O-Level Physics Potential Dividers: Mark the Output Terminals First

A student in a public SGExams D.C. circuits question asked why one answer option was correct rather than another. The discussion centred on a thermistor, an LDR and how the supply voltage was shared. The transferable skill is to identify the output terminals before reasoning about resistance.

The MOE upper-secondary Physics syllabus includes series-circuit relationships and the use of NTC thermistors and light-dependent resistors in potential dividers. The worked circuits below are original ideal examples. They use a constant supply, negligible connecting-wire resistance and a voltmeter that draws negligible current.

Identify the two points being measured

A potential difference is measured between two points. Trace the voltmeter connections, or the two output terminals, and bracket the component between them. If an output is described as the voltage across the lower resistor, label that resistor before calculating.

With two resistors in series, the same current passes through both. Their individual voltage drops add to the supply voltage. Applying V = IR to each gives a useful ratio: the voltage across a chosen resistor equals the supply voltage multiplied by that resistor's resistance divided by the total series resistance.

Write this as Vout = Vs × Rchosen ÷ (R1 + R2). The numerator is determined by the output terminals. It is not automatically the sensor resistance merely because the question mentions a sensor.

Calculate an original thermistor example

A 6.0 V supply is connected across a 2.0 kΩ fixed resistor and an NTC thermistor in series. At the first temperature, the thermistor resistance is 4.0 kΩ. The output is measured across the fixed resistor.

The fixed resistor receives 2.0 ÷ (2.0 + 4.0) of the supply, so its voltage is 2.0 V. The thermistor receives the remaining 4.0 V. Keeping both answers on the page makes the voltage-sharing relationship visible.

The thermistor is then heated until its resistance is 1.0 kΩ. The fixed resistor's voltage becomes 6.0 × 2.0 ÷ (2.0 + 1.0) = 4.0 V. The thermistor's voltage is now 2.0 V. The output has increased because the specified output is across the fixed resistor.

Check using current instead of repeating the fraction

Initially, the total resistance is 6,000 Ω. The current is 6.0 ÷ 6,000 = 0.001 A, or 1.0 mA. Across the fixed 2,000 Ω resistor, V = IR gives 2.0 V. After heating, the total resistance is 3,000 Ω, giving a current of 2.0 mA and a fixed-resistor voltage of 4.0 V.

This independent route catches a reversed numerator. It also explains why “the resistance falls, so the voltage falls” is incomplete: the current changes too. You must identify whose resistance and whose voltage you mean.

Move the output and reconsider the explanation

Keep the components and temperatures unchanged, but connect the output across the thermistor. The measured voltage now falls from 4.0 V to 2.0 V. The same heating event therefore gives opposite output trends at the two possible pairs of terminals.

For this two-component circuit, an explanation can follow three sentences: heating lowers the NTC thermistor's resistance; the fixed resistor then forms a larger fraction of the total resistance; therefore the voltage across the fixed resistor increases. If the output is across the thermistor, change the final two sentences accordingly.

Apply the reading habit to an LDR

In the usual LDR model, greater illumination reduces resistance. Draw the output bracket again rather than borrowing the thermistor example's conclusion. If both a thermistor and an LDR change, compare the two resistance values or their ratio. Tracking only one component can give the wrong conclusion when the other changes as well.

For practice, choose a relevant circuit question from the Secondary paper collection. Record the supply, the measured component and the sensor change before working. Check that each calculated voltage lies between zero and the supply voltage, and that the two drops add to the supply. Older papers can supply useful practice, but check their subject and syllabus against your current course.