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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