Calculating the Resistance of an Electric Bulb: A Common Misconception

Electric bulbs have often been a subject of both curiosity and confusion, especially when it comes to understanding their electrical properties. A common question that often arises is, 'If an electric bulb connected to 220V line draws an electric current of 0.5A, what will the resistance of the filament of a bulb be?' This article aims to clarify this myth, explaining why the conventional approach using Ohm's Law might not always be applicable and when it is appropriate.

Myth: Applying Ohm's Law to Filament Lamps

Many resources, including textbooks, provide straightforward answers to this question. For instance:

According to Ohm's Law, V IR, where V is the voltage, I is the current, and R is the resistance. If a bulb is connected to a 220V supply and draws 0.5A, then the resistance ( R ) is calculated as:

R V / I 220V / 0.5A 440Ω.

However, this simple calculation ignores a crucial aspect of filament lamps: they are not Ohmic devices. Therefore, the resistance is not constant and cannot be accurately determined using Ohm's law alone.

What is Ohm's Law and Why Does it Apply?

Ohm's Law, formulated by Georg Ohm, states that the voltage ( V ) across a conductor is proportional to the current ( I ) flowing through it, with the constant of proportionality being the resistance ( R ). Mathematically, it is expressed as:

In an ideal scenario, resistance is constant, and Ohm's law accurately describes the relationship between voltage, current, and resistance. However, in real-world scenarios, such as the filament of a light bulb, the resistance changes with temperature and voltage, making the device non-Ohmic.

Why Ohm's Law Fails for Filament Lamps

It is important to note that filament lamps, like the one in question, do not follow the constant ratio of voltage to current required for Ohm's law. The resistance of a filament increases as it heats up, meaning that the resistance is temperature-dependent. When the lamp is first turned on, the resistance is low, and it increases as the filament reaches its operating temperature.

For a filament lamp, the resistance can vary widely depending on the operating conditions and temperature. Thus, the resistance cannot be calculated using a simple voltage-to-current ratio alone.

Conclusion: A Real-World Example

Given the initial conditions of a 220V supply and a current of 0.5A, a quick calculation might give a resistance of 440Ω. However, in reality, this resistance is not constant, and the actual resistance will depend on the current flowing through the filament and its temperature.

For a more accurate understanding, it is essential to consider the temperature dependence of the filament's resistance. If you were to apply the same principle in practical scenarios that involve Ohmic conductors, like resistors, then the calculation would be fundamentally sound. However, for non-Ohmic devices like filament lamps, the resistance concept becomes less straightforward.

To summarize, the resistance of a filament bulb cannot be determined using a simple Ohm's law calculation due to the non-Ohmic nature of the filament. Understanding the temperature dependence and other physical properties of the filament is crucial for accurate calculations in real-world applications.