Formula for Incandescent Lamps

(Actual Life/Rated Life) = (Rated Volts/Actual Volts)^13.

Take a 130 volt, 1000hr rated bulb and feed it 123 volts and you get:
AL/1000=(130/123)^13 or 2053 hours actual life.

In contrast, take a 120 volt 1000hr bulb and feed it 123 volts and you get:
AL/1000=(120/123)^13 or 725 hours actual life.

Those 130v bulbs are life savers in hard to reach fixtures.

Ohms Law

Electricity is the force that energizes all that we do. One concept that must be understood is power. All lamps are rated in watts, a measure of power. We will begin by defining a few terms related to electricity. The four terms we need to understand are Voltage, Amperage, Resistance, and Wattage. We will use a water model to help define and understand these terms. If we look at a water pipe as an example of an electrical wire, and in the example, the water pipe is hooked up to a water wheel, then we could call the friction that the wheel has while turning "the resistance". All light bulbs present a certain resistance to the flow of electricity. If we turn on or open a faucet, water starts to flow. This flow is just like bringing the level up on a dimmer. The pressure of the water in the pipe is directly comparable to the voltage in an electrical circuit. As you bring up a dimmer you are increasing the voltage. In our water model we could say we have increased the water from a trickle to a torrent. The next term to consider is amperage. The size of the pipe carrying the water is the corollary for amperage. The larger the diameter of a pipe, the more water can flow. The larger the gauge, or diameter of a wire, the more current can flow. Fuses and circuit breakers are rated in amperage. They provide protection in an electrical circuit. When you try to draw more amperage through the circuit than the fuse or circuit breaker is rated for, the fuse or circuit breaker will "blow". The larger the fuse or circuit breaker, the more lighting fixtures you could use. In our water model we could measure the amount of water flowing past the wheel as it "spins" the wheel. The amount of water flowing as well as the pressure and rate of flow controls the speed of the spinning wheel. In the case of our lighting instrument, we control the power with our dimmer. The measurement of the amount of power flowing past the light bulb, our spinning  wheel in the water model, is called wattage. In electrical terms we measure wattage, the amount of amperage or current flowing past a point at a certain voltage or pressure. We can define "Power" as the measurement of how much work is being done. In the case of the water model example, we would multiply the amount of water that flows by the pressure, or how much we opened the tap. If the friction or resistance is a small number and we open the tap all the way then the amount of water will be large. If the friction is large then the amount of water flowing will drop down. However, the resistance provided by the wheel is not a factor we need to be concerned about in lamps. Most of the time we are concerned with how much amperage is being used by a lamp, not how much resistance it places in the circuit. Long ago a man named Ohms figured out these relationships and set them down. We know them as Ohms Law. He set them down using the following variables in 2 basic formulas. Here are the 2 formulas that we use most.

Wattage = W
Voltage = V
Amperage = A
Resistance = R

A = V / R
Amperage = Volts divided by Resistance

R = V/A
Resistance = Voltage divided by Amperage

W = V * A
Wattage = Voltage times Amperage

Wattage: The measure of the amount of work being done.
Amperage: The availability of power (controlled by the gauge of the wire and breaker or fuse rating.)
Voltage: The pressure of flow.
Resistance: The friction of the light bulb or other device.

Some people remember the second formula as the mnemonic "West Virginia".

Load Calculation

One of the single most important things you need to understand is load calculating. Load calculation is done to insure that you do not exceed the available power. The first step is to determine what is the configuration of available power. Talk with an electrician or maintenance staff worker about available power. There are 3 basic options, 1.) 15 amp wall outlets, 2.) Single Phase power in a breaker panel, or 3.) Three Phase power in a breaker panel. You need to know which option you have and what is the available amperage per hot leg, or you need to know the total amperage. Load calculation is not a difficult task to perform; here are two methods of calculating your needs.

1.Add up the wattages of all the fixtures that you plan to use and divide that by the voltage on a single hot wire. For example, 24 fixtures at 500 watts equals 12,000 watts. In the US the voltage is a nominal 120 volts. 12,000 watts = 120 volts x what amperage? Using the formula above, you can see the required amperage would be 100 amps to utilize all 24 fixtures at once. The next step is to divide this by the number of hot legs of power connected to your dimmers. This would be either 2 or 3, based on single phase or three phase power. In the case of single phase power you would need to have 50 amps of power available per leg. In the case of three phase power you would need 33.33 amps per leg. 

2.Find out the available power and calculate the maximum wattage. This way you can calculate the maximum number of fixtures that you can turn on in any given cue. For example, if you have a three phase power service that is fused (or breakered) at 100 amps per leg, the total available amperage is 300 amps at 120 volts. You would solve for wattage by multiplying the amps times the volts. 120 volts times 300 amps equals 36,000 watts. If you are using 500 watt lamps then you can use 72 fixtures in any given cue. 

AC Versus DC Current

There is no inductance (or capacitance) due to a “coiled or coiled coil” filament. DC current is based on simple ohm’s law is E/R = I, the effective current in a AC circuit is E(rms)/R = I.

RMS “root means square” voltage is .707 of applied voltage, therefore the rms voltage/current on AC is only .707 compared to a DC circuit. The AC equivalent of 12vdc is 17vac. (This is also a significant factor for LED MR16’s, the light output depends on whether the step-down transformer produces AC or DC voltage. There is a substantial difference in current through the LED’s depending on whether run on 12vac or 12vdc. MR16 LED lamps are dimmer when operated on 12vac electronic transformers versus 12dc voltage, again the equivalent AC voltage would need to be 17vac to match the light output of a lamp operated on pure 12vdc.)

The life rating of most general purpose incandescent lamps is based on AC voltage/current. When operated from a DC voltage the actual “steady state” current is 1/3 higher than on AC and filament life is reduced substantially.

There are incandescent lamps designed specifically for DC voltage/current and those lamps have life ratings based appropriately for current supplied by a DC source. The filaments are generally a larger diameter to handle higher “steady state” currents.

Just look at an AC sinusoidal wave and you can see that maximum current flows only during the peak of the waveform. The current varies from plus “peak to zero” and then “zero to minus peak”, it is not a steady state, constant current.

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