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.

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 Σpd = ΣIR

As charge flows around a circuit it uses up its energy (its electrical potential energy) and turns it into other forms, such as heat and light.

Fortunately for us, electrons use more energy going through larger resistances and less energy going through smaller resistances. This means the larger the resistor, the greater the voltage needed across it for the same current to flow through it. In maths language, the ratio of resistances gives you the ratio of voltages.

Let me show you with a simple example:

Imagine the current leaves the cell with 3V. The current will use 1V (1JC^-1) in going through the 1Ω resistor and 2JC^-1 in getting through the 2Ω resistor.

In this circuit you have a long piece of resistance wire.

As the charge passes through the wire it uses up its potential. Note this simple connection:-

Halfway through the wire it has used half the potential

1/4 of the way through the wire it's used a 1/4 of the potential.

1/8 of the way through the wire it's used an 1/8 of the potential.

You can write this as a ratio:

Potential dividers can be used to find the emf of a cell.

Remember:

This ratio can be used to measure all sorts of resistances, potential differences and emfs.