Home › Experiments › Physics Experiments › Verification of Kirchhoff's Laws Using Virtual Simulation

Verification of Kirchhoff's Laws Using Virtual Simulation

Kirchhoff's Current Law and Kirchhoff's Voltage Law verification using a virtual circuit simulation environment.

Physics Experiments 20 September, 2026 5 min read
Physics Simplified

Verification of Kirchhoff's Laws Using Virtual Simulation

Last updated: January 2024 | Virtual Lab Experiment

Aim

To verify Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) using a virtual circuit simulation environment, and to demonstrate that the algebraic sum of currents at any junction is zero and the algebraic sum of voltages around any closed loop is zero.

Software / Tools Required

Virtual Circuit Simulator
PhET Circuit Construction Kit, Tinkercad Circuits, or EveryCircuit
Web Browser
Chrome, Firefox, or Edge with JavaScript enabled
Screen / Notebook
For recording observations and taking screenshots
Recommended: PhET Circuit Construction Kit: DC — Virtual Lab is freely available at phet.colorado.edu and runs directly in a browser. Tinkercad Circuits at tinkercad.com offers drag-and-drop circuit building with built-in simulation.

Theory & Principle

Kirchhoff's laws, formulated by Gustav Kirchhoff in 1845, are two fundamental rules governing the distribution of current and voltage in electrical circuits. These laws apply to both real hardware circuits and virtual simulations. In a virtual environment, the underlying mathematical models solve the same network equations, but with the significant advantage of ideal component behavior.

Kirchhoff's Current Law (KCL) — Junction Rule

Kirchhoff's Current Law (KCL)
The algebraic sum of all currents entering and leaving any junction (node) in a circuit is zero.
Σ Iin = Σ Iout    or equivalently    Σ I = 0  (at any node)

KCL is a direct consequence of the conservation of electric charge. Since charge cannot accumulate at a junction in a steady-state circuit, the total current flowing into a node must equal the total current flowing out.

Kirchhoff's Voltage Law (KVL) — Loop Rule

Kirchhoff's Voltage Law (KVL)
The algebraic sum of all potential differences (voltages) around any closed loop in a circuit is zero.
Σ V = 0  (around any closed loop)    or    Σ EMF = Σ IR

KVL is a consequence of the conservation of energy. A charge moving around any closed loop returns to its starting point with the same potential energy, so the net energy gained from sources must equal the energy lost across resistive elements.

Why Use Virtual Simulation?

  • Ideal conditions: Virtual resistors have exact values with zero tolerance, wires have zero resistance, and measuring instruments have no loading effect (ammeter internal resistance = 0, voltmeter internal resistance = infinity).
  • Rapid parameter changes: Component values can be modified instantly by clicking and typing — no physical rewiring needed. This allows testing multiple configurations in minutes.
  • Drag-and-drop measurements: Virtual ammeter and voltmeter probes can be placed anywhere in the circuit by simply dragging them to the desired branch or across the desired component.
  • Perfect repeatability: Every simulation run with identical parameters produces identical results, eliminating random experimental errors.

Virtual Setup Diagram

The following diagram shows a two-loop resistive network as it would appear inside a virtual circuit simulator. Three resistors (R1, R2, R3) are connected to a 10V DC source, with virtual ammeter probes (yellow, marked A) placed in series at key branches and voltmeter probes (red, marked V) connected in parallel across each component.

Virtual Circuit Simulator v2.0 + − 10V R₁ = 100Ω R₂ = 200Ω R₃ 300Ω A B C D E F A₁ A₂ A₃ V₁ V₂ V₃ I II Ammeter Voltmeter Junction Loop direction

Figure: Two-loop DC network inside a virtual circuit simulator with ammeter and voltmeter probes placed for verifying KCL and KVL.

Circuit Topology: R1 (100Ω) is in series with the parallel combination of R2 (200Ω) and R3 (300Ω). Node B is the key junction where current splits into two branches. Loop I passes through the source, R1, and R3. Loop II passes through the source, R1, and R2.

Procedure

Part A: Verification of Kirchhoff's Current Law (KCL)

  1. 1Open the virtual circuit simulator (PhET Circuit Construction Kit or Tinkercad Circuits) in your web browser. Select the DC mode and ensure the workspace is clear.
  2. 2Build the two-loop network: Place a 10V DC battery, then connect R1 = 100Ω in series from terminal A to junction B. From junction B, connect R2 = 200Ω leading to node C and R3 = 300Ω leading to node E. Complete the circuit by connecting C–F and D–E along the bottom rail back to the battery's negative terminal.
  3. 3Place virtual ammeter probes in series at three key branches: A1 in the R1 branch (measures total current entering junction B), A2 in the R2 branch (measures current leaving B through R2), and A3 in the R3 branch (measures current leaving B through R3).
  4. 4Run the simulation and record the ammeter readings at junction B. Verify that the current entering the junction (A1 reading) equals the sum of currents leaving (A2 + A3 readings).
  5. 5Change R1 to 150Ω, R2 to 220Ω, and R3 to 330Ω by clicking on each resistor and editing its value. Record the new ammeter readings and verify KCL again.
  6. 6Change the supply voltage to 12V (keeping R1 = 100Ω, R2 = 200Ω, R3 = 300Ω) to create a third data set. Record readings and verify KCL at junction B for this configuration as well.

