A "75 -watt" lightbulb uses an average power of 75 w when connected to an rms voltage of 120 V .

step 1 In this question, a light bulb is connected to an average RMS voltage of 120 volts and uses an a

A "75 -watt" lightbulb uses an average power of 75 w when...

A "75 -watt" lightbulb uses an average power of 75 $\mathrm{w}$ when connected to an rms voltage of 120 $\mathrm{V}$ . (a) What is the resistance of the lightbulb? (b) What is the maximum current in the bulb? (c) What is the maximum power used by the bulb at any given instant of time?

A "75 -watt" lightbulb uses an average power of 75 $\mathrm{w}$ when connected to an rms voltage of 120 $\mathrm{V}$ . (a) What is the resistance of the
lightbulb? (b) What is the maximum current in the bulb? (c) What
is the maximum power used by the bulb at any given instant of time?

Key Concepts

Ohm's Law

Ohm's Law is a fundamental concept in electrical circuits that defines the relationship between voltage, current, and resistance. It states that the current flowing through a resistor is directly proportional to the voltage across it and inversely proportional to its resistance, expressed by the equation V = IR. This principle is essential for calculating unknown quantities in circuits, such as determining the resistance when voltage and current (or power) are known.

Root-Mean-Square (rms) Values

In AC circuits, the voltage and current vary sinusoidally over time rather than remaining constant. The rms value is a statistical measure that represents the equivalent direct current (DC) value which would produce the same amount of power in a resistive load. It is crucial for analyzing AC circuits because it allows us to use conventional formulas for power and resistance as if a constant voltage or current were applied.

Sinusoidal AC Waveforms

Sinusoidal AC waveforms are the standard form of alternating current in electrical systems. They are characterized by their periodic oscillations between positive and negative values, with specific properties such as peak (maximum) values and rms (effective) values. Understanding the sinusoidal nature is critical for converting between peak and rms values and for analyzing the behavior of AC circuits with resistive loads.

Instantaneous versus Average Power in AC Circuits

In AC circuits, the instantaneous power fluctuates over time as the voltage and current vary, reaching a maximum value at certain points within the cycle. However, for practical purposes like assessing energy consumption or device ratings, the average power over a complete cycle is used. The relationship between the peak values and the average (rms) power is important for understanding the performance limits of AC devices and for ensuring safe and effective circuit design.

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