Electrical – Is it safe to use a string of lights with one shattered

TL;DR: the dimmers aren't switching off completely: they're allowing some current to leak through, which is why you're seeing a voltage across the CFL. A different make of bulb may behave better with the leakage current that you're getting. Or perhaps a different brand of fan (if you haven't installed them all already).

I do know that operating CFLs in those sort of conditions will shorten their lives considerably, so you might actually be cheaper for you to use incandescents instead (a quick calculation says about 12 kWh per year for a 60 W bulb).

Read on for the technical explanation...

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This is a circuit diagram of the innards of your fans:

The voltage across the bulbs, V_b is determined by the formula:

V_b = V_in * R_bulb / (R_dimmer + R_bulb)

where:

• V_in is the mains voltage (120Vac or 240Vac depending on country).
• R_bulb is the resistance across the bulb or bulbs.
• R_dimmer is the resistance across the dimmer.

The dimmer is a solid-state electronic circuit, so it has a very high effective resistance -- 10s of megohms is not unreasonable. Ditto for the control circuitry in the CFL. An incandescent bulb is a simple piece of resistive wire; a 60 W / 120 V bulb will have a resistance of 240 ohms.

Now, suppose the dimmer has a resistance of 50 MOhms and the CFL has a resistance of 10 MOhms; plugging the numbers into the equation above gives you 20 V across the bulb. OTOH, the voltage across a 60 W incandescent bulb will be about 600 microVolts, nowhere near enough to make the bulb glow.

If you have two bulbs in the light fixture, the resistance, R, of the two in parallel is given by:

R = R₁*R₂/(R₁ + R₂)

So if you have a CFL and an incandescent installed, the effective resistance is going to be very close to that of the incandescent alone:

R = 10,000,000 * 240 / (10,000,000 + 240) = 239.99 Ohms

Again, not enough to turn on either bulb.

With two incandescent bulbs, the effective resistance is half that of a single incandescent, so you have half the voltage across them.

The flickering you see with two CFLs is because the light you see is basically a high-voltage spark through the tube. The CFL contains circuitry to amplify the incoming voltage up to the point where the spark can occur. Under normal circumstances, the input voltage is enough to cause this spark 100 or 120 times per second (depending on mains frequency), which is far too frequent for the human eye to notice. With the reduced input voltage, it takes longer to reach the required voltage, so you notice the flicker. No two bulbs will be exactly identical, so they'll flicker at different rates and take different times to recover between discharges.

Often with light fixtures, each light has a pair of wires that come up and out of the fixture. You wire all of the hots together with the line hot, and all of neutrals together with the line neutral. If the wire nuts that connect all of the wires were not installed properly, it is possible that one of the wires is no longer making a solid electrical connection. It is also possible that one of the wires is damaged.

I would suggest that you remove the light fixture and examine all of the connections. Look for loose wires (you should not be able to easily pull them out of the wirenut), nicks, burns, etc.

If everything is visually OK you should test each wire to each socket with a multimeter. Test for continuity by ensuring resistance goes close to 0 when you make a connection. Repeat this until you find the problem. Make sure the power is off when you do this.