Impedances and Admittance

Impedance is the ratio of phasor voltage to phasor current in an AC circuit, representing resistance to sinusoidal current flow. It is a complex quantity expressed in rectangular form with a real part denoting resistance and an imaginary part representing reactance. Impedance can also be represented in polar form by its magnitude and phase angle.

At zero frequency (DC), inductors act as short circuits with zero impedance, while capacitors function as open circuits with infinite impedance. At high frequencies, this behavior reverses: inductors become open circuits and capacitors become short circuits. This frequency-dependent behavior is fundamental to understanding AC circuit analysis.

Inductive impedance has positive reactance, causing current to lag behind voltage. Capacitive impedance has negative reactance, causing current to lead voltage. The sign of reactance in the imaginary part of impedance determines whether the circuit exhibits inductive or capacitive characteristics in AC operation.

Admittance is the reciprocal of impedance, measured in Siemens (S), representing the ease with which current flows through a circuit. In rectangular form, admittance comprises conductance as the real part and susceptance as the imaginary part. Like impedance, admittance is essential for analyzing AC circuits with phasor relationships for circuit elements.

In rectangular form, impedance consists of resistance (real part) and reactance (imaginary part). In polar form, impedance is characterized by its magnitude and phase angle. Both representations are equivalent and useful for different types of AC circuit calculations and analysis.

Resistors, inductors, and capacitors are passive elements characterized by phasor voltage and current in AC circuits. Each contributes differently to impedance: resistors provide pure resistance, inductors provide inductive reactance, and capacitors provide capacitive reactance. Together, they determine the overall impedance behavior of AC circuits.

Impedance is complex because it combines resistance and reactance, requiring representation with both real and imaginary components. This complex nature allows engineers to account for both energy dissipation (resistance) and energy storage (reactance) in AC circuits simultaneously, enabling accurate circuit analysis and design.