The potential divider equation, the use of dividers to provide a variable potential difference, and sensor circuits using thermistors and LDRs.

What this dot point is asking

Edexcel wants you to use a series pair of resistors to split a supply voltage in a chosen ratio, to understand how a sliding potentiometer gives a continuously variable output, and to analyse sensing circuits in which a thermistor or light-dependent resistor (LDR) makes the output respond to temperature or light.

The answer

The divider equation

Two resistors $R_1$ and $R_2$ in series carry the same current $I = \frac{V_{\text{in}}}{R_1 + R_2}$. The potential difference across $R_2$ is therefore:

The output is the supply voltage scaled by the fraction of the total resistance that the chosen resistor represents. This is exact only when nothing draws current from the output. If a load is connected across $R_2$, it sits in parallel with $R_2$, lowers the effective resistance there, and pulls the output below the no-load value. For accurate division the load must have a much higher resistance than $R_2$.

Variable dividers

A potentiometer is a single resistive track with a sliding wiper. Sliding the wiper changes the ratio of the two parts of the track continuously, so the output can be set anywhere from zero to the full supply. This is the standard way to provide a smoothly adjustable voltage, used in volume controls and as a calibration input. A rheostat (variable resistor in series) only limits current and cannot give a true zero output, which is why a divider is preferred when a full-range adjustable voltage is needed.

Sensor circuits

Place a thermistor as one arm of a divider and a fixed resistor as the other. As the temperature rises, the thermistor resistance falls; its share of the supply falls; the share across the fixed resistor rises. Taking the output across the fixed resistor therefore gives a voltage that rises with temperature. Swap which resistor the output is taken across (or use an LDR) to reverse or change the response. The output voltage can be fed to a comparator or transistor to switch a heater, fan, or lamp at a set threshold.

Examples in context

A car's coolant temperature gauge uses a thermistor divider: as the engine warms, the thermistor resistance drops and the changing output voltage drives the dashboard gauge. A camera's automatic exposure and a phone's auto-brightness use LDR (or photodiode) dividers to sense ambient light. Garden lights use an LDR divider feeding a transistor switch so the lamp comes on only when the output crosses the darkness threshold. In each case the divider converts a resistance change into a usable voltage signal.

Try this

Q1. Write the potential divider equation for the output across $R_2$. [1 mark]

• Cue. $V_{\text{out}} = V_{\text{in}} \times \frac{R_2}{R_1 + R_2}$.

Q2. A $3.0$ k-ohm and a $1.0$ k-ohm resistor are in series across $12$ V. Find the output across the $3.0$ k-ohm resistor. [2 marks]

• Cue. $V_{\text{out}} = 12 \times \frac{3.0}{4.0} = 9.0$ V.

Q3. Explain why connecting a low-resistance load across the output of a divider reduces the output voltage. [2 marks]

• Cue. The load is in parallel with that arm, lowering its effective resistance, so its share of the supply falls below the no-load value.