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If the bulbs are in parallel, other bulbs aren't affected, so I guess you mean a series circuit.

A string of light bulbs connected in series (like a Christmas light string) connected to a specific supply voltage can be visualised as a string of rubber bands, knotted to each other in a line, and stretched to a specific distance.

If all the rubber bands are the same, they will all stretch equally, i.e. if all bulbs are the same, they will all have the same voltage across them.

Increasing the resistance of one bulb is like making one rubber band thinner than the others, and you can imagine what will happen.

The thin rubber band will stretch more than the others, and the others will take up the slack and become a bit shorter, i.e. the bulb with higher resistance will have more voltage across it, and the remaining bulbs will have slightly less than before.

The current (i.e. the tension in the string of rubber bands) reduces slightly.

Looking at the power dissipation for that light bulb, which is voltage x current, voltage will increase, and current will drop slightly, so the overall effect is that the bulb with the higher resistance will dissipate more power than the others.

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If you add an extra bulb to your series circuit what will happen to the brightness of your bulbs?

They will dim because you have more resistance in the circuit. More resistance means less current which means less light. The power is P=V*I = I/R*I = I²/R Think of blowing through one straw. Now attach a second straw end on with no leaks between joints and then attach a third straw in a long line. Which one is the easiest to blow?