Bulb Brightness When the Circuit Changes

Brightness tracks power dissipated in the bulb, P = I² R = V²/R. In a parallel arrangement across an ideal battery (zero internal resistance), every branch sees the full terminal voltage no matter what the other branches are doing. Unscrew one bulb and you break only that branch; the voltage across every remaining bulb is still the battery voltage, so their currents and brightness don't budge. The battery simply supplies less total current, since one path for charge is gone.

A switch that opens a new branch adds a parallel path. Current through existing branches is set by V/R for each, unchanged, while the battery now delivers the sum of all branch currents, so total current goes up. A switch that shorts out one bulb is different: it gives charge a zero-resistance detour around that bulb, so essentially all current takes the short path, the shorted bulb goes dark, and the other bulbs in the circuit are unaffected if they're on separate parallel branches tied to the same ideal source.

This connects to the next idea: real batteries have internal resistance, so adding or removing parallel bulbs does change the terminal voltage and therefore does dim or brighten the others. That's the bridge from this ideal-battery intuition to analyzing circuits with internal resistance, where every branch's current depends on everyone else's.