At its simplest, a potential divider is a circuit with a voltage source and resistors in series. The potential of the voltage source (e.g. power supply) is divided in the ratio of the resistances. This means that if you had a 2 ohm resistor and a 3 ohm resistor, there would be 2/5 of the p.d. across the 2 ohm resistor and 3/5 of p.d. across the 3 ohms. Therefore resistances can be chosen to get a required voltage across one of the resistors.
A series circuit is set up with a switch and two resistors. In the circuit R1 has R1 / R1+R2 of total resistance. Therefore Vout = R1 / R1+R2 * Vs (voltage at switch)
If Vs = 9V and you wanted Vout to be 6V then R1 / R1+R2 would have to be 2 / 3 which gives the ratio of R1 to R2 as 1:2. This would mean that you could have a resistance of 200 ohms for R1 and 100 ohms for R2.
This type of circuit is mainly used for calibrating voltmeters, which have a very high resistance. If…