EE 151: Applied Electricity - Circuit and Network Theorems

Comprehensive vocabulary flashcards covering fundamental electrical quantities, circuit elements, network topologies, reduction rules, and circuit analysis theorems for EE 151.

Electric Current

The movement or flow of electrical charge in a conductor, defined mathematically as the time rate of charge flow $i = \frac{dq}{dt}$ and measured in amperes ($\text{A}$).

Current Density ($J$)

The amount of electric current flowing per unit cross-sectional area ($J = \frac{I}{A}$), expressed in units of $\text{A/m}^2$.

Voltage

The electric force or potential difference created by the separation of charge, defined as energy expended per unit charge ($v = \frac{dw}{dq}$) and measured in volts ($\text{V}$).

Volt ($\text{V}$)

The potential difference between two points when one joule ($1\,\text{J}$) of energy is used to move one coulomb ($1\,\text{C}$) of charge from one point to the other.

Electric Charge

A fundamental bipolar quantity of electricity carried by electrons ($-e$) and protons ($+e$), which is conserved, quantized in multiples of $e = 1.6 \times 10^{-19}\,\text{C}$, and measured in Coulombs ($\text{C}$).

Electric Power

The time rate of expending or absorbing energy, expressed mathematically as $p = \frac{dw}{dt} = vi$, with the basic SI unit of watt ($\text{W}$) where $1\,\text{W} = 1\,\text{J/s}$.

Power Sign Convention

A reference standard where current enters the positive voltage terminal of an element: a positive power calculation ($P > 0$) indicates absorption, while a negative power calculation ($P < 0$) indicates delivery or supply.

Active Element

A circuit element capable of generating electric energy, such as batteries, generators, solar cells, and operational or transistor models.

Passive Element

A physical circuit component incapable of generating electric energy, such as resistors, inductors, and capacitors.

Dependent Sources

Sources whose output voltage or current is governed by a voltage or current existing elsewhere in the network, categorized into: (a) VCVS ($v_s = \mu v_x$), (b) CCVS ($v_s = \rho i_x$), (c) VCCS ($i_s = \alpha v_x$), and (d) CCCS ($i_s = \beta i_x$).

Electric Resistance (Ohm's Law)

The property of a circuit element to resist or limit the flow of current, establishing proportionality between terminal voltage and current ($V = IR$) under constant temperature.

Resistivity ($\rho$)

The intrinsic material property that determines electrical resistance for a conductor of length $l$ and cross-sectional area $A$, according to $R = \frac{\rho l}{A}$.

Conductance ($G$)

The reciprocal of electrical resistance ($G = \frac{1}{R}$), representing how readily an element conducts electric current, measured in Siemens ($\text{S}$).

Conductivity ($\sigma$)

The inverse of electrical resistivity ($\rho$), characterizing a material's inherent ability to allow electric charge flow.

Capacitor

A passive circuit component typically formed by two parallel conducting plates separated by a dielectric/non-conducting medium, storing electric charge according to $Q = CV$.

Farad ($\text{F}$)

The basic SI unit of capacitance, defined as the capacity to store one coulomb ($1\,\text{C}$) of charge when a potential difference of one volt ($1\,\text{V}$) is applied.

Capacitor Current-Voltage Relation

The constitutive relation stating that current only enters or leaves a capacitor when the terminal voltage changes with time: $i_c = C \frac{dv_c}{dt}$.

Capacitor Energy Storage ($W_c$)

The recoverable energy stored in the electrostatic field between capacitor plates, given by $W_c = \frac{1}{2} C V^2$.

Inductor

A passive device constructed as a coiled conductor that opposes changes in electric current through the creation of a self-induced back electromotive force (back emf).

Henry ($\text{H}$)

The SI unit of inductance ($L$), defined as the inductance of a circuit in which an electromotive force of $1\,\text{V}$ is induced when the current changes uniformly at a rate of $1\,\text{A/s}$.

Inductor Energy Storage ($W_L$)

The energy stored within the magnetic field of an ideal current-carrying inductor, expressed as $W_L = \frac{1}{2} L I^2$.

Node

A connection point in an electrical network where two or more circuit elements join together.

Essential Node

A junction point in a circuit where three or more circuit elements connect together.

Branch

Any continuous path within an electrical circuit that directly connects two nodes.

Essential Branch

A path in a circuit network connecting two essential nodes without passing through any intermediate essential node.

Loop

Any closed path through a circuit network wherein the starting node and the finishing node are identical.

Mesh

A closed loop within a planar circuit that does not contain any other internal loops.

Short-Circuit

A circuit branch with theoretically zero resistance ($R = 0$) that diverts all current from adjacent parallel branches connected to the same node, excluding branches containing independent sources.

Open Circuit

A circuit branch possessing theoretically infinite resistance ($R = \infty$), completely preventing electric current from flowing across it.

Series Circuit Connection

A topological configuration where components are connected end-to-end along a single path, forcing the exact same current to flow through each element.

Parallel Circuit Connection

A topological arrangement where components share two common end nodes, subjecting every element to the exact same terminal voltage.

Voltage Divider Rule

A network analysis method where the voltage drop across a specific resistor $R_1$ in a series loop is calculated as a fraction of the total applied voltage: $v_1(t) = v(t) \frac{R_1}{R_1 + R_2}$.

Current Division Rule

A formula used to distribute total incoming current between two parallel branches inversely proportional to branch resistances: $I_1 = I \frac{R_2}{R_1 + R_2}$.

Kirchhoff's Current Law (KCL)

A circuit principle based on charge conservation stating that the algebraic sum of electric currents entering any node is equal to the algebraic sum of currents exiting that node.

Kirchhoff's Voltage Law (KVL)

A circuit principle based on energy conservation stating that the algebraic sum of all voltages around any closed loop is zero, or the sum of source voltages equals the sum of voltage drops.

Thévenin's Theorem

A network theorem stating that any linear two-terminal circuit can be replaced by an equivalent circuit comprising an open-circuit voltage ($V_{TH}$) in series with an equivalent resistance ($R_{TH}$).

Norton's Theorem

A network theorem stating that any linear two-terminal circuit can be replaced by an equivalent circuit consisting of a short-circuit current source ($I_N$) in parallel with an equivalent resistance ($R_N = R_{TH}$).

Source Transformation

The equivalence relationship permitting a real voltage source $v_s$ in series with a resistor $R$ to be replaced with a current source $i_s = \frac{v_s}{R}$ in parallel with resistor $R$, or vice versa.

Superposition Theorem

A theorem stating that the current through or voltage across any element in a linear multisource network equals the algebraic sum of currents or voltages caused by each independent source acting alone while all other sources are deactivated.

Reciprocity Theorem

A network theorem stating that an ideal voltage source and an ideal ammeter (or an ideal current source and an ideal voltmeter) positioned in two separate branches of a linear bilateral network can be mutually interchanged without altering the meter reading.

Delta ($\Delta$) Arrangement

A three-terminal circuit topology where three resistors are connected head-to-tail to form a closed three-sided loop or delta structure.

Star (Y / Wye) Arrangement

A three-terminal circuit configuration where three resistors each connect from an external terminal to a single common central junction node.

Delta-Star Transformation

A conversion method for networks where resistors are neither in series nor in parallel, converting delta resistances to star values using $R_a = \frac{R_2 R_3}{R_1 + R_2 + R_3}$, where equal resistors satisfy $R_\Delta = 3 R_Y$.