3.1. The plate on the back nf a certain computer scanner...

3.1. The plate on the back nf a certain computer scanner says that the unit draws 0.34 $\mathrm{A}$ of current from a $120-\mathrm{V}, 60-\mathrm{Hz}$ line. Find (a) the root-mean-square current, (b) the current amplitude, (c) the average current; (d) the average square of the current.

Key Concepts

Amplitude of AC Current

The amplitude of an alternating current, often referred to as the peak current, is the maximum value that the current reaches during each cycle. This is a key parameter in describing sinusoidal waveforms and is essential in converting between amplitude and RMS values for sinusoidal signals.

Average (Mean) Current

The average current in an AC circuit is determined by calculating the arithmetic mean of the current over one complete cycle. For symmetric AC waveforms, such as a pure sine wave, this average value is zero because the positive and negative halves of the cycle cancel each other out.

Root-Mean-Square (RMS) Current

The RMS current is a measure of the effective or equivalent DC value of an alternating current. It is calculated by taking the square root of the mean (average) of the square of the instantaneous current values over one complete cycle. In AC circuits, the RMS value is used because it directly relates to the amount of power that the current can deliver to a resistive load.

Average Square of the Current

The average square of the current is obtained by squaring the instantaneous current values and then taking the mean over one complete cycle. This concept is directly related to the RMS value, since the square of the RMS current is equal to the average of the squared instantaneous current values. It plays a crucial role in power calculations in AC circuits.

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