Master circuit analysis with KCL and KVL — solve any linear circuit systematically.
KCL — Current Law
The algebraic sum of currents at any node is zero (what goes in = what comes out). Charge cannot accumulate at a node. In water analogy: water flowing into a pipe junction equals water flowing out. KCL is based on conservation of charge. Mathematically: Σ I_in = Σ I_out or Σ I = 0 (with sign convention).
Total current entering a node = Total current leaving
KVL — Voltage Law
The algebraic sum of voltages around any closed loop is zero. As you travel around a loop, voltage rises (batteries) must equal voltage drops (resistors). KVL is based on conservation of energy — the electric field is conservative. Pick a direction, assign polarities, sum to zero.
Sum of all voltages around a closed loop = 0
Sign Conventions
For KVL: Going through a resistor in the direction of current: -IR (voltage drop). Going against: +IR (voltage rise). Going through a battery from - to +: +V (rise). Going from + to -: -V (drop). For KCL: Current entering node: positive. Leaving: negative. Or vice versa — just be consistent.