AC Circuits: Reactance, Impedance, and Resonance

Understanding Reactance and Impedance

In AC circuits, reactance and impedance are crucial concepts that help us understand how circuit elements like resistors, inductors, and capacitors behave.

Reactance

• Reactance ( $X$ ): It is the opposition that inductors and capacitors provide to the change in current in an AC circuit. It is measured in ohms ( $\Omega$ ).
• Inductive Reactance ( $X_L$ ): For an inductor, reactance is given by $X_L = 2\pi f L$ , where $f$ is the frequency and $L$ is the inductance.
• Capacitive Reactance ( $X_C$ ): For a capacitor, reactance is given by $X_C = \frac{1}{2\pi f C}$ , where $C$ is the capacitance.

Impedance

• Impedance ( $Z$ ): It is the total opposition to the flow of current in an AC circuit, combining both resistance ( $R$ ) and reactance ( $X$ ). It is also measured in ohms ( $\Omega$ ).
• For a series circuit, impedance is calculated using $Z = \sqrt{R^2 + (X_L - X_C)^2}$ .

Resonance in AC Circuits

Resonance occurs in an AC circuit when the inductive reactance equals the capacitive reactance ( $X_L = X_C$ ), resulting in the impedance being purely resistive.

Applications of Resonance

• Tuning Circuits: Resonance is used in tuning radios and televisions to select desired frequencies.
• Maximizing Power Transfer: At resonance, power transfer in the circuit is maximized.