A 3.33-k Ωresistor is connected to an AC generator with a maximum voltage of 141 V. Find (a) th

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A 3.33-k Ωresistor is connected to an AC generator with a...

A 3.33-k $\Omega$ resistor is connected to an $\mathrm{AC}$ generator with a maximum voltage of $141 \mathrm{~V}$. Find (a) the average power and (b) the maximum power delivered to this circuit.

Key Concepts

Average and Maximum Power

The average power delivered to a resistor in an AC circuit is calculated using the RMS voltage (P = V_RMS^2/R), representing the continuous energy conversion over a cycle. Conversely, the maximum (or instantaneous) power occurs at the peak voltage of the waveform (P_max = V_max^2/R), which is the highest power the resistor experiences at any moment in the cycle.

AC Voltage Waveforms

AC voltage in circuits is typically represented by a sine wave, meaning that the voltage oscillates periodically between a positive and negative peak value. Understanding the nature of these waveforms is crucial when analyzing how power is delivered over time, as both the instantaneous and average values depend on the periodic behavior of the waveform.

Root Mean Square (RMS) Voltage

The RMS voltage is a measure of the effective value of an AC voltage, which is used to compute the equivalent DC power dissipation in resistive loads. For a sinusoidal waveform, the RMS voltage is calculated by dividing the maximum (peak) voltage by the square root of two, accounting for the time-varying nature of the AC signal.

Power Dissipation in Resistors

In resistive circuits, power is dissipated as heat and is determined by Ohm’s law. The instantaneous power can be expressed as the square of the instantaneous voltage divided by the resistance. Understanding this concept is vital for accurately calculating both average and peak power levels in AC circuits.

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