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I read this about Christmas mini-lights in series: "When one bulb's filament breaks, current stops flowing, so the remaining lights go out, and the full 120V appear across the broken filament. This means that even though the bulbs are designed to operate at 2V, they have to withstand 120V across the broken filament."

What does it mean "120V "appear across the broken filament"? Is this because the other bulbs are cold so their resistance is near 0Ω?

And what does it mean "withstand 120V across the broken filament"?

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  • \$\begingroup\$ 'withstand 120 V' means safely, without catching fire, or creating a shock hazard to somebody touching the holder. \$\endgroup\$
    – Neil_UK
    Jan 14, 2022 at 19:34

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Let's use resistors instead of lightbulbs...

With N identical resistors of value R in series, total resistance will be N*R. With a voltage source V, a current V/NR will flow, and there will be V/N volts across each resistor.

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If one resistor (lightbulb) is removed, the circuit is open, so there will be no current.

enter image description here

With no current, there is no voltage drop across the remaining resistors (R*I=0 because I=0), therefore the full voltage V appears across the missing resistor.

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    \$\begingroup\$ And the important bit is that when you poke your fingers in the sockets you are exposed to the full line voltage. \$\endgroup\$
    – Transistor
    Jan 14, 2022 at 19:58
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    \$\begingroup\$ If I understand, in an open circuit the resistors, lamps and any other loads all have zero resistance because there is 0 current, so they all behave as if they were wires? \$\endgroup\$ Jan 15, 2022 at 13:55
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    \$\begingroup\$ They still have their resistance, but since there is no current flowing through it, the resistance doesn't matter. \$\endgroup\$
    – bobflux
    Jan 15, 2022 at 15:43
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    \$\begingroup\$ So it's just that there will be no voltage drops over the resistors and other loads when there is no current. \$\endgroup\$ Jan 15, 2022 at 20:42
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    \$\begingroup\$ Yes, that is correct. \$\endgroup\$
    – bobflux
    Jan 15, 2022 at 21:08
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There is no current flowing so there is no voltage drop across any of the other bulbs.

So, the open circuit voltage at the broken filament is equal to the applied voltage.

The circuit, when all bulbs are working, is designed that each bulb drops a fraction of the total voltage applied, so 10 bulbs of 12V each is 120V, or for 240V there can be 20 bulbs. Of course if 6V bulbs are used then you can have a 40 bulb string.

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