Part B: Verification of Kirchhoff's Voltage Law (KVL)

  1. 1Using the same circuit from Part A (Trial 1 configuration), place virtual voltmeter probes across each component: V1 across R1, V2 across R2, and V3 across R3. Also note the source voltage displayed on the battery.
  2. 2Run the simulation and record all voltage readings. Note: In a virtual simulator, voltmeters have infinite internal resistance, so they do not affect the circuit behavior.
  3. 3Choose a closed loop (e.g., Loop II: source → R1 → R2 → return). Sum the voltages algebraically around the loop: +Vsource − VR1 − VR2. Verify that the sum equals zero.
  4. 4Repeat for the other loop (Loop I: source → R1 → R3 → return) and verify that +Vsource − VR1 − VR3 = 0.
  5. 5Change the resistor values (Trial 2: R1 = 150Ω, R2 = 220Ω, R3 = 330Ω) and repeat the voltage measurements and loop verification for the new configuration.
  6. 6Change the supply voltage to 12V (Trial 3 configuration) and verify KVL once more. Record all voltages and confirm the algebraic sum around each loop equals zero.
Advantages of simulation over physical lab: You can reset the circuit instantly if a mistake is made. There is no risk of damaging equipment with incorrect connections. Measurement results appear immediately without instrument settling time. You can quickly test dozens of configurations in a single session, building deeper intuition for circuit behavior.

Observation Tables

Table A: KCL Verification — Currents at Junction B

Trial V (V) R1 (Ω) R2 (Ω) R3 (Ω) Iin at B (mA)
[A1 reading]		 IR2 (mA)
[A2 reading]		 IR3 (mA)
[A3 reading]		 IR2 + IR3 (mA) ΣIin − ΣIout
1 10 100 200 300 45.45 27.27 18.18 45.45 0.00
2 10 150 220 330 35.46 21.28 14.18 35.46 0.00
3 12 100 200 300 54.55 32.73 21.82 54.55 0.00

Table B: KVL Verification — Voltages Around Closed Loops

Trial Vsource (V) R1, R2, R3 (Ω) Loop Path +Vsource (V) −VR1 (V) −VR (V)
[R2 or R3]		 ΣV (V)
1 10 100, 200, 300 V → R1 → R2 +10.00 −4.55 −5.45 0.00
2 10 150, 220, 330 V → R1 → R2 +10.00 −5.32 −4.68 0.00
3 12 100, 200, 300 V → R1 → R3 +12.00 −5.45 −6.55 0.00
Observation: In all three trials and across both loops, the algebraic sum of currents at junction B is zero (KCL verified) and the algebraic sum of voltages around each closed loop is zero (KVL verified). The virtual simulation yields exact agreement with theory.

Calculations

We perform a detailed theoretical calculation for Trial 1 (V = 10V, R1 = 100Ω, R2 = 200Ω, R3 = 300Ω) and compare with the simulation values.

Step 1: Equivalent Resistance of R2 || R3

Req = (R2 × R3) / (R2 + R3)
Req = (200 × 300) / (200 + 300)
Req = 60000 / 500
Req = 120 Ω

Step 2: Total Circuit Resistance

Rtotal = R1 + Req = 100 + 120
Rtotal = 220 Ω

Step 3: Total Current (through R1)

I = V / Rtotal = 10 / 220
I = 0.04545 A = 45.45 mA   [Simulation: 45.45 mA]

Step 4: Voltage Across the Parallel Combination

VR1 = I × R1 = 0.04545 × 100 = 4.55 V
Vparallel = V − VR1 = 10 − 4.55
Vparallel = 5.45 V   (= VR2 = VR3)

Step 5: Branch Currents

IR2 = Vparallel / R2 = 5.45 / 200
IR2 = 27.27 mA   [Simulation: 27.27 mA]
IR3 = Vparallel / R3 = 5.45 / 300
IR3 = 18.18 mA   [Simulation: 18.18 mA]

Verification

KCL at node B: Iin = IR2 + IR3
45.45 = 27.27 + 18.18 = 45.45 mA   ✔ Verified
KVL Loop (V → R1 → R2 → return):
+10.00 − 4.55 − 5.45 = 0.00 V   ✔ Verified
KVL Loop (V → R1 → R3 → return):
+10.00 − 4.55 − 5.45 = 0.00 V   ✔ Verified
Simulation vs. Theory: The percentage error between simulation and theoretical values is 0% in all cases. This is expected because virtual simulators solve the exact same Ohm's law and Kirchhoff's equations that we use for analytical calculations. The only difference would be floating-point rounding at the last decimal place, which is negligible.

Result

Result:
  1. Kirchhoff's Current Law (KCL) is verified: At every junction in the virtual circuit, the algebraic sum of currents was found to be zero across all three trials. The current entering junction B equaled the sum of currents leaving it with 0% error.
  2. Kirchhoff's Voltage Law (KVL) is verified: Around every closed loop in the virtual circuit, the algebraic sum of voltages was found to be zero across all three trials and both loops, with 0% deviation from the theoretical value.

