Calculating the Resistance of a Light Bulb Using 15 Watts of Power

Introduction

Light bulbs are essential components of electrical circuits, providing illumination in homes, offices, and public spaces. Understanding the electrical characteristics of light bulbs is crucial for designing and maintaining efficient electrical systems. One key parameter is resistance, which determines how much current flows through the bulb and influences its brightness.

Relationship Between Power, Voltage, and Resistance

The power (P) consumed by a light bulb is directly proportional to the square of the current (I) flowing through it and the resistance (R):

P = I²R

Additionally, the current is directly proportional to the voltage (V) applied across the bulb:

I = V/R

Calculating Resistance Using Power and Voltage

To determine the resistance of a light bulb using 15 watts of power, we can rearrange the power equation as follows:

R = P/I²

Since we know the power (P = 15 watts), we need to determine the current (I) using the voltage. However, the voltage applied to the bulb is not specified in the given information.

Typical Voltage for Light Bulbs

The typical voltage used for household lighting is 120 volts (V) in North America and 230 volts (V) in Europe. Assuming the light bulb is intended for household use, we can use these voltage values to calculate the resistance.

Resistance for 120V Voltage

For a 120V voltage, using Ohm’s law (I = V/R), we can calculate the current:

I = 120V/R

Substituting this expression for current into the resistance equation, we get:

R = P/(120²/R)

Solving for R, we find the resistance to be:

R = 960 ohms

Resistance for 230V Voltage

Similarly, for a 230V voltage, the current is:

I = 230V/R

And the resistance becomes:

R = P/(230²/R)

Solving for R, we obtain:

R = 3456 ohms

Conclusion

Based on the typical voltage used for household lighting, the resistance of a light bulb using 15 watts of power is approximately 960 ohms for 120V voltage and 3456 ohms for 230V voltage. These calculations demonstrate the relationship between power, voltage, and resistance in electrical circuits.

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