As I have been recently toying with the idea of using step up transformers to run HID lamps on reactor ballasts, I am also starting to toy with the idea of resistively ballasting HID lamps on step up transformers too where the step up transformer’s secondary coil provides the open circuit voltage to the lamp

For this to work, can I simply determine the appropriate resistance of a resistor by substituting the transformer’s secondary voltage and the lamp’s operating current into Ohm’s Law V = IR?

In addition, should I also be fine with using P = IV to determine an appropriate incandescent lamp wattage for ballasting HID and fluorescent lamps using incandescent lamps?

In addition, can a rheostat function as a resistive ballast for fluorescent and HID lamps too?

This is all possible, but you must give the due attention to detail to get it right. Here are some of the things :

For this to work, can I simply determine the appropriate resistance of a resistor by substituting the transformer’s secondary voltage and the lamp’s operating current into Ohm’s Law V = IR?

When you use Ohms law (V = IR) or power calculation (P = IV etc), you must use all resistance, voltage, current measurements/specs of the same component that you are calculating. Then the result applies to the same component

What you asked here would work if you are simply using the transformer to power a resistor. V (of the resistor, which is connected directly to the transformer) = I R

When you connect the resistor in series with a HID lamp (or in any series connection with anything), then to find R of the resistor you must use V measured across this resistor, not the transformer output. In a ballast application, Vresistor = Voc - Varc



For some components, the resistance is not a meaningful value you can use in calculations. Physically it exists, but it depends in complicated ways on other things which are likely the ones you are trying to calculate :

Electrical arcs (including the discharge in a mercury lamp) have a voltage drop which depends on the arc physical properties - Gas type and pressure, gap between electrodes, etc. It is virtually independent of the current - The same or nearly the same voltage drop could exist in the same lamp with very different current conditions

If you look at this from the other side, it means that the lamp arc current cannot be controlled by controlling the applied voltage. This is why discharge lamps need a ballast in the first place - The current must be controlled directly, as controlling the voltage has no effect

Example : Find resistance of 125W Mercury lamp. On its proper ballast it will run with arc = 125V 1.15A. R = 125/1.15 = 109 Ohms. On a 80W ballast the arc V might stay the same or drop a little, but current will be around 0.8A. R = 120/0.8 = 150 Ohms. If overpowered on a 250W ballast it may be something like 140V/2.5A = 56 Ohms

In addition, discharge lamps have a non unity lamp power factor, even when resistively ballasted. It is caused by the arc extinguishing when the sine wave voltage is too low, and restriking with a delay and at a different voltage in the next AC half cycle. The lamp power factor is typically around 0.85 for mercury and fluorescent lamps on magnetic ballast, might be a bit lower on resistive ballast. This may cause some mismatch in your calculations and measurements

Incandescent lamp resistance is changing with the filament temperature

Example : 120V 100W Incandescent lamp. 100W/120V = 0.83A, 120V/0.83A = 145 Ohms. If you measure the resistance of a cold lamp with a multimeter you'll get on the order of 10 Ohms. (I tested and got about 40 Ohms with a 230V lamp, i assume it will be 1/4 that in 120V lamp). If the lamp is powered at some power level other than 100W (say on a dimmer), its resistance will be somewhere inbetween accordingly

In addition, should I also be fine with using P = IV to determine an appropriate incandescent lamp wattage for ballasting HID and fluorescent lamps using incandescent lamps?

When used as a ballast, the voltage the lamp gets will be what it gets in the series circuit (generally Voc - Varc). You have to design the circuit so that you don't exceed the voltage rating of the incandescent lamp (or it will burn out). This generally means that in the final working state with a fully warmed up HID lamp, the incandescent will be working at reduced voltage, so lower power than its rating

Be aware that HID lamp voltage drop varies as the lamp warms up. In particular, a cold lamp just ignited can have arc voltage in the <20V range, which means almost the full transformer Voc applied to the incandescent lamp for a moment. So you cannot, for example, use 120V lamp to ballast a mercury lamp on a 208/220V transformer, as in the first moments of switch on the lamp could get over 200V and burn out immediately. In a setup like this use 240V lamps or 2x 120V lamps in series. (x one or more lamp sets in parallel to get the wanted current)

In addition, can a rheostat function as a resistive ballast for fluorescent and HID lamps too?

