Beginner Fundamentals

Kirchhoff's Laws

KVL: voltages around any closed loop sum to zero. KCL: currents into any node sum to zero. This series-parallel circuit demonstrates both.

// Kirchhoff's Laws

Simulator: Falstad CircuitJS1 (GPL-2.0) — hosted by falstad.com

This circuit has a 12 V source, R1 = 1 kΩ in series, and R2 = 2 kΩ in parallel with R3 = 3 kΩ. The parallel combination is the load.

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R_parallel = (R2 × R3)/(R2 + R3) = (2000 × 3000)/5000 = 1200 Ω
Apply KVL to the outer loop: V_source = V_R1 + V_load. The voltage across the parallel combination is V_junction.

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V_junction = 12 × 1200/(1000+1200) = 12 × 1200/2200 ≈ 6.545 V
Apply KCL at node n2 (junction): I_R1 = I_R2 + I_R3. Verify by computing each current from the node voltage.

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I_R1 = (12 − 6.545)/1000 ≈ 5.45 mA; I_R2 = 6.545/2000 ≈ 3.27 mA; I_R3 = 6.545/3000 ≈ 2.18 mA; 3.27 + 2.18 ≈ 5.45 ✓
KVL check: V_R1 + V_junction = V_source. Confirm: V_R1 = 12 − 6.545 ≈ 5.455 V; 5.455 + 6.545 = 12 V ✓

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KVL holds for every closed loop in the circuit, regardless of its complexity.

Expected values

Probe	Value	Unit
V_source	12	V
V_junction	6.545	V