Glossary: Kirchhoff's Laws and Circuit Topology

Key terms and definitions for Chapter 3. Definitions follow ISO 11179 metadata registry standards — precise, concise, distinct, and non-circular.

B

Branch — A path containing a single circuit element that connects two nodes. Each branch carries its own current.

C

Circuit Simplification — The process of reducing a complex circuit to a simpler equivalent form using series, parallel, and delta-wye techniques while preserving electrical behavior at the terminals.

Circuit Topology — The study of how circuit components are interconnected, independent of component types or values, described in terms of nodes, branches, loops, and meshes.

Conductance Matrix — A symmetric matrix \(\mathbf{G}\) used in the node voltage method where diagonal entries are the sum of conductances connected to each node, and off-diagonal entries are the negatives of shared conductances.

D

Delta Configuration (Δ) — A three-terminal resistor arrangement where three resistors are connected in a triangle, with each resistor directly linking two of the three terminals. Also called a pi (π) configuration.

E

Equivalent Resistance — A single resistance value that replaces a network of resistors while drawing the same total current from the source as the original network.

K

Kirchhoff's Current Law (KCL) — The principle that the algebraic sum of all currents at any node equals zero, based on conservation of electric charge.

Kirchhoff's Voltage Law (KVL) — The principle that the algebraic sum of all voltages around any closed loop equals zero, based on conservation of energy.

L

Load Resistance — The resistance of the component or subsystem that receives and consumes power from the circuit.

Loop — Any closed path through a circuit that starts and ends at the same node without passing through any node more than once.

M

Mesh — A loop that does not enclose any other loops within it; the smallest possible loop in a planar circuit.

Mesh Current Method — A systematic circuit analysis technique that assigns a circulating current to each mesh and writes KVL equations, requiring \(m\) equations for \(m\) meshes.

N

Node — A point in a circuit where two or more components connect. All points joined by ideal wire form a single node.

Node Voltage Method — A systematic circuit analysis technique that defines voltages at each non-reference node and writes KCL equations, requiring \(n-1\) equations for \(n\) nodes.

R

Reference Node — The node assigned a voltage of 0 V, against which all other node voltages are measured. Also called the ground node or datum node.

Resistance Matrix — A symmetric matrix \(\mathbf{R}\) used in the mesh current method where diagonal entries are the sum of resistances in each mesh, and off-diagonal entries are the negatives of shared resistances.

S

Supermesh — A combined loop formed when a current source is shared between two meshes, allowing KVL to be written around the outer boundary while using the current source value as a constraint equation.

Supernode — A combined region formed when a voltage source connects two non-reference nodes, allowing KCL to be applied to the boundary while using the voltage source value as a constraint equation.

Superposition Principle — The principle that in a linear circuit, the response at any point equals the algebraic sum of responses due to each independent source acting alone, with all other independent sources deactivated.

W

Wye Configuration (Y) — A three-terminal resistor arrangement where three resistors share a common central node, with each resistor extending to one of the three external terminals. Also called a T configuration.