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# The V-I Characteristics of Filament Lamps

Updated February 26, 2018

Filament lamps give off light because the metal filament in the bulb becomes hot and glows brightly. As the filament gets hot, its electrical resistance increases. An increase in resistance limits the current flowing in the filament. The relationship between the current, voltage and resistance in the lamp is called its V-I characteristic. If you graphed it, it would make a curve instead of a straight line.

## Ohm's Law

Ohm's Law is one of the cornerstones of electrical theory. It relates resistance, voltage and current with the equation: "R = V / I," or resistance in ohms equals voltage in volts divided by current in amps.

If the resistance of an electronic device is constant and you made a graph of voltage versus the current flowing though it, you'd get a straight line. If its resistance changes, the graph becomes curved.

## Ohmic Devices

Electrical devices called "resistors" have been designed to have constant resistance over a wide range of voltage, current and temperature. An electronic engineer needs to know its resistance will hold steady so her circuit will be reliable. Other components, such as diodes and transistors, don't have constant resistance, but this property isn't important for them. The engineer calls a device with constant resistance an "ohmic device." Devices, including filament lamps, whose resistance varies are called "non-ohmic."

## Molecular Effects

Even at room temperature, the molecules in a filament lamp's wire vibrate, randomly bumping and jostling their neighbours. As the filament heats up and begins to glow, the molecules vibrate with more energy. These random vibrations impede the flow of current, increasing the filament's resistance. The hotter the wire gets, the more resistance it has.

## Temperature Coefficient

Every electronic component has a multiplier, called a temperature coefficient, that tells you how its resistance changes when temperature changes. A filament lamp has a large, positive temperature coefficient --- its resistance goes up when temperature goes up. Resistors, made of carbon or metal film, also have a positive temperature coefficient, but it's very small. Silicon semiconductors, such as diodes and thermistors, can have positive or negative coefficients.