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All the bulbs should be the same brightness because they are all receiving the same voltage, which would be half the voltage of the original source. To visualize why this is the case, imagine the electrons moving through the circuit. The electrons can take two paths through the circuit but either way they have to pass through two light bulbs. The two bulbs in parallel may, however, appear slightly dimmer because the current is split between them and restricted by the third bulb.

Assume that the resistance of all light bulbs are equal. The current through the light bulbs in parallel will be 1/2 that through the one in series as it is split equally between the two of them. The intensity of each light bulb is proportional to the power through each bulb. Power is I2R. So, if the total current is 1 amp the power through the series light bulb is R, where the power through the parallel light bulbs will be 1/4R. Therefore the intensity of the parallel bulbs will be 1/4 the light bulb in series.

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Q: If you have three light bulbs two are connected in parallel This combination is connected in series with the third bulb What is the relative intensity of each bulb?
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