Circuit Analysis and Network Theorems

Vocabulary flashcards covering electrical components, Kirchhoff's laws, voltage and current division, Thevenin's theorem, reactances, and network theorems.

Active Components

Components that require an external power supply for their basic operation and can amplify electrical signals (e.g., Transistors, Op-Amps).

Passive Components

Components that do not require an external power supply for their basic operation and cannot amplify electrical signals (e.g., Resistors, Capacitors, Inductors).

Role of Passive Components in an Electrical Filter

Resistors, capacitors, and inductors used to control the frequency response of a filter by determining which frequencies are allowed to pass or be blocked (e.g., in an RC low pass filter).

Role of Active Components in an Electrical Filter

Transistors and operational amplifiers used to amplify signals, provide gain, and prevent signal loss in active filters alongside resistors and capacitors.

Ideal Current Source

A source that supplies a constant current to a circuit irrespective of the voltage across its terminals, possessing infinite internal resistance.

Kirchhoff's Current Law (KCL)

A law stating that the total current entering a junction equals the total current leaving the junction ($\sum I_{\text{in}} = \sum I_{\text{out}}$ or $\sum I = 0$).

Ideal Voltage Source

An active element that maintains a constant voltage across its terminals irrespective of the current flowing through it or the load connected to it.

Kirchhoff's Voltage Law (KVL)

A law stating that the algebraic sum of all voltages around any closed loop in an electrical circuit is zero ($\sum V = 0$).

Voltage Division

A technique used to calculate the voltage across each individual resistor in a series circuit using the formula $V_i = V \frac{R_i}{R_T}$.

Thevenin's Voltage ($V_{th}$)

The open-circuit voltage calculated across the load terminals after disconnecting the load resistance ($R_L$).

Thevenin's Resistance ($R_{th}$)

The equivalent resistance calculated across the open load terminals after replacing all independent voltage sources with short circuits and all independent current sources with open circuits.

Thevenin's Equivalent Circuit

A simplified circuit formed by connecting Thevenin's voltage source ($V_{th}$) in series with Thevenin's resistance ($R_{th}$), to which the load resistance ($R_L$) is reconnected.

Thevenin Load Current Formula

The equation used to determine current through the reconnected load resistance: $I_L = \frac{V_{th}}{R_{th} + R_L}$.

Inductive Reactance ($X_L$)

The opposition offered by an inductor to the flow of alternating current (AC), given by $X_L = 2\pi f L\,\Omega$, which increases with frequency.

Capacitive Reactance ($X_C$)

The opposition offered by a capacitor to the flow of alternating current (AC), given by $X_C = \frac{1}{2\pi f C}\,\Omega$, which decreases with frequency.

Maximum Power Transfer Theorem

A theorem stating that maximum power is transferred to the load when the load resistance equals the Thevenin's resistance of the network ($R_L = R_{th}$).

Superposition Theorem

A theorem stating that in a linear circuit with multiple independent sources, the response in any branch equals the algebraic sum of responses caused by each source acting independently, with other independent voltage sources short-circuited and current sources open-circuited.

Current Division

A technique used to calculate current through parallel branch resistors, given for two resistors by $I_1 = I \frac{R_2}{R_1 + R_2}$ and $I_2 = I \frac{R_1}{R_1 + R_2}$.