Determining Bulb Brightness and Safety in Series Wiring to 220V Mains

In this article, we will explore the behavior of two bulbs with different power ratings (60 W 120 V and 100 W 220 V) when connected in series to a 220V mains supply. We will determine which bulb will glow brighter and if either bulb will be at risk of fusing.

Introduction to the Problem

When electrical components are connected in series, the total resistance of the circuit changes. Understanding how this affects the brightness and safety of bulbs is crucial for electrical design and maintenance.

Step-by-Step Analysis

The first step in analyzing the behavior of the bulbs is to calculate the resistance of each bulb. We will then determine the current flowing through the circuit and the voltage drop across each bulb.

Step 1: Calculate the Resistance of Each Bulb

The resistance where: V is the voltage rating of the bulb P is the power rating of the bulb

Step 1.1: Bulb A (60 W, 120 V)

Step 1.2: Bulb B (100 W, 220 V)

Step 2: Calculate Equivalent Resistance in Series

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

Step 3: Calculate the Current in the Circuit

Using Ohm's Law, the current flowing through the series circuit can be calculated as:

Step 4: Calculate the Voltage Across Each Bulb

The voltage drop across each bulb can be calculated using Ohm's Law:

For Bulb A:

For Bulb B:

Step 5: Compare with Rated Voltages

Bulb A is rated for 120 V and will receive approximately 73 V. It will glow but not fuse.

Bulb B is rated for 220 V and will receive approximately 147 V. It will also glow but may be at risk of being overdriven since it is designed for a higher voltage.

Conclusion

Brightness: Bulb B will glow brighter because it is receiving a higher voltage (147 V) compared to Bulb A (73 V).

Fusing: Neither bulb is likely to fuse in this configuration. Bulb A is under its rated voltage while Bulb B, although above its rated voltage, is not significantly so as to guarantee fusing. However, Bulb B may have a reduced lifespan or risk of damage due to the higher voltage.

In summary, Bulb B will glow brighter, and neither bulb is expected to fuse under these conditions.