Understanding Power Consumption in Series Bulbs: A Practical Example

When dealing with electrical circuits, understanding how different components affect the overall performance can be crucial. This article will explore the case of connecting a 200 W and a 100 W bulb in series to a 220 V power source, focusing on calculating the power consumption.

Setting Up the Problem

First, we need to find the resistance of each bulb. This is important because the resistance affects how current flows through the series circuit.

Calculating Resistance

The power dissipated by a bulb is given by the formula:

P V^2 / R

Rearranging this formula to find resistance:

R V^2 / P

For the 200 W bulb:

R_{200} 220^2 / 200 48400 / 200 242Omega

For the 100 W bulb:

R_{100} 220^2 / 100 48400 / 100 484Omega

Total Resistance in Series

When components are in series, the total resistance is the sum of individual resistances:

R_{total} R_{200} R_{100} 242 484 726Omega

Current in the Circuit

Using Ohm's Law, which states V IR, we can calculate the total current in the circuit:

I V / R_{total} 220 / 726 approx 0.303 A

Power Consumption

The total power consumed by the circuit is calculated using:

P_{total} I^2 times R_{total} 0.303^2 times 726 approx 0.0918 times 726 approx 66.6 W

Theoretical vs. Practical Considerations

It is important to note that the resistance of a tungsten filament varies greatly with temperature. In reality, a cold tungsten filament can have about 1/20th the resistance it has when operating at its rated voltage. Therefore, using a linear relationship to calculate power consumption might not be accurate.

At 2500 degrees Celsius, the resistance of the tungsten filament is much higher, leading to a deviation from the theoretical calculation. Thus, the actual power consumption might differ significantly from 66.6 W. This makes it crucial to consider the non-linear behavior of the filament's resistance when dealing with practical applications.

Conclusion

This example demonstrates the importance of understanding the behavior of components in electrical circuits, especially when dealing with temperature-dependent elements such as tungsten filaments. By recognizing the limitations of theoretical models, we can better predict and design systems that accurately reflect real-world conditions.