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Inductive reactance is a crucial concept when working with alternating current (AC) circuits involving inductors. It represents the opposition that an inductor offers to the change in current flow. The formula to calculate inductive reactance is given by:\[ X_L = 2\pi fL \]where:

• \( X_L \) is the inductive reactance measured in ohms (\( \Omega \))
• \( f \) is the frequency of the AC supply in hertz (Hz)
• \( L \) is the inductance of the inductor in henrys (H)

In the exercise, you need to determine the inductive reactance by plugging in the values for frequency (1.25 kHz) and inductance (20 mH). The calculation shows that the inductor creates significant opposition, indicating how it influences the circuit's response to the AC voltage.

Capacitive reactance is equally important and describes the opposition to current flow posed by a capacitor in an AC circuit. This concept is essential for understanding how capacitors influence the phase and magnitude of circuit currents. The capacitive reactance can be calculated using:\[ X_C = \frac{1}{2\pi fC} \]where:

• \( X_C \) is the capacitive reactance in ohms (\( \Omega \))
• \( f \) is the frequency in hertz (Hz)
• \( C \) is the capacitance in farads (F)

In the example, substituting the frequency and capacitance values yields a capacitive reactance that is much larger than the inductive reactance. This disparity is essential when analyzing the total impedance in the circuit. Similarly, understanding the lead-lag relationship between current and voltage across a capacitor helps in visualizing the behavior in AC applications.

Impedance is a vital parameter in L-R-C circuits as it combines the effects of resistance, inductive reactance, and capacitive reactance. It provides a comprehensive measure of the circuit's total opposition to AC electricity. The impedance is often calculated using the formula:\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]where:

• \( Z \) is the total impedance (\( \Omega \))
• \( R \) is the resistance (\( \Omega \))
• \( X_L \) and \( X_C \) are the inductive and capacitive reactances respectively

For this calculation, the relative magnitudes of \( X_L \) and \( X_C \) greatly affect the result of \( Z \). A larger capacitive reactance than inductive reactance suggests a net capacitive behavior, impacting the circuit's phase angle and power factor.

Power dissipation in resistors is a fundamental concept, especially in AC circuits like L-R-C circuits. Unlike reactance, power in resistors is dissipated as heat, indicating energy loss in the circuit. The power dissipated can be calculated by:\[ P_R = I^2 R \]where:

• \( P_R \) is the power dissipated in the resistor (watts)
• \( I \) is the current through the circuit (amps)
• \( R \) is the resistance (\( \Omega \))

In the L-R-C circuit exercise, once the circuit current is known, one simply applies the formula to find the power dissipated across the resistor. Notably, this power loss matches the power supplied by the generator in this lossless circuit, illustrating the key resistor's role in AC power analysis.