Kirchhoff's Current Law
Electricity and Magnetism

Episode 117: Kirchhoff’s laws

Lesson for 16-19 IOP TAP

This episode links Kirchhoff's circuit laws to conservation of charge and energy. Students can verify the laws experimentally, and use them to solve simple circuit problems.

Lesson Summary

  • Demonstration and discussion: Explaining the laws (15 minutes)
  • Student experiment: Verifying the laws (30 minutes)
  • Worked example: Focussing on the Second law (10 minutes)

Discussion and demonstrations: Explaining the laws

Remind the class that charge and energy are conserved quantities. This is best done in the context of a demonstration – e.g. an electric motor lifting a load (or any other device that transfers energy electrically – perhaps an electric heater).

Episode 117-1: Energy transfer by an electric motor (Word, 33 KB)

The current is the same before and after the motor. The voltage drop across the motor is a measure of the electrical work done (energy transferred) per coulomb of charge passing a point. It is simple to verify that the pd across the motor and across the supply are the same, leading to the idea that the electrical work done by the supply is equal to the energy transferred out of the circuit by the motor. This can be generalized to the ideas:

  • Charge simply flows around a circuit – it is not used up.
  • The electrical work done (by cell/power pack/generator etc...) is equal to the energy transferred to the surroundings by the circuit.
  • The first of these statements leads to Kirchhoff’s first law, the second to his second law.

Episode 117-2: Kirchhoff's Laws 1 (Word, 31 KB)

Student experiment: Verifying the laws

With a less able group (or simply to provide more opportunities to build and test circuits) you might get them to build a sequence of circuits and to measure currents and voltages. The parallel circuits are particularly good practice and the exercise will reinforce their understanding that ammeters must be connected in series and voltmeters in parallel.

Episode 117-3: Verifying Kirchhoff's Laws (Word, 64 KB)

Worked examples: Focussing on the second law

Students are unlikely to be required to solve complex problems involving circuits with two or more loops. However, they should be able to apply Kirchhoff's laws to simple circuits.

The first law is not difficult; the second law is harder. Teach your students to use a finger to trace round a complete loop in a circuit, starting at a source of emf. The first time round, they add up all the emfs (taking account of their directions). The second time round, they add up the values of IR for each component (again, algebraically, and including contributions for internal resistance). These two quantities are then equal.

Show a worked example on the board.

Episode 117-4: Kirchhoff's Laws 2 (Word, 41 KB)

Episode 117-5: Questions on Kirchhoff's Laws (Word, 43 KB)

Kirchhoff's Current Law
can be derived from Adding Resistors in a Circuit
is expressed by the relation I_1+I_2=I_3+I_4
is used in analyses relating to Electrical Circuit
involves the quantity Electric Current
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