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Potential divider practice

Calculate outputs, choose a resistor and predict LDR, thermistor and loading effects.

Practise

Choose a resistor value

An unloaded divider has R2 = 3 kΩ and supply 12 V. Choose R1 to give 3 V across R2. Find R1 in kΩ. Give your answer to 3 significant figures.

Ideal DC voltage source. Output is measured by an ideal voltmeter. R1 is upper, R2 lower; no load unless RL is explicitly shown.

Ideal supply connected across series R1 and R2. Output across R2. Output has no load.+Vs0 VR1R2VoutVout is across R2 (lower resistor)
R1 is upper; R2 lower. Read the stated output terminals.
Diagram text alternative

Output across R2; no load.

Larger diagram
Ideal supply connected across series R1 and R2. Output across R2. Output has no load.+Vs0 VR1R2VoutVout is across R2 (lower resistor)

Treat the given values as exact unless an uncertainty is stated.

Use decimals or e notation, e.g. 4.2e-3. Enter the unit separately.

Hint

Rearrange Vout = Vs R2/(R1 + R2) to R1 = R2(Vs/Vout − 1).

Worked solution
  1. R1 = 3 × (12/3 − 1) kΩ.
  2. Answer: 9.00 kΩ (3 significant figures).
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Question type: Mixed practice
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Identify the output resistor

For an unloaded series divider, Vout across R2 = Vs R2/(R1 + R2). Across R1, use R1 in the numerator. Resistances can stay in kΩ when all use the same unit.

Predict sensor effects

Brighter light lowers an LDR’s resistance. Warming an NTC thermistor lowers its resistance. Reducing the lower resistance reduces output across it; reducing the upper resistance increases output across the lower resistor. Predict the fraction before calculating.

Include a load

A load across R2 puts two resistances in parallel. Replace them by R2 RL/(R2 + RL), then use that equivalent in the divider equation. A finite load reduces the lower output for an ideal source. These tasks use ideal voltmeters and ideal DC supplies; source internal resistance is excluded.

A-level relevance

AQA 7408: 3.5.1.4–5 (selected); OCR A H556: 4.3.3 (selected). Tasks cover the selected skills listed above.

AQA electricity specification · OCR A specification

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