A lightbulb uses an average power of 75 W when connected to a source that supplies an rms volta

step 1 Hi, here in this given problem, average power used by the light bulb that is given as B, AB stan

A lightbulb uses an average power of 75 W when connected to...

A lightbulb uses an average power of $75 \mathrm{~W}$ when connected to a source that supplies 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 lightbulb uses an average power of $75 \mathrm{~W}$ when connected to a source that supplies 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

Instantaneous vs Average Power

Instantaneous power in an AC circuit is the power at a specific moment in time, often varying sinusoidally, whereas the average power is the mean value over one complete cycle. Due to the periodic nature of AC, the instantaneous power can reach values significantly higher than the average power, with the maximum power corresponding to the peak values of voltage and current in the cycle.

Power in Resistive AC Circuits

In purely resistive AC circuits, the average power consumed can be calculated using the formula P = V_rms^2 / R. This relationship helps in determining unknown circuit parameters, such as resistance, when the power consumption and RMS voltage are known, and it underpins the analysis and design of AC circuits.

Root Mean Square (RMS) Voltage

RMS voltage is a measure of the effective value of an alternating voltage, equating it to a direct current voltage that would produce the same heating effect in a resistor. It is calculated by taking the square root of the average of the squares of the instantaneous voltage values over a complete cycle, providing a convenient way to relate AC and DC circuit behaviors.

Ohm's Law

Ohm's Law is a fundamental principle stating that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. In the context of AC circuits, for purely resistive loads, this law is applied using RMS values to relate voltage, current, and resistance.

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