Circuit Theory and Electromagnetism

Vocabulary practice flashcards covering fundamental concepts, components, circuit laws, network theorems, electromagnetic induction, and alternating-current analysis from the CSM 153 Circuit Theory course.

Electric charge

An intrinsic, conserved property of elementary particles (such as electrons and protons) that gives rise to electric fields and forces, where total electric charge is neither created nor destroyed in any interaction.

Coulomb's Law

A fundamental law stating that the electrostatic force ($F_e$) between two stationary charged particles is directly proportional to the product of their charges ($q_1$ and $q_2$) and inversely proportional to the square of their separation distance ($r$): $F_e = k_e \frac{q_1 q_2}{r^2}$, where $k_e = 8.9875 \times 10^9\,\text{N}\cdot\text{m}^2/\text{C}^2$.

Electric field ($\mathbf{E}$)

A region in space around a charged body where electrostatic forces can be experienced by other electric charges, defined such that the electrostatic force exerted on a charge $q$ is $\mathbf{F}_E = q\mathbf{E}$.

Electric potential ($V$)

A scalar quantity defined as the electric potential energy per unit charge ($V = \frac{U}{q}$) or the negative of the work done per unit charge in moving a charge from infinity to a given point ($V = -\frac{W_\infty}{q}$), measured in volts ($\text{V}$) or joules per coulomb ($\text{J}/\text{C}$).

Electronvolt ($\text{eV}$)

A unit of energy defined as the energy gained or acquired by a particle carrying the elementary charge of an electron ($q = e$) when accelerated through an electric potential difference of $1\,\text{V}$.

Conductor

A metallic material in which valence electrons are very loosely bound to the nucleus and can move freely through the crystal structure as conduction electrons, enabling electrical conduction via electronic conduction.

Insulator

A material whose electrons are firmly bound to atomic nuclei and cannot move freely under an applied potential difference, conducting electricity only through dielectric conduction.

Semiconductor

A material whose electrons are relatively loosely bound compared to insulators, allowing only a few electrons to move under an applied electric field unless additional carriers are generated.

Resistor

A circuit element specifically designed to provide a definite resistance ($R$) that relates to material resistivity ($\rho$), length ($l$), and cross-sectional area ($A$) by $R = \frac{\rho l}{A}$, and whose resistance remains independent of applied voltage polarity.

Resistor reliability band

The optional fifth colored band on a resistor that statistically indicates the expected percentage of components that will deviate from their nominal resistance value after $1000\,\text{hours}$ of operation.

Capacitor

An electrical device consisting of two conductors separated by an insulating dielectric material, designed to store electrical energy as potential energy within an electric field.

Capacitance ($C$)

The ratio of the magnitude of electric charge ($Q$) on either plate of a capacitor to the potential difference ($V$) established between them ($C = \frac{Q}{V}$), measured in farads ($\text{F}$).

Dielectric

An insulating material (such as mica, paper, mineral oil, or ceramic) placed between the conducting plates of a capacitor that increases capacitance by a factor $\kappa$ (or $\varepsilon_r$) by weakening the internal electric field.

Dielectric strength

The maximum electric field (potential gradient) that an insulating dielectric material can withstand without electrical breakdown and physical spark formation.

Inductor

A circuit component typically consisting of a coil of wire that opposes changes in electric current by storing energy in a concentrated magnetic field ($U_B = \frac{1}{2} L I^2$).

Self-inductance ($L$)

The property of a circuit loop whereby a time-varying current induces an electromotive force within that same loop, mathematically defined by $\varepsilon_L = -L \frac{di}{dt}$, with units of henrys ($\text{H}$).

Mutual inductance ($M$)

The property of two magnetically coupled circuits where a time-varying current in one coil induces an electromotive force in an adjacent coil, given by $\varepsilon_2 = -M \frac{di_1}{dt}$, where $M_{12} = M_{21} = M$.

Ohm's Law

A law stating that the electric current ($I$) through a metallic conductor is directly proportional to the applied potential difference ($V$), provided temperature and other physical parameters remain constant ($V = IR$).

Node

A junction point in an electrical network where two or more circuit elements or branches form a common connection.

Branch

A single continuous path in an electrical network composed of one circuit element connected between two terminal nodes.

Loop

Any closed conduction path in an electrical circuit traversed such that no circuit element or intermediate node is encountered more than once.

Kirchhoff's Current Law (KCL)

Kirchhoff's first law, grounded in the conservation of electric charge, stating that the algebraic sum of all electric currents entering and exiting any node or junction must equal zero ($\sum I = 0$).

Kirchhoff's Voltage Law (KVL)

Kirchhoff's second law, grounded in the conservation of energy, stating that around any closed loop in an electrical network, the algebraic sum of emfs equals the algebraic sum of potential drops ($\sum E = \sum IR$).

Voltage Divider Theorem

A principle stating that the potential difference across a specific resistor $R_x$ in a series string equals the total voltage $V$ multiplied by the ratio of that resistance to the total equivalent series resistance: $V_x = V \frac{R_x}{R_{\text{eq}}}$.

Current Divider Theorem

A principle stating that the current $I_x$ through any individual parallel branch equals the total input current $I_T$ multiplied by the equivalent parallel resistance divided by the resistance of that branch: $I_x = I_T \frac{R_{\text{eq}}}{R_x}$.

