The Glowing Exception: Why a Filament Lamp Breaks Ohm's Law
Ohmic vs. Non-Ohmic: The Fundamental Difference
To understand why a filament lamp is special, we must first grasp the rule it breaks: Ohm's Law. This is a fundamental principle in electronics that states the current ($I$) flowing through a conductor between two points is directly proportional to the voltage ($V$) across the two points, and inversely proportional to the resistance ($R$) between them. It is neatly summarized by the formula:
An Ohmic conductor, like a standard resistor made of carbon or metal film, has a constant resistance. If you double the voltage across it, the current also doubles. The relationship is linear and predictable. If you were to plot this on a graph of Current (I) vs. Voltage (V), you would get a perfectly straight line.
A non-ohmic conductor, like the filament in a light bulb, does not follow this rule. Its resistance is not constant. For a filament lamp, the resistance increases as the voltage and current increase. This happens because the electrical energy is converted into heat and light, causing the filament's temperature to rise significantly.
The Heart of the Matter: The Tungsten Filament
At the core of a traditional incandescent light bulb is a thin, coiled wire called the filament. This filament is almost always made of Tungsten, a metal chosen for its exceptionally high melting point of 3,422°C (6,192°F). This property is crucial because the filament must become white-hot to emit visible light without melting.
When you flip the switch, electrons begin to flow through the filament. They collide with the fixed atoms that make up the tungsten metal. Each collision transfers kinetic energy, causing the atoms to vibrate. We perceive this increased atomic vibration as an increase in temperature. The key physics concept here is resistivity. For most metals, resistivity increases with temperature. The hotter the metal gets, the more it "resists" the flow of electric current.
| Material | Melting Point (°C) | Why Used/Not Used |
|---|---|---|
| Tungsten | 3,422 | Ideal for filaments due to its extremely high melting point. |
| Carbon (Historical) | 3,550 (sublimes) | Used in early bulbs; higher resistance but fragile and inefficient. |
| Copper | 1,085 | Melts at a temperature far too low for an effective filament. |
Visualizing the Behavior: The I-V Characteristic Curve
The best way to see the non-ohmic nature of a filament lamp is by looking at its I-V characteristic curve. This is a graph that plots the current (I) on the vertical axis against the voltage (V) on the horizontal axis.
- For an Ohmic Resistor: The graph is a straight line passing through the origin. The slope of this line is constant and equals $1/R$.
- For a Filament Lamp: The graph is a curve. It starts steeply, showing that a small increase in voltage causes a large increase in current when the filament is cool and its resistance is low. As the voltage continues to increase, the filament heats up, its resistance rises, and the curve flattens out. This means that for the same increase in voltage, you get a smaller increase in current than you would with an ohmic conductor.
Imagine a graph where the line for the ohmic conductor is like a steady ramp. The line for the filament lamp, however, starts like a steep hill but quickly levels off into a gentle slope. This "leveling off" is the visual proof of its changing resistance.
A Practical Investigation: Measuring Lamp Resistance
You can explore this concept with a simple thought experiment or a real lab setup. You would need a power supply, a filament lamp, a voltmeter (connected in parallel across the lamp), and an ammeter (connected in series with the lamp).
Start with a very low voltage and record the voltage and current. Using Ohm's Law ($R = V / I$), you can calculate the resistance at that point. Now, gradually increase the voltage in small steps, calculating the resistance each time. You will observe a clear trend:
| Voltage (V) | Current (I) | Calculated Resistance (R = V/I) |
|---|---|---|
| 1.0 V | 0.10 A | 10.0 Ω |
| 3.0 V | 0.20 A | 15.0 Ω |
| 6.0 V | 0.30 A | 20.0 Ω |
| 12.0 V | 0.40 A | 30.0 Ω |
This table clearly shows that the resistance is not a fixed value; it triples as the voltage increases from 1 V to 12 V. This is the essence of non-ohmic behavior.
Common Mistakes and Important Questions
Q: If the resistance increases with temperature, why does the bulb get brighter with more voltage? Doesn't higher resistance mean less current?
This is an excellent question that highlights the dynamic interplay of variables. While it's true that the rising resistance tries to limit the current, the increase in voltage has a stronger effect in pushing the current. The power dissipated by the bulb, which determines its brightness, is given by $P = V \times I$. Even though the current doesn't increase linearly, both V and I are still getting larger, so the power (and thus the brightness) increases significantly. The filament also gets hotter, emitting more light and shifting its color towards white.
Q: Is a filament lamp the only non-ohmic component?
No, many common electronic components are non-ohmic. Diodes only allow current to flow in one direction. Light-Emitting Diodes (LEDs)[1] and transistors are also non-ohmic. Even a thermistor[2], a resistor whose resistance decreases when it gets hot, is non-ohmic but in the opposite way to a filament lamp. The world of electronics is full of non-ohmic devices that enable complex circuits.
Q: Why do light bulbs often burn out when you first turn them on?
This is a direct consequence of the filament's non-ohmic property. When the bulb is off and cool, the filament's resistance is at its lowest. When you first flip the switch, a very large "inrush" of current surges through the cold, low-resistance filament for a split second. This intense current causes rapid and uneven heating and mechanical stress on the delicate filament. Over time, this thermal shock weakens the filament until it finally breaks, causing the bulb to "burn out."
Footnote
[1] LED (Light-Emitting Diode): A semiconductor light source that emits light when current flows through it. It is highly efficient and, unlike a filament lamp, is cool to the touch because it produces little heat.
[2] Thermistor: A type of resistor whose resistance is significantly dependent on temperature. There are two main types: NTC (Negative Temperature Coefficient), where resistance decreases with rising temperature, and PTC (Positive Temperature Coefficient), where resistance increases with rising temperature. A filament lamp behaves like a PTC thermistor.