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The phase angle in an L-R-C circuit represents the difference in phase between the source voltage and the current flowing through the circuit. It is a crucial concept in AC (Alternating Current) circuit analysis. The phase angle indicates how much the voltage leads (or lags) the current:

• A positive phase angle means the voltage leads the current.
• A negative phase angle means the current leads the voltage.

In this exercise, the phase angle is 40 degrees, meaning the voltage leads the current. This angle is related to the reactive components of the circuit—the inductor and capacitor—and their reactances. By using trigonometric functions, we derive the phase angle from the L-R-C circuit parameters. Specifically, the tangent of the phase angle can be calculated by the formula: \[\tan(\phi) = \frac{X_L - X_C}{R}\]where \(X_L\) is the inductive reactance, \(X_C\) is the capacitive reactance, and \(R\) is the resistance. Understanding this relationship allows us to calculate the missing parameters in the circuit.

Inductive reactance represents the "opposition" to the change in current by an inductor in an AC circuit. It is denoted as \(X_L\) and is measured in ohms (\(\Omega\)). The formula to calculate inductive reactance is:\[X_L = 2\pi f L\]where \(f\) is the frequency of the AC source and \(L\) is the inductance of the coil. In the context of the given problem, we determine the inductive reactance by using the known phase angle and the given circuit parameters like capacitance and resistance using the relation:\[\tan(\phi) = \frac{X_L - X_C}{R}\]By rearranging and solving this equation, we find that the inductive reactance \(X_L\) is 568 \(\Omega\). Inductive reactance plays a vital role in defining how an inductor affects the overall impedance of the circuit, hence influencing both the phase angle and the total power factor.

RMS stands for Root Mean Square, a statistical measure used widely in dealing with sinusoidal waves like those in AC circuits. The RMS current \(I_{rms}\) is a representation of the effective value of the alternating current, which amounts to the equivalent DC current that would produce the same power. The formula to determine the RMS current in an L-R-C circuit using the average power and component parameters is:\[I_{rms} = \sqrt{\frac{P}{R \cos(\phi)}}\]where \(P\) is the average power, \(R\) is the resistance, and \(\cos(\phi)\) is the power factor. In this problem, the RMS current comes out to be approximately 1.25 A. The significance of \(I_{rms}\) lies in its ability to simplify the calculation of AC parameters like power, no matter how complex the waveform of the current is.

The RMS voltage \(V_{rms}\) is a key factor in AC circuits and represents the effective voltage, similar to what RMS current does for current. It is used to quantify the net voltage level of an AC supply. The formula to calculate \(V_{rms}\) in a series L-R-C circuit is:\[V_{rms} = I_{rms} \times \sqrt{R^2 + (X_L - X_C)^2}\]This formula incorporates the impedance of the circuit, which includes both resistance and reactance. By substituting the previously found RMS current and reactances into this formula, we calculate that \(V_{rms}\) is approximately 328 V for the given circuit. Understanding RMS voltage helps in designing systems that rely on AC power, ensuring they can withstand the equivalent voltages they are subjected to.