Electric Circuits 1 - Final Exam Review

Flashcards covering key definitions and theoretical concepts of electric circuits based on the final exam transcript, including graph theory, matrix methods, and magnetic coupling.

Linear Element

An element that satisfies the properties of homogeneity and additivity.

Passive Element Characteristic

A characteristic that resides only in the I and III quadrants and passes through the coordinate origin.

Active Element Characteristic

A characteristic that does not pass through the coordinate origin.

Subgraph Tree (Stablo)

A connected subgraph that contains all nodes ($N_n$) and a number of branches equal to $N_n - 1$, but contains no loops.

Loop Voltage Matrix Elements ($e_{pj}$)

Represent the algebraic sum of the voltages of voltage generators in branches belonging to loop $j$, assuming all current generators have been transformed into voltage generators.

Incidence Matrix $M$ Dimensions

For an electric circuit with 5 nodes and 7 branches, the dimensions of the reduced incidence matrix are $4 \times 7$.

Tellegen's Theorem

States that the sum of powers that independent sources deliver to the network is equal to the sum of powers received by branches that do not contain independent sources at every moment $t$, regardless of their nature.

Node Admittance Matrix Off-diagonal Element ($y_{jk}$)

The negative sum of the admittances of the branches that are incident with nodes $j$ and $k$.

Equivalent Inductance of Ideally Coupled Inductors (Parallel Discordant)

For $L_1 = 9 \text{ mH}$ and $L_2 = 4 \text{ mH}$ connected in parallel discordantly with ideal magnetic coupling, the equivalent value is $0 \text{ mH}$ because $L_1 L_2 - M^2 = 0$.

Equivalent Reciprocal Inductance (\text{\Gamma}) - Parallel Concordant

The reciprocal inductance for two concordantly magnetically coupled coils connected in parallel is expressed as \text{\Gamma} = \text{\Gamma}_1 + 2\text{\Gamma}_{12} + \text{\Gamma}_2.

Ideal Transformer Input Impedance

For a transformer with $N_1 = 50$, $N_2 = 10$, and a secondary load of R = 50 \text{ \Omega}, the input impedance is calculated as (\frac{N_1}{N_2})^2 \times R = 1250 \text{ \Omega}.

Zero Component of Line Voltages

In a three-phase system connected to a load, the zero component of the line voltages is identically equal to zero.