Kirchoff's First and Second Laws
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Kirchoff's First and Second Laws
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 buildup 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
I_{1} = I_{2} + I_{3} + I_{4}
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 = pd_{1} + pd_{2} + pd_{3} + pd_{4}
The reason Kirchoff's Laws strike fear into Alevel 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.
Example Questions using Kirchoff's Laws:

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

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
Now it's your turn!
A Question to Try:
Use Kirchoff's Laws to find the the E.m.f. of the cell reading on cellvoltmeter and the value of the unknown resistor.