Optional Practical: Kirchoff's laws (Geogebra and PhET)


In this exercise you will learn how use Geogebra to solve circuit problems using Kirchoff's laws. The solutions will also be checked using the PhET circuit simulator.

Consider the following circuit:

The problem here is to find the current through each resistor. So that we can write equations for the circuit we first need to label the currents. These are often labeled I1, I2 etc. but here we will use a,b and c since this will make writing the equations easier.

In this example the direction of currents is obvious but in others it may not be, this doesn't matter, if you guess wrong the answer comes out negative.

Kirchoff's 1st

Currents in = currents out

a + b = c

Kirchoff's 2nd

Σ EMF's = Σ PD's (around any closed loop)

Outer loop: 6 = 6a + 12c

Inner loop: 12 = 12b +12c

small loop: 6 - 12 = 6a - 12b

Using GeoGebra

This example isn't that difficult so you can solve it on paper. Try this before using GeoGebra.

  • Open a new GeoGebra file and select CAS view. This doesn't stand for Creative Active Service it stands for "Computer Algebra System".
  • In the CAS pane type "solutions" then choose Solutions[list of equations, list of variables ] (solve will also work)

(Note: All the <> brackets are removed by my html editor.)

  • Replace "list of equations" with your equations separated by commas and enclosed in curly brackets { }
  • Replace "list of variables" with your list of variables {a,b,c}
  • Press return and the solutions will be give (provided you applied Kirchoff's Laws correctly)

Using the circuit simulator

There are many circuit simulators available, here we will use the PhET version:

Circuit construction kit

  • Now solve the following.

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