Tutorial 7 A  Kirchhoff's Laws and Circuit Analysis 

Learning Objective 
To understand and use Kirchhoff’s Laws; 

Key Question 
What are Kirchhoff’s Laws? How do we use Kirchhoff's Laws? 

Kirchhoff's LawsWhen we started this course, we looked at Ohm’s Law and simple series and parallel circuits. In this topic, we are going to see how more complex circuit can be analysed using two simple laws that were formulated by the German physicist Gustav Robert Kirchhoff (1824 – 1887). He did a lot of work on electrical engineering, as well as spectroscopy work with Robert Bunsen (1811 – 1899) who invented our old friend, the Bunsen burner.
Kirchhoff I is to do with the current and it states: At any junction in an electric circuit the total current flowing towards that junction is equal to the total current flowing away from that junction.
Kirchhoff II is to do with voltages. It states: In any closed loop in a network, the algebraic sum of the potential differences (i.e. the products of current and resistance) is equal to the resultant EMF acting in that loop.
Kirchhoff came up with these laws as a twenty year old student. He doesn't look it in the picture. Kirchhoff ICurrents going into a junction are the same as currents coming out. By convention the currents leaving a junction are negative.
The law says S I = 0
The strange looking symbol, S, is “Sigma”, a Greek Capital letter ‘S’. It means “sum of”. Therefore:
So we can write:




Kirchhoff IIVoltages add up to the sum of the EMFs. EMF stands for electromotive force. It’s not a force at all, but a voltage (energy per unit charge). Conventional currents go from positive to negative. Follow the current round anticlockwise, as current from E_{1} goes from positive to negative. As we are going the wrong way through E_{2}, E_{2} is negative. As we go through the resistors, the voltage drop is negative, as we are going down the potential hill. So let’s sum the voltages:
We can write this more meaningfully as:


Using Kirchhoff's Laws Kirchhoff laws allow us to analyse some scary looking circuits. Adopt this problem solving strategy:
In this example we only used Kirchhoff II. Let’s do another example that requires is to use both laws.
Do not be tempted simply to split the two loops and do separate calculations on each loop, then adding the currents. This will give you different voltages across the 4 ohm resistor and that will make the calculation go wrong. The voltage across the 4 ohm resistor is the same for both the loops.
So what is the point of all of this, other than to make a complicated problem to annoy students?
Some complex electronic circuits may have multiple power supplies feeding in to different points in the circuit, especially in computers.
Another use of network theory is the national grid that consists on many loads (transformers that give power supplies to industry and homes), and many sources (power stations).
The picture shows the distribution of French power stations. There is a similar network in the UK.
Now you can have a go…