Mesh analysis

A planar circuit analysis method that assigns independent loop or mesh currents and applies Kirchhoff's Voltage Law (KVL) around each mesh to formulate a solvable system of simultaneous linear equations.

Nodal analysis

A circuit analysis method that selects node voltages relative to an arbitrary reference (ground) node and applies Kirchhoff's Current Law (KCL) at all other essential nodes to solve for unknown electrical potentials.

Delta-Wye ($\Delta\text{-}Y$) transformation

A mathematical conversion technique used to simplify three-terminal resistor networks between a delta ($\Delta$) arrangement and an equivalent wye ($Y$) configuration.

Superposition Theorem

A network theorem stating that in any linear resistive network containing multiple independent sources, the voltage across or current through any element equals the algebraic sum of the individual voltages or currents produced by each source operating alone, with all other independent voltage sources short-circuited and current sources open-circuited.

Thevenin's Theorem

A network theorem stating that any two-terminal linear network containing sources and resistors can be replaced at its open terminals by an equivalent circuit consisting of a single independent open-circuit voltage source ($V_{\text{Th}}$) in series with a single equivalent resistance ($R_{\text{Th}}$).

Norton's Theorem

A network theorem stating that any two-terminal linear bilateral direct-current network can be replaced by an electrically equivalent circuit consisting of a single short-circuit current source ($I_N$) in parallel with an equivalent internal resistance ($R_N$).

Magnetic force ($\mathbf{F}_B$)

A vector force exerted on an electric charge $q$ moving with velocity $\mathbf{v}$ in a magnetic field $\mathbf{B}$, given by the cross product $\mathbf{F}_B = q(\mathbf{v} \times \mathbf{B})$, with magnitude $F_B = q v B \sin(\theta)$.

Ampere's Law

A magnetic law stating that the line integral of the tangential component of magnetic field $\mathbf{B}$ evaluated around any closed Amperian loop equals the permeability of free space ($\mu_0$) multiplied by the total enclosed electric current: $\oint \mathbf{B} \cdot d\mathbf{s} = \mu_0 I$.

Biot-Savart Law

An empirical equation providing the differential magnetic field ($d\mathbf{B}$) generated by an infinitesimal current-carrying length element ($I\,d\mathbf{s}$) at a displacement distance $r$: $d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I\,d\mathbf{s} \times \hat{\mathbf{r}}}{r^2}$.

Faraday's Law of Induction

A law stating that the magnitude of electromotive force ($\varepsilon$) induced in a conducting loop is directly proportional to the time rate of change of magnetic flux ($\Phi_B$) linking that loop: $\varepsilon = -\frac{d\Phi_B}{dt}$.

Lenz's Law

A qualitative law dictating that the direction of an induced electromotive force and resulting induced current is always such that its own magnetic field opposes the primary change in magnetic flux that induced it.

Transformer

An electrical device that utilizes mutual electromagnetic induction between primary ($N_1$) and secondary ($N_2$) windings wound on a common iron core to step up or step down alternating voltages according to $\frac{V_2}{V_1} = \frac{N_2}{N_1}$.

AC generator

A machine that converts mechanical rotational energy into alternating electrical energy by rotating a conducting loop inside a uniform magnetic field, delivering sinusoidal output via slip rings and stationary brushes: $\varepsilon = \varepsilon_{\text{max}} \sin(\omega t)$.

Inductive reactance ($X_L$)

The frequency-dependent opposition to alternating current flow exhibited by an inductor, defined by $X_L = \omega L = 2\pi f L$, with units of ohms ($\Omega$), causing circuit voltage to lead current by $90^\circ$.

Capacitive reactance ($X_C$)

The frequency-dependent opposition to alternating current flow exhibited by a capacitor, defined by $X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C}$, with units of ohms ($\Omega$), causing circuit current to lead voltage by $90^\circ$.

Phasor

A directed vector rotating counterclockwise at angular velocity $\omega$ whose length corresponds to the peak amplitude of an alternating quantity and whose angle represents its instantaneous phase.

Impedance ($Z$)

The total effective opposition presented by an alternating-current circuit to current flow, incorporating both resistance and reactive elements, given in a series $RLC$ circuit by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.

Resonant frequency ($f_0$)

The specific frequency of an applied alternating signal at which inductive and capacitive reactances cancel exactly ($X_L = X_C$), minimizing circuit impedance to $R$ and maximizing current: $f_0 = \frac{1}{2\pi\sqrt{LC}}$.

Quality factor ($Q$ factor)

A dimensionless figure of merit measuring the sharpness of resonance in an oscillating system, defined as the ratio of center resonant frequency ($f_0$) to the half-power bandwidth ($\Delta f$): $Q = \frac{f_0}{\Delta f}$.

Power factor

The dimensionless coefficient $\cos(\phi)$ in the alternating-current average power formula $P_{\text{av}} = I_{\text{rms}} V_{\text{rms}} \cos(\phi)$, representing the cosine of the phase angle difference between applied voltage and current.

RL circuit time constant ($\tau$)

The characteristic parameter of a series resistor-inductor circuit representing the time required for current to transition through an exponential factor of $(1 - e^{-1})$, defined as $\tau = \frac{L}{R}$.

RC circuit time constant ($\tau$)

The characteristic scaling time for charging or discharging a capacitor through a resistor, defined by the product $\tau = RC$.