Are We Buying Proper Light Bulbs ?

Hi Readers! Do you really peep into the back side of the cover-writing when you buy a bulb? These say something important to you. You'll really be astonished about the maths behind those writings. Knowing this simple maths will let you be the most clever person while buying any bulb. Incandescent light bulbs produce light by passing electricity through a thin metal coil, called a filament (see Figure 1). When electricity is passed through the filament, it glows and illuminates the light bulb. The electricity also produces heat as it passes through the filament. In fact, special bulbs, called heat lamps, are intended to produce heat for purposes such as heating food and drying plants but in most light bulbs, heat is an undesired (and unavoidable) side effect which eventually causes the filament to burn out. The amount of time that a light bulb can be turned on for before it is expected to burn out is printed on most packages so that shoppers(or us) can compare the life expectancy of the various available bulbs. It turns out that the amount of electricity that passes through the filament when the light bulb is turned on is all that is needed to predict how long a light bulb will last.

By logging and analyzing the results of various experiments to test the life of light bulbs under different conditions, the life expectancy of a light bulb has been found to be inversely proportional to the voltage that is applied to the filament. That is, the life expectancy is equal to some number divided by the number of volts raised to a power; when two values are inversely proportional, decreasing one value causes an increase in the other value. The life expectancy of most incandescent light bulbs is inversely proportional to the 12th power of the applied voltage and can be expressed as

where, 'L' represents the life expectancy, 'a' is a constant, and 'V' represents the applied voltage. This expression indicates that using a lower value for the variable V results in the constant a being divided by a smaller number as long as V is >1, so that the life expectancy L is equal to a larger number. This means that lowering the voltage that is allowed to surge through the filament increases the life expectancy of the light bulb.

On the other hand, less light is produced if less electricity is allowed to pass through the filament. The amount of light that is produced is dependent on the voltage and can be expressed as

where, 'X' represents the amount of light produced by the light bulb, 'b' is a constant, and 'V' (which is raised to a power of 3.3) represents the voltage. In contrast to the relationship between voltage and life expectancy, it is said that the amount of light produced is directly proportional to the voltage, meaning that the amount of light is equal to some number multiplied by the voltage raised to a power. In this type of relationship, increasing the value of one variable also increases the value of the other variable. As can be deduced by examining these two equations, lowering the voltage has a much smaller effect on the amount of light produced than it does on the life expectancy of the light bulb. In other words, a small decrease in voltage increases the life expectancy by a relatively substantial amount, but decreases the amount of light produced only slightly. Therefore, buying light bulbs with lower voltage values usually increases the amount of time before light bulbs need to be replaced without resulting in a marked decrease in illumination.

Thanks for reading :)