How it works
KVL (Kirchhoff's Voltage Law): the algebraic sum of all voltages around any closed loop is zero, Σv = 0. Sign convention: assign a loop current direction; for a resistor, voltage rise is in the direction against the assumed current. For a voltage source, voltage rise is from − to + terminal. KCL (Kirchhoff's Current Law): the algebraic sum of all currents at any node is zero, Σi = 0. Current entering a node is positive; current leaving is negative (or vice versa — pick one convention and stick to it). For a circuit with B branches, N nodes, and L independent loops: L = B − N + 1 independent KVL equations are available.
Key points to remember
For N nodes, only N−1 independent KCL equations exist — one node is taken as reference (ground). For L loops, L independent KVL equations give L mesh currents. A circuit with 3 nodes and 4 branches has 4 − 3 + 1 = 2 independent loop equations. Dependent sources (VCVS, CCCS, VCCS, CCVS) are included in KVL and KCL equations exactly like independent sources — their controlling variable must be expressed in terms of mesh currents or node voltages. Supernode forms when a voltage source connects two non-reference nodes: combine KCL for both nodes and add the voltage constraint equation. Supermesh forms when a current source shares a branch between two meshes.
Exam tip
The examiner always asks you to write the KVL mesh equations or KCL node equations for a given circuit with at least one dependent source — identify supermesh or supernode conditions first, because missing them causes all equations to be wrong.