Kirchhoff Circuit Laws

Kirchhoff's Circuit Laws are fundamental principles used to analyze complex electrical circuits. Kirchhoff's Current Law (KCL) states that the sum of currents entering a junction must equal the sum of currents leaving it (conservation of charge). Kirchhoff's Voltage Law (KVL) states that the directed sum of the electrical potential differences (voltage) around any closed network is zero (conservation of energy). In this module, we use mesh analysis to apply KVL directly, generating a system of linear equations to solve for the unknown currents.

Experiment

Use the interactive controls in the Kirchhoff Circuit Laws module to observe how the mesh currents shift. These examples demonstrate the superposition principle and current reversal based on relative source strengths.

1. Set Left source E1 to 6 and Right source E2 to 6, with all resistors at 2 Ω. Observe that I₁ and I₂ both become 3 A. The shared branch current cancels out to exactly 0 A.
2. Set Left source E1 to 0 and Right source E2 to 6. Notice that the shared branch current reverses direction (becomes -1 A), which is indicated by the arrow in the schematic reversing its orientation.
3. Set Left source E1 and Right source E2 both to 0. Every current, supplied power and dissipated power is 0. The shared-current arrow disappears rather than claiming a direction for zero.
4. Set Left resistance R1 to 0. The genuine visible input error replaces computed values; ideal shorts are outside this model. Restore R1 to 1, then set Right resistance R2 and Shared resistance R3 to 1 and both sources to 12. Both mesh currents are 12 A, shared current is 0 and both powers are 288 W.
5. Clear Right source E2 and observe the accessible raw-input error. Restore 0; the circuit and physical results recover. A residual is a computed floating-point check, not a forced zero label.