The potential divider is one of the most useful circuits your students will meet so it is particularly important that they understand how it works and how to calculate the voltage across each of its resistors. For an unloaded potential divider the current through each resistor is the same so the voltage is proportional to the resistance. This means that the pd across the pair of resistors is divided in the same ratio as the resistors themselves:

i.e. V_{1} / V_{2} = I R_{1} / I R_{2} **or** V_{1} / V_{2} = R_{1} / R_{2}

It is worth emphasizing the practical implication of this - if R_{1} >> R_{2} then V_{1} is more or less the supply voltage and if R_{1} << R_{2}then V_{1} is close to 0 V. You could encourage them to see V_{S} as an input to the potential divider and V_{1} as an output. The circuit itself provides a way to tap off a voltage between 0 V and V_{S}.

This can, of course be done continuously using a rheostat or potentiometer and it is well worth demonstrating a variety of these including the rotary potentiometers used as volume controls in hi-fi systems.

The potential divider equation can be derived by rearranging the ratios above to give:

V_{1} = R_{1} / (R_{1}+R_{2}) ยด V_{S}