Kirchhoff's laws

How to use this resource

Please download the PDF of this resource using the Download PDF link in the banner above.

Below are a series of interactives which support the resource. Each interactive can be launched by clicking on its image, or through links in the PDF itself.

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Topic areas

Electrical and electronic engineering

  • Ohm's law
  • Electrical power
  • Kirchhoff's current law (Kirchhoff's first law)
  • Kirchhoff's voltage law (Kirchhoff's second law)
  • Resistors in series and parallel


  • Simultaneous equations



Problem statement

Simple circuits, for example those with a single power supply connected in series to a load, are straightforward to analyse in terms of current, voltage drop across loads and power dissipated, using the expressions V = IR and P = IV. In practice however, circuits are generally much more complex than this, with multiple components and multiple paths for the current to flow.

How can complex circuits be analysed? What can such an analysis tell us about how the circuit will behave if one or more components fails?


Click the image to load Kirchhoff 1. 

Kirchhoff 1

The above interactive all shows a junction in a circuit and lets you practice applying Kirchhoff's first law for various junction configurations.

Click the image to load Kirchhoff 2. 

Kirchhoff 2

The above interactive shows either a simple loop with power source, s simple loop without a power source that is part of a larger circuit, or more complex circuit. It lets you practice applying Kirchhoff's second law.

Click the image to load Kirchhoff 3. 

Kirchhoff 3

Supported by

  • Royal Academy of Engineering
  • Motorola Solutions Foundation