The virtual simulation confirms that both Kirchhoff's laws hold exactly under ideal circuit conditions. Any minor discrepancy (beyond the fourth decimal place) would be attributable to floating-point rounding within the simulator's computation engine, not to any physical limitation.

Advantages of Virtual Lab

  • Zero equipment cost: No physical resistors, ammeters, voltmeters, power supplies, or connecting wires are needed. The entire experiment runs on freely available software accessible from any computer or tablet with a browser.
  • Perfect repeatability: Every simulation run with identical parameters produces identical results, eliminating random experimental errors. This makes it ideal for understanding the underlying theory before entering a physical lab.
  • No risk of damage: Incorrect connections in a virtual simulator do not burn out components, blow fuses, or create short circuits. Students can freely experiment without fear of costly mistakes.
  • Instant measurements: Current and voltage readings appear immediately upon running the simulation, with no instrument settling time, no parallax error, and no need to interpolate between scale markings. All values are displayed digitally to multiple decimal places.
  • Easy parameter variation: Changing a resistor value takes a single click and keystroke, whereas in a physical lab it requires de-soldering or replacing the component and re-checking connections. This allows rapid exploration of how the circuit responds to different component values and source voltages.

Viva Voce Questions

Q1. Why do virtual simulation results match theoretical values exactly?

Virtual circuit simulators use ideal mathematical models for all components. Resistors have the exact specified resistance with zero tolerance, wires have zero resistance, ammeter probes have zero internal resistance, and voltmeter probes have infinite internal resistance. The simulator solves the circuit equations (based on Kirchhoff's laws and Ohm's law) numerically using the precise given values. Since the theory and the simulator use the same equations and the same ideal assumptions, the results match perfectly. The only possible deviation is floating-point rounding at very high decimal precision, which is negligible for practical purposes.

Q2. How would real-world experimental results differ from simulation?

Real-world results deviate from ideal theory due to multiple factors:

  • Resistor tolerance: Commercial resistors have 1–10% tolerance, meaning a "100Ω" resistor could actually be 95–105Ω.
  • Contact and wire resistance: Physical connections add small parasitic resistances (typically 0.01–1Ω) that are absent in simulations.
  • Instrument loading: Real ammeters have non-zero internal resistance (lowering current) and real voltmeters have finite resistance (drawing current from the circuit).
  • Temperature effects: Resistor values change with temperature as current flows through them and generates heat.
  • Power supply regulation: Real sources have internal resistance, causing their terminal voltage to drop under load.

Typically, real-world experiments show 2–5% deviation from theoretical values, which is considered acceptable.

Q3. Can Kirchhoff's laws fail? When?

Kirchhoff's laws are derived under the lumped circuit approximation, which assumes that all electromagnetic effects are confined to discrete components and that the circuit dimensions are much smaller than the wavelength of any signal. They can appear to fail in these situations:

  • KCL limitation: At very high frequencies, displacement currents (time-varying electric fields) can cause current to effectively flow through the dielectric of a capacitor without physical charge transport across the gap, making it appear as if charge is accumulating at a node.
  • KVL limitation: When a changing magnetic flux threads a circuit loop (as described by Faraday's law of electromagnetic induction), an EMF is induced that is not associated with any lumped component. The voltage around the loop is then non-zero unless the induced EMF is explicitly accounted for.

In such cases, the full Maxwell's equations must be used instead of the simplified Kirchhoff's formulation.

Q4. What is the difference between ideal and practical circuits?

Ideal circuits (as modeled in most virtual simulators) use perfect components:

  • Voltage sources with zero internal resistance (deliver constant voltage regardless of load)
  • Resistors with exact specified values, no parasitic inductance or capacitance, and no temperature dependence
  • Wires with zero resistance (perfect conductors)
  • Ammeters with zero internal resistance and voltmeters with infinite resistance

Practical circuits have components with manufacturing tolerances (typically 1–20%), parasitic elements (every resistor has some inductance and capacitance), temperature coefficients (resistance changes with heating), aging and drift effects, and non-linear behavior at extreme voltages or currents. Advanced simulators like SPICE can model these practical effects using detailed component models.

Q5. Name some engineering applications of Kirchhoff's laws.

Kirchhoff's laws are foundational to virtually all branches of electrical and electronics engineering:

  • Circuit analysis: Mesh analysis and nodal analysis techniques for solving complex networks are direct applications of KVL and KCL respectively.
  • PCB and IC design: Printed circuit board layout and integrated circuit design rely on Kirchhoff's laws for signal integrity, power distribution, and ground plane analysis.
  • Power systems: Load flow analysis, fault current calculations, and power distribution in electrical grids all use Kirchhoff's laws.
  • Battery management: Modeling multi-cell battery packs and balancing circuits uses KCL for current distribution and KVL for voltage monitoring.
  • Simulation software: SPICE, Multisim, LTspice, and all other circuit simulation tools solve circuit matrices built from Kirchhoff's law equations (Modified Nodal Analysis).
← Back to Kirchhoff's Law Derivation & Wheatstone Bridge