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An AC (Alternating Current) power supply provides voltage in a waveform that alternates in polarity over time. This means that the direction of current flow changes periodically. The voltage provided by an AC power source is constantly changing, typically in a sinusoidal manner. This type of power supply is distinct from a DC (Direct Current) power supply, where the voltage remains constant.

AC power supplies are common in household and industrial settings. The voltage can be described using several terms:

• Peak Voltage (V_max or V_peak): The maximum voltage value reached during one cycle of the waveform.
• RMS (Root Mean Square) Voltage (V_rms): A measure of the effective value of an AC voltage, often used in calculations involving power. The RMS voltage is related to the peak voltage by the formula: \( V_{rms} = \frac{V_{max}}{\sqrt{2}} \).

AC voltage frequency, such as the 300 Hz given in the exercise, indicates how fast the waveform repeats per second. In this scenario, the inductor connects to an AC source with a sinusoidal voltage having a maximum value of 4.00 V.

Inductive reactance is a property of inductors in an AC circuit that opposes the change in current. It is represented by \(X_L\) and is measured in ohms (\(\Omega\)). Unlike resistance, which affects both AC and DC, inductive reactance only affects AC circuits.

Inductive reactance can be calculated with the formula:
\[ X_L = 2\pi f L \]
Here:

• \(X_L\) is the inductive reactance,
• \(f\) is the frequency of the AC supply, and
• \(L\) is the inductance of the coil.

The higher the frequency or the larger the inductance, the greater the inductive reactance. This means that the inductor will "resist" the alternating current more strongly, reducing the amount of current that flows for a given voltage. In our problem, the inductive reactance is calculated to be 2000 \(\Omega\).

RMS (Root Mean Square) current is a measure used in AC circuits that describes the amount of current effectively delivered throughout a cycle. RMS values enable us to compare AC and DC circuits on equivalent terms.

To understand RMS current, consider it as the equivalent value of DC current that would produce the same power effect in the circuit. It's an important metric because alternating current varies constantly, and RMS offers a standardized measure.

RMS current is calculated differently than regular current in DC. For a sinusoidal waveform, which is very common in power supplies, the formula for RMS current is:
\[ I_{rms} = \frac{I_{peak}}{\sqrt{2}} \]
In our exercise, we aimed for an RMS current maximum of 2.00 mA, or 0.002 A, in the given AC power circuit.

The inductance (L) of an inductor is a measure of how effectively it can oppose changes in current, reflecting its ability to store energy in a magnetic field. Inductance is measured in henries (H).

To find inductance when given the inductive reactance and the frequency of the AC power source, use the formula:
\[ L = \frac{X_L}{2\pi f} \]
In this equation:

• \(L\) is the inductance,
• \(X_L\) is the inductive reactance, measured in ohms, and
• \(f\) is the frequency, measured in hertz.

In the given exercise, calculating using \(X_L\) of 2000 \(\Omega\) and a frequency of 300 Hz, the inductance required was approximately 1.06 H. This tells us the inductor should be capable of limiting the RMS current to 2.00 mA under the specified conditions.