First off, a recap of Kirchhoff's laws:
Kirchhoff's 1st Law
Since charge is conserved in a circuit, none can be lost at path junctions. The rate of flow of this charge is also unchanged, meaning the total current going into a branch equals the total current coming out of the branch, regardless of how many points are on the branch.
Current/charge is conserved around a circuit – when the current reaches a branch it splits so that the total current in the branches is equal to the current before splitting.
Kirchhoff's 2nd Law
This law applies the principle of conservation of energy to electrical circuits. It says that the amount of energy being put into the circuit (the E.M.F.) must equal the amount of energy coming out of the circuit (the P.D.):
Electrical energy is conserved in a circuit - the sum of the e.m.f.s around any closed loop equals the sum of the p.d.s around the closed loop.
Practically, these laws mean that in series, the voltage across all components adds up to the supply voltage and the current is the same across each component, while in parallel, the total voltage in each branch is the same and the current in the branches add up to the pre-branching current.
Resistors in Circuits
The layout of resistors in a circuit makes a big difference. In Series, the values of the resistors are just added together to find the total resistance. In parallel, however, the sum of one over each resistance value gives one over the total resistance.
All sources of e.m.f. have internal resistance, because the electrons collide with the atoms inside the power supply – this is what causes them to warm up.