With any resistor, you must observe its power rating. Calculating P = VI (or P = V^2 / R, or P = I^2 R) if the power dissipation on the resistor is higher than the resistor's power rating, it will burn

If you are calculating the power dissipation of the resistor, then you use the voltage, current and resistance values measured on this resistor and not on the main supply or somewhere else

If your resistor is a rheostat, the part of the resistor that is active is changed by a slider. So does also its power rating. If say you have a 500W rheostat and the slider is positioned so only 1/4 of the resistance is in circuit, then the power rating is also only 1/4 of the full 500W

All power resistors get very hot. It is not uncommon for chassis mount power resistors to get over 200C (392F) when used at their rated power - by design. With a big enough resistor, just the IR emitted from it can melt things around it. If you dont want the resistor to get to such temperatures, you must use it way below its max ratings

A space heater which is just resistive (IR heater, bar heater, oil filled radiator) without built in fans or fancy controls, can be used as a high power resistor

Power resistors, space heater elements etc. are a better ballast for HID lamp starting, as they dont have as much inrush current as incandescents

As I have been recently toying with the idea of using step up transformers to run HID lamps on reactor ballasts, I am also starting to toy with the idea of resistively ballasting HID lamps on step up transformers too where the step up transformer’s secondary coil provides the open circuit voltage to the lamp

For this to work, can I simply determine the appropriate resistance of a resistor by substituting the transformer’s secondary voltage and the lamp’s operating current into Ohm’s Law V = IR?

In addition, should I also be fine with using P = IV to determine an appropriate incandescent lamp wattage for ballasting HID and fluorescent lamps using incandescent lamps?

In addition, can a rheostat function as a resistive ballast for fluorescent and HID lamps too?

Yes you can, that is the way self-ballasted mercury lamps work.

You can *approximately* use Ohms law on the difference between OCV and lamp running voltage. This is only a rough first approximation, you should measure the resulting current and adjust the resistance accordingly, as lamp's voltage and current is not exactly sinewave.

You can use adjustable rheostats but you need to account for a huge dissipated power (usually about the same as lamp's power) and be careful with electrical safety of many open parts.

Resistive ballast will lack re-ignition kicks that inductive circuits have. Usually mercury lamps are OK with this with their clean burner fill atmosphere, but MH lamps may have trouble.

In addition, should I also be fine with using P = IV to determine an appropriate incandescent lamp wattage for ballasting HID and fluorescent lamps using incandescent lamps?

Approximately, but beware incandescent lamp resistance is hugely non-linear depending on filament temperature (~=applied voltage). So while for the lamp running at full line voltage calculated resistance will approximate etch stated power, for a lamp running at half voltage the resistance will be a bit lower, and actual current a bit higher that 1/2 of nominal. That of course can be adjusted experimentally.

BUT... The problem with HID lamps and mercury vapor especially is that actual lamp burning voltage varies rather wildly, often even seriously outside IEC 188 prescribed voltage. As an example recently I acquired a couple of Soviet deluxe HPM 125 lamps. IEC 188 prescribed current is 1.15A as we all know, but when run on a healthy Helvar choke one actually consumes 1.05A and the second just about ~1A, sure having higher than expected burning voltages. Naturally if you force them to run at 1.15A as prescribed, lamps will end up somewhat overpowered. I know no way around this other than having proper inductive ballasts with IEC stated impedances for the exact lamp types. This is also very common with metal halides, while many European lamps state sodium ballast and 100V 3A, actual running parameters are more likely 2.6-2.7A and arc voltages of 120-130V actually. Not knowing this, if you force such a lamp to 3A again you will severely overdrive it. To complicate things even more, HID lamps sure display some negative resistance behavior, so when forced to 3A, MH lamp will drop arc voltage to ~110V, while being still overpowered, but not as much as 3.0/2.6A current ratio you may think...