Suppose that the resistors in the various circuit diagrams represented the resistances of lightbulbs. When a lightbulb "burns out," the circuit is open through that particular component, that is R is infinite. Would the remaining bulbs continue to burn?

The Remaining Bulbs will either burn out( draw more current ) or Not burn out depending on the arrangement of the bulbs in the circuit

Explanation:

The Remaining Bulbs will either burn more brightly ( draw more current ) or Burn less brightly ( draw less current).and this depends on the arrangement of the light bulbs in the various circuit.

If the light bulbs are connected in series the remaining bulbs will burn out as soon as  any light bulb burns out and this is because bulbs connected in series receive the same amount of current ,

If the light bulbs are connected in parallel the remaining bulbs will not burn out because each bulb receives current based on its resistance.

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