Kirchhoff's Voltage Law (KVL) Virtual Laboratory

Multi-Loop DC Schematic & Particle Flow

KVL Loop Analysis

Loop Voltage Profile

Potential V(x) vs Path

Live Measurements & Digital Probes

V1 Source 12.0 V

V2 Source 9.0 V

VR1 Drop 4.20 V

VR2 Drop 7.80 V

VR3 Drop 1.20 V

I1 (Branch 1) 0.42 A

I2 (Branch 3) 0.04 A

I3 (Middle R2) 0.39 A

Digital Voltmeter Probes

Red Probe (+)

Black Probe (-)

V(Red, Black) +7.80 V

Digital Ammeter Probe

Select Branch

Current I 0.39 A (B → E)

Observation Log & Verification Record

Trial	V1	V2	R1	R2	R3	Loop 1 Sum	Loop 2 Sum	I1	I2	I3	KVL Error	Status

Circuit Controls

Voltage Source 1 V1

Voltage Source 2 V2

Resistor 1 R1

Resistor 2 (Shared) R2

Resistor 3 R3

KVL Summary

Loop 1 Sum: +0.0000 V

Loop 2 Sum: +0.0000 V

Max KVL Error: 0.0000 V

Experiment Challenge Mode

TRY AGAIN

Guided Procedure

Observe the complete 2-mesh multi-loop DC circuit.

Identify DC voltage sources V1 and V2 and resistors R1, R2, R3.

Select Loop 1 (Left Mesh: D → A → B → E → D).

Follow the clockwise traversal path.

Identify potential rise (+V1) and potential drops across R1 and R2.

Verify that the algebraic sum around Loop 1 equals 0 V.

Select Loop 2 (Right Mesh) and analyze rises/drops.

Observe the Loop Voltage Profile graph for potential step transitions.

Use the Digital Voltmeter Probe to measure node potential differences V(A,B).

Toggle Node Voltages to display absolute potential at all nodes.

Adjust sliders to change source voltages and resistor values.

Observe live particle current updates and sign changes.

Click Add Current Reading to log observations into the table.

Theory & Reference

Kirchhoff's Voltage Law (KVL) states that the directed algebraic sum of potential differences (voltages) around any closed loop in a circuit is identically zero.

$$\sum_{k=1}^N V_k = 0$$

Sign Convention Rules:

Voltage Source: Traversing from (−) to (+) terminal is a Voltage Rise (+V). Traversing (+) to (−) is a Voltage Drop (−V).
Resistor: Traversing in the direction of current flow is a Voltage Drop (−I·R). Traversing against current flow is a Voltage Rise (+I·R).

Because electrostatic force is conservative, electric potential is single-valued at every point in space. Completing a closed circuit path returns to the initial potential, ensuring KVL holds globally.