What is Kirchhoff's Current Law (KCL)?

Kirchhoff's Current Law states that the algebraic sum of all currents entering and leaving any node (junction) in a circuit is zero. This means the total current flowing into a node equals the total current flowing out, which is a consequence of charge conservation. For example, if 5A enters a junction and splits into two branches, those branches must carry currents that sum to 5A.

How do you solve a circuit using mesh analysis?

Mesh analysis uses Kirchhoff's Voltage Law (KVL) to write equations around each independent loop. Assign a mesh current to each loop, write KVL equations summing voltage drops (IR products) around each loop equal to the voltage sources, then solve the resulting system of linear equations. For a 2-loop circuit: V1 = I1*R1 + (I1-I2)*R2 and V2 = I2*R3 + (I2-I1)*R2.

What is the difference between mesh analysis and node voltage method?

Mesh analysis assigns loop currents and writes KVL equations around each mesh, best for circuits with fewer loops. Node voltage method assigns voltages at each node and writes KCL equations, ideal for circuits with fewer nodes than loops. Both methods yield the same results but one may be simpler depending on circuit topology.

Kirchhoff’s Circuit Solver

KCL • KVL • Mesh Analysis • Node Voltages • Power — Simulate • Explore • Practice • Quiz

Mode

Circuit Preset

V1 (V) 12.0 V

V2 (V) 8.0 V

R1 (Ω) 100 Ω

R2 (Ω) 200 Ω

R3 (Ω) 150 Ω

Show Mesh Currents Show Node Voltages Show Power

I1 (Mesh 1)

0.0 mA

I2 (Mesh 2)

0.0 mA

I3 (Mesh 3)

0.0 mA

I_R2 (Branch)

0.0 mA

V Node B

0.0 V

P (R1)

0.0 mW

P (R2)

0.0 mW

P (R3)

0.0 mW

P Total

0.0 mW

Kirchhoff’s Circuit Laws — Free Interactive Multi-Loop DC Circuit Solver

Kirchhoff’s laws are the foundation of electrical circuit analysis. Kirchhoff’s Current Law (KCL) states that the total current entering any junction equals the total current leaving it — a consequence of charge conservation. Kirchhoff’s Voltage Law (KVL) states that the sum of all voltage drops around any closed loop equals zero — reflecting energy conservation. Together, KCL and KVL allow engineers to analyze circuits of arbitrary complexity by writing and solving systems of linear equations. Our interactive simulator lets you build 2-loop and 3-loop DC circuits with multiple voltage sources and resistors, then visualize mesh currents, node voltages, and power dissipation in real time.

Mesh Analysis — Solving Multi-Loop Circuits

Mesh analysis (also called loop analysis) is a systematic method for solving planar circuits. You assign a mesh current to each independent loop, then apply KVL around each mesh. For a 2-loop H-bridge circuit with voltage sources V1 and V2 and resistors R1, R2, R3, the equations are: V1 = I1×R1 + (I1−I2)×R2 and V2 = I2×R3 + (I2−I1)×R2. This gives a 2×2 system that can be solved using Cramer’s rule or matrix methods. The branch current through the shared resistor R2 is simply I_R2 = I1 − I2. This simulator solves the system automatically and shows how mesh currents relate to branch currents.

Node Voltage Method & Superposition

The node voltage method assigns a voltage variable to each non-reference node and writes KCL equations. It is particularly efficient when a circuit has fewer nodes than meshes. Superposition analyzes multi-source circuits by considering one source at a time (deactivating others) and summing individual contributions. Both methods are equivalent to mesh analysis and produce identical results. Our simulator demonstrates these concepts through visual overlays showing node potentials and current flow directions.

Power Dissipation in Multi-Loop Circuits

Each resistor in a circuit dissipates power as heat, calculated as P = I²R where I is the actual branch current through that resistor. In multi-loop circuits, the branch current may be the difference of two mesh currents if the branch is shared between loops. The total power delivered by all sources equals the total power dissipated across all resistors — conservation of energy. Our simulator displays a heat glow on each resistor proportional to its power dissipation, giving an intuitive visual representation of energy distribution.

Who Uses This Simulator?

This Kirchhoff’s circuit solver is designed for electrical engineering students learning circuit analysis, physics students studying DC circuits, TVET trainees practicing mesh and node methods, and instructors teaching Kirchhoff’s laws. It provides hands-on, visual understanding of multi-loop circuit behaviour without requiring laboratory equipment or professional simulation software like SPICE.

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