UNIT B.1 — CIRCUIT ANALYSIS

Kirchhoff's Laws: KCL and KVL

BRIDGE · EE Foundations Bridge · ~11 min

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Series and parallel rules (Unit 1.6) are special cases of two universal laws. Kirchhoff's Current Law (KCL): the current entering any node equals the current leaving it — charge doesn't pile up. Kirchhoff's Voltage Law (KVL): around any closed loop, the voltage rises and drops sum to zero — you always come back to the potential you started at.

These two laws analyze ANY circuit, however tangled. A junction where 8 A enters and two branches leave carrying 3 A and x A? KCL says x = 5 A, instantly. A 120 V loop dropping 70 V across one load? KVL says the rest of the loop drops exactly 50 V.

Engineering circuit analysis is just KCL and KVL applied systematically — write one equation per node or loop, then solve the system (which is where Unit B.3's linear algebra earns its keep).

Go deeper: 'Fundamentals of Electric Circuits' (Sadiku) and MIT's Circuits and Electronics series — linked in the Go Deeper pathway, Semester 3.

KCL

ΣI in = ΣI out

KVL

ΣV around loop = 0

Scope

Any circuit, any topology

Knowledge check

Quiz — 3 questions

1. A node has 10 A entering and two exit branches: 6 A and x. KCL gives x =

2. In a single loop with a 240 V source and drops of 90 V and 60 V across two loads, the third load drops:

3. KVL is a statement of conservation of:

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