The formula
KCL: ΣI_in = ΣI_out | KVL: ΣV around any closed loop = 0
- I_in, I_out
- currents entering and leaving a node (amperes)
- V
- each rise or drop around a closed loop (volts)
Worked example
3 A enters a node; one branch carries 1.2 A away. A 12 V loop has drops of 5 V and 4 V.
- KCL: 3 = 1.2 + I₂ → I₂ = 3 − 1.2
- KVL: 12 − 5 − 4 − V₃ = 0
- V₃ = 12 − 9
The second branch carries 1.8 A; the remaining element drops 3 V.
Where you'll use it
The foundation of mesh and nodal analysis, and the first step in any circuit too tangled for series-parallel reduction. Sign convention is what trips people: pick a loop direction and stay with it.