13.1 Basic potential divider

A potential divider consists of two or more series resistors connected across a supply. The output p.d. is taken across one resistor. Because the same current passes through both, the supply voltage divides in proportion to resistance.

For R1 above R2 and output across R2, Vout = Vin × R2/(R1 + R2). This assumes the output is connected to a very high-resistance device so it does not significantly load the divider.

13.2 Reasoning without memorising

The divider current is I = Vin/(R1 + R2). The output is Vout = IR2. Combining gives the standard equation. This method helps when the output is taken across a different resistor or when more components are present.

A larger fraction of the total series resistance receives a larger fraction of the supply voltage. If R2 increases while R1 stays fixed, output across R2 increases.

13.3 Variable potential divider

A potentiometer has a resistive track and a movable contact. Moving the contact changes the fraction of the track across which output is taken, giving a smoothly adjustable voltage from nearly zero to nearly the full supply.

Applications include volume controls, position sensors and reference-voltage settings. When used with significant load current, output changes from the ideal division because the load forms a parallel resistance.

13.4 Thermistors

An NTC thermistor has resistance that falls as temperature rises. In a divider, the direction of output change depends on whether the thermistor is the upper or lower component. If output is across a lower thermistor, warming lowers its fraction of total resistance and Vout falls.

Thermistors are used in thermostats, fire alarms and temperature monitoring. A comparator, transistor or relay can turn an output device on when the sensor voltage crosses a threshold.

13.5 Light-dependent resistors

An LDR has high resistance in darkness and lower resistance in bright light. If output is across a lower LDR, brighter light lowers output. If the LDR is the upper component and output is across the fixed lower resistor, brighter light can increase output.

Automatic street lights require an arrangement that activates the lamp when darkness causes the desired threshold change. Simply saying “LDR resistance changes” is insufficient; identify direction and circuit position.

13.6 Sensor circuit design

Choose the sensor position according to whether output must rise or fall with the physical variable. Select the fixed resistor so the divider is most sensitive near the required operating point. The output may feed an electronic switch rather than power a lamp directly.

A relay provides isolation and can control a larger current, but the coil may require a transistor driver. At O Level, the key reasoning is the sensor resistance change, output voltage change and resulting switch action.

13.7 Loading and measurement

An ideal voltmeter has high resistance and minimally loads the divider. A low-resistance load connected across R2 effectively reduces that branch resistance, lowering the output relative to the unloaded calculation.

This explains why a divider is suitable for signal voltages but may not be suitable as a high-power supply. The source and resistors must also be rated for current and power dissipation.

Worked examples

Practical focus

Examination guidance

Check your understanding

1. Find Vout across 4 kΩ in series with 6 kΩ across 15 V, where output is across 4 kΩ.
2. What happens to NTC resistance when heated?
3. Why does a voltmeter need high resistance in a divider?