Understanding Voltage and Power in Series Circuits: A Case Study with Tungsten Filament Lamps

The study of electrical circuits is crucial for understanding how devices operate and consume energy. This article delves into a specific scenario where two tungsten filament lamps, each rated at 200 watts and 240 volts, are connected in series and supplied by a 240-volt AC mains supply. This example will illustrate the fundamental principles of voltage, resistance, and power in a series circuit configuration.

Circuit Configuration

When two lamps are connected in series, the current flowing through both lamps is identical, and the total voltage across the lamps is the sum of the individual voltages. This configuration is ideal for understanding the interplay between voltage, resistance, and power in an electrical circuit.

Calculating Resistance

First, let's calculate the resistance of each lamp using the given power rating and supply voltage. The formula for resistance is:

P frac{V^2}{R}, which can be rearranged to:

R frac{V^2}{P}

For each lamp

R frac{240^2}{200} frac{57600}{200} 288 Omega

Total Resistance in Series

In a series circuit, the total resistance is the sum of the individual resistances. For two lamps with the same resistance, the total resistance R_{total} is:

R_{total} R_1 times R_2 288 Omega times 288 Omega 576 Omega

Current in the Circuit

The current flowing through the circuit can be calculated using Ohm's Law:

I frac{V_{total}}{R_{total}} frac{240 V}{576 Omega} approx 0.4167 A

Power Consumed

The total power consumed in the circuit is calculated as:

P_{total} I^2 cdot R_{total} 0.4167 A^2 cdot 576 Omega approx 0.1736 cdot 576 approx 100 W

Therefore, the total power consumed in the circuit when two 200-watt lamps are connected in series across a 240-volt AC mains supply is approximately 100 watts.

Practical Considerations

It's important to note that the above calculation assumes ideal conditions, without considering the thermal coefficient of resistance. In a real-world setting, particular attention must be paid to the practical resistances, especially for tungsten filament lamps. When these lamps heat up, their resistances change, affecting the overall power consumption.

Conclusion

Understanding the behavior of lamps in a series circuit is crucial for electrical engineers and enthusiasts. The case study presented here clearly demonstrates the calculations and considerations required to accurately assess power consumption. This knowledge is foundational for designing efficient electrical systems and understanding the energy consumption of electronic devices in series configurations.

Frequently Asked Questions (FAQs)

Q: What if the lamp ratings are different?

A: If the power ratings of the lamps are different, say P1 and P2, the combined resistance and therefore the power consumption can be calculated as follows:

Pnew frac{P1 times P2}{P1 P2}

Q: How does the resistance change with temperature?

A: Tungsten filament lamps exhibit a significant change in resistance with temperature due to the thermal coefficient of resistance. As the lamps heat up, their resistances increase, which must be accounted for in real-world applications.

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