What are the pros and cons for using electrolytic capacitors in a voltage divider circuit to provide about 24 volts AC to a heater cable from the 120 volt AC line?
Is there a possibility of having a capacitor explode from overheating? If so, could that be prevented by stringing several capacitors in parallel to provide for additional heat dissipation?
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Electrolytic capacitors are polarized and every half cycle of the powerline their polarity will be reversed. Depending on the values and types, they may get hot, or more exciting, blow out their pressure relief attended by a puff of smoke and fumes. In any case, their life is rapidly shortened if reversed. Non polarized caps are available but it all depends on the values needed. Most other capacitors are non-polpoarized and they should work for you.
Mr. Gotts seeks information on employing the reactive property of a capacitor to reduce AC line voltage to 24 volts.
The short answer is “Don’t do it.”
Been there. Done that. Didn’t know any better. In my case, I had a small circuit comprising one vacuum tube having a 12-volt filament drawing 0.15 amperes. Dropping the voltage from 120 volts required a series impedance of 720 ohms. Like you, it occurred to me that the reactive impedance of a capacitor might provide the needed voltage drop, eliminating a large (and hot) series resistor. A capacitor of 3.7 uF at 60 Hz provided the necessary 720-ohm impedance.
The technique worked and nothing blew up. I was lucky. Seventy subsequent years of experience, however, lead me to consider the reasons NOT to use this technique:
One would never use an electrolytic capacitor for this job. Film-dielectric non-polarized motor-start and motor-run capacitors are available with operating voltage ratings suitable for the job. But the off-the-shelf tolerances of such devices is relatively large, running to 6% for motor-run capacitors and 10% for motor-start capacitors. For a 24-volt resistive load supplied through an off-the-shelf motor-run capacitor, the load voltage may be anything from 22 to 25 volts.
A small transformer is less expensive than a motor-start or -run capacitor, it provides safety isolation from the AC line, and the load voltage won’t oscillate.
That is not at all practical. Use a 24 volt transformer from a sprinkler timer or thermostat.
Most aluminum electrolytic capacitors are not suited to having large amounts of AC voltage on them. Also they have to be used in pairs, to handle both polarities of voltage. And yes, you may have them overheat and "rapidly disassemble."
Also the heater cable will not be isolated from the AC line, which may be hazardous under fault conditions. You didn't say how much current you needed at 24VAC, but I assume it might be more than an ampere. My first choice would be a 120:24V transformer. You'd get decent efficiency and isolated power.