Kirchoff's of laws

Kirchoff's First Law

Kirchoff got himself a huge name in physics by simply applying two principles of physics to electrical circuits. This is the first:

At any junction in a circuit, the sum of the currents arriving at the junction = the sum of the currents leaving the junction.

In other words - charge is conserved. If this doesn't happen you'd either get a massive build-up of electrons at a junction in a circuit or you would be creating charge from nowhere! That's not going to happen.

Current in = Current out

I1 = I2 + I3 + I4

Kirchoff's Second Law

Here is the second principle:

In any loop (path) around a circuit, the sum of the emfs = the sum of the pds.

In other words - energy is conserved. The total amount of energy put in (sum of the emfs) is the same as the total amount of energy taken out (sum of the pds).

Note: pd = V = IR so 

Energy in = Energy out

emf = pd1 + pd2 + pd3 + pd4

The reason Kirchoff's Laws strike fear into A-level students is because you have to be careful about how you apply them. Once you've got the hang of them, they aren't that hard. Stick to these rules and you'll be OK.

Using Kirchoff's Laws

Example Questions using Kirchoff's Laws:

1. Use Kirchoff's Laws to find the internal resistance of the cell.
   
   There are a number of ways to attempt this question, but here is one example using the 2nd Law...
   Energy in = Energy out, and V = IR, so
   10 V = (0.3 x 4) + (0.3 x 3) + (0.3 x r)
   10 = 1.2 + 0.9 + 0.3r
   7.9 = 0.3r, so r = 26.3 Ω
2. Use Kirchoff's Laws to find the emf of the cell.
   
   Again, this can be approached a number of ways, but this time we will start with Law 1...
   Current in = Current out
   This tells us that the current through each 5 Ω resistor is 1.5 A.
   Law 2 tells us that:
   Emf = (3x4) + (1.5x5) + (3x2.5)
   Emf = 12 + 7.5 + 7.5 = 27 V