Free Physics Simulation

Explore the Kirchhoff's Rules: Multi-Loop Circuit Lab

Change the EMFs and resistors in a real two-loop circuit and watch all three branch currents solve live from Kirchhoff's voltage and current laws.

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Free to use
No signup
Nothing to install
Runs in your browser

Free to use

No signup

Kirchhoff's Rules: Multi-Loop Circuit Lab

Setting

Open the Kirchhoff's Rules: Multi-Loop Circuit Lab

Illustration. Open the tool for the real thing.

See it in action

The Kirchhoff's Rules: Multi-Loop Circuit Lab with sample data entered and the result showing.

Screenshot of the Kirchhoff's Rules: Multi-Loop Circuit Lab with sample data entered: The Kirchhoff's Rules: Multi-Loop Circuit Lab with sample data entered and the result showing. — Sample data entered into the Kirchhoff's Rules: Multi-Loop Circuit Lab. Open the tool to try your own.

Explained

What is the Kirchhoff's Rules: Multi-Loop Circuit Lab?

Change the EMFs and resistors in a real two-loop circuit and watch all three branch currents solve live from Kirchhoff's voltage and current laws. It runs in your browser, so a change to a setting or a drag on an object shows up at once.

Electrical engineers use Kirchhoff's rules and mesh analysis exactly like this to design and troubleshoot multi-branch circuits in everything from car wiring to power distribution networks.

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Key idea 1Key idea 2Key idea 3

3 steps to your result

Open the tool and follow along. Nothing to install.

In the Kirchhoff's Rules: Multi-Loop Circuit Lab, use the controls to change EMF ε₁ (left battery), EMF ε₂ (right battery), Resistor R₁ (left branch), Resistor R₂ (right branch), Resistor R₃ (middle branch). The simulation reacts instantly.

Start with this experiment: Set both EMFs equal and see how the middle-branch current behaves. Drag any glowing handle, object or slider with your mouse or finger and the Kirchhoff's Rules: Multi-Loop Circuit Lab responds in real time.

Change one setting at a time and watch which readout moves, then compare it with this idea: Kirchhoff's voltage law (KVL): the sum of EMFs and voltage drops around any closed loop is zero.

What you get

Key idea 1

Kirchhoff's voltage law (KVL): the sum of EMFs and voltage drops around any closed loop is zero.

Key idea 2

Kirchhoff's current law (KCL): the total current flowing into a junction equals the total current flowing out.

Key idea 3

A circuit with more than one loop generally needs both laws together, solved as a system of simultaneous equations, to find every branch current.

Experiment 1

Set both EMFs equal and see how the middle-branch current behaves.

Experiment 2

Raise R3 (the shared branch) very high and see the loops nearly decouple.

Experiment 3

Try the middle-branch current challenge.

Used for

Pick one to see how it fits.

Use case

Physics learners

Physics students in middle school, high school and first-year university, teachers who want a quick demonstration for the projector, and anyone revising for exams.

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How it compares

A plain look at this tool next to the usual alternative.

	This simulation	Textbook diagram
Interactive	Drag, tap and change settings	Fixed picture
Install	Nothing to install	Not needed
Cost	Free to use	Depends on the book

Questions people ask

Why can't Ohm's law alone solve a two-loop circuit?

Ohm's law only relates voltage, current and resistance for a single resistor; a multi-loop circuit has multiple unknown currents linked by shared branches, so you need Kirchhoff's two laws together to get enough independent equations.

What does it mean if the junction check (I1 - I2 - I3) isn't exactly zero?

In a real solved circuit it should be extremely close to zero; a large mismatch would mean the current directions or the mesh equations were set up incorrectly.

Is the Kirchhoff's Rules: Multi-Loop Circuit Lab free to use?

Yes. The Kirchhoff's Rules: Multi-Loop Circuit Lab is free, needs no signup or download and runs in your web browser. It is part of the Physics group of AZRS simulations.

Does the Kirchhoff's Rules: Multi-Loop Circuit Lab work on a phone or tablet?

Yes. The Kirchhoff's Rules: Multi-Loop Circuit Lab takes touch input as well as mouse input, so you can use its 5 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.

How do I use the Kirchhoff's Rules: Multi-Loop Circuit Lab?

1. In the Kirchhoff's Rules: Multi-Loop Circuit Lab, use the controls to change EMF ε₁ (left battery), EMF ε₂ (right battery), Resistor R₁ (left branch), Resistor R₂ (right branch), Resistor R₃ (middle branch). The simulation reacts instantly. 2. Start with this experiment: Set both EMFs equal and see how the middle-branch current behaves. Drag any glowing handle, object or slider with your mouse or finger and the Kirchhoff's Rules: Multi-Loop Circuit Lab responds in real time. 3. Change one setting at a time and watch which readout moves, then compare it with this idea: Kirchhoff's voltage law (KVL): the sum of EMFs and voltage drops around any closed loop is zero.