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When we talk about AC circuits, the term RMS (Root Mean Square) voltage is often used to describe the effective value of the alternating voltage. Unlike direct current (DC) where the voltage is constant, AC voltage varies with time. The RMS voltage is a way to express this varying voltage as an equivalent DC value that would deliver the same power to a load.

For example, household electricity is usually rated at an RMS voltage of about 120 V or 230 V, depending on the country. This RMS value is key because it helps in designing electrical devices to work efficiently. It's also the value you see on most meters, making it a practical measure for comparing different sources of electricity.

Calculating the RMS voltage involves taking the square root of the average of the squares of all instantaneous voltages over one cycle. While this sounds complex, it's typically simplified by formulas in practical applications.

In the problem provided, the RMS voltage is given as 15.0 V. This is the effective voltage needed for the inductor to be connected across the generator, and it helps in calculating other components like RMS current and inductive reactance.

RMS current, similar to RMS voltage, refers to the effective value of an alternating current (AC). It represents the equivalent direct current (DC) value that would produce the same heat in a resistor. This concept is crucial for understanding how AC circuits work, as it provides a consistent way to describe AC currents in terms that are comparable to DC.

To calculate RMS current, you may again square the instantaneous current values over a full cycle, find the average, and then take the square root of this average. However, in typical situations, especially with sinusoidal sources, it becomes straightforward with standard electrical formulas.

In this exercise, the RMS current is given as 0.610 A. This value is used along with the RMS voltage in applying Ohm's Law for AC circuits to determine other quantities, such as inductive reactance. Knowing the RMS current allows us to predict the behavior of the circuit when subjected to the RMS voltage.

Ohm's Law is a fundamental principle in electronics, and it extends into AC circuits with some adjustments. In AC circuits, the standard Ohm's Law must be stated in terms of impedance due to the presence of inductors and capacitors, which introduce phase differences between voltage and current.

The law in AC form is written as: \[ V_{rms} = I_{rms} \times Z \]where \( V_{rms} \) is the RMS voltage, \( I_{rms} \) is the RMS current, and \( Z \) represents the impedance of the circuit.

For circuits with only inductors, like the exercise, the impedance is specifically the inductive reactance \( X_L \). Therefore, Ohm's Law becomes:\[ V_{rms} = I_{rms} \times X_L \]

Rearranging gives the formula used to find inductive reactance:\[ X_L = \frac{V_{rms}}{I_{rms}} \]

This relationship is fundamental in calculating the inductive reactance when both RMS voltage and current are known, as seen in this problem. By substituting the given values, we determined that the inductive reactance \( X_L \) is approximately \( 24.59 \Omega \), which helps us understand how the inductor will behave in the circuit.