, we simplify the circuit where the light bulbs are in parallel.
The total resistance of the parallel circuit is
1/Rparallel = 1/R + 1/R
or
Rparallel = R/2.
Thereby, the power for the light bulbs in series is
Pseries = V2/2R    (2)
and the power for the light bulbs in parallel is
Pparallel = 2V2/R    (3)
Now we can divide equation (2) by equation (3) and we get
Pseries/Pparallel = 1/4
Finally, we can see that in parallel circuit the bulbs will shine brightly.

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