AC Circuit Analysis Flashcards

Comprehensive vocabulary flashcards covering the fundamental concepts of AC circuit analysis, including phasors, impedance forms, circuit elements, and power calculations.

Alternating Current (AC)

An electrical current that changes magnitude and direction periodically with time, serving as the standard form of electricity for homes and industries.

$V_m$ or $I_m$

The peak or maximum value of a sinusoidal AC voltage or current signal.

Angular Frequency ($\omega$)

The rate of change of the phase of a sinusoidal waveform, measured in $\text{rad/s}$ and calculated as \omega = 2\text{\pi}f.

Phase Angle ($\theta$)

The initial displacement of a sinusoidal AC signal at time $t = 0$.

Frequency ($f$)

The number of cycles per second, measured in $\text{Hz}$, calculated as $f = \frac{1}{T}$ where $T$ is the period.

Phasors

Rotating vectors used to simplify sinusoidal functions into algebraic form by removing time dependence and converting differential equations into algebraic equations.

Resistor ($R$) Phase Relationship

In an AC circuit, the voltage ($V$) and current ($I$) are in phase with no difference between them.

Inductor ($L$) Phase Relationship

A circuit element that opposes changes in current, where the voltage leads the current by 90^\text{\circ}.

Inductive Reactance ($X_L$)

The opposition to AC current flow by an inductor, defined by the formula X_L = \text{\omega}L.

Capacitor ($C$) Phase Relationship

A circuit element that stores energy in an electric field, where the current leads the voltage by 90^\text{\circ}.

Capacitive Reactance ($X_C$)

The opposition to AC current flow by a capacitor, defined by the formula X_C = \frac{1}{\text{\omega}C}.

Impedance ($Z$)

The total opposition to AC current, composed of resistance and reactance, expressed as $Z = R + jX$.

$$j$$

The imaginary unit used in AC complex representation, equivalent to $\sqrt{-1}$.

Rectangular Form of Impedance

Representation of impedance as $Z = a + jb$, where $a$ is resistance ($R$) and $b$ is reactance ($X$).

Polar Form of Impedance

Representation of impedance as |Z| \text{\angle} \text{\theta}, where |Z| = \text{\sqrt{R^2 + X^2}} and \text{\theta} = \text{\tan^{-1}}(\frac{X}{R}).

Ohm’s Law in AC

The relationship between voltage, current, and impedance expressed as $V = IZ$.

RL Circuit Impedance

The impedance of a series Resistor-Inductor circuit, expressed as $Z = R + jX_L$, identified by a positive imaginary part ($+j$).

RC Circuit Impedance

The impedance of a series Resistor-Capacitor circuit, expressed as $Z = R - jX_C$, identified by a negative imaginary part ($-j$).

Real Power ($P$)

The actual power consumed by the resistive part of a circuit, calculated as P = VI \text{\cos}(\text{\theta}) and measured in Watts ($W$).

Reactive Power ($Q$)

Power that circulates between source and load, calculated as Q = VI \text{\sin}(\text{\theta}).

Apparent Power ($S$)

The product of the RMS voltage and current without considering phase, calculated as $S = VI$.

Power Factor

The ratio of real power to apparent power, calculated as \text{\cos}(\text{\theta}) = \frac{P}{S}.

\text{\theta} = \text{\theta}_V - \text{\theta}_I

A key shortcut for determining the circuit phase angle by subtracting the current phase angle from the voltage phase angle.

Inductive Circuit Angle Rule

A circuit is identified as inductive if the phase angle (\text{\theta}) is positive (+\text{\theta}).

Capacitive Circuit Angle Rule

A circuit is identified as capacitive if the phase angle (\text{\theta}) is negative (-\text{\theta}).