Potential dividers — OCR A-Level Physics
Test yourself on Potential dividers with OCR A-Level practice questions.
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Potential dividers explained
A potential divider consists of two or more components in series across a supply, so the supply p.d.
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is shared between them in proportion to their resistances. For two resistors R₁ and R₂ in series across a supply of p.d. V_in, the p.d. across R₂ is V_out = V_in × R₂/(R₁ + R₂). The same current flows through both components, so the larger resistance takes the larger share of the p.d. Potential dividers are used to obtain a smaller p.d. from a larger supply, for example to provide a fixed reference voltage. If a load is connected across the output, the effective resistance of that part of the circuit changes and the output p.d. falls.
(b) potential divider circuits with variable components e.g. LDR and thermistor
A potential divider can include a variable component so that the output p.d. changes with a physical condition. A light-dependent resistor (LDR) has a resistance that decreases as light intensity increases. A thermistor has a resistance that decreases as temperature increases (for an NTC thermistor). If the variable component is in series with a fixed resistor across a supply, the output p.d. across either component changes as the condition changes. For example, with an LDR in the upper position and a fixed resistor below, increasing light intensity lowers the LDR resistance, so the output p.d. across the fixed resistor rises. Such circuits are used in sensing and switching applications.
(c)
This row is a specification sub-heading, not an examinable fact. It introduces the potential divider content that follows in section 4.3.3, so treat it as a signpost telling you what to study next: the divider equations and the practical investigation of divider circuits, possibly using a sensor such as a thermistor or an LDR. When reading the specification, use sub-headings like this to build a checklist. For each following statement, ask what physical quantity is being related, what equation or procedure is named, and what practical work is implied. Then locate the matching pages in your textbook or class notes and work through a worked example, such as finding the output voltage across the lower resistor of a two-resistor divider.
(i) potential divider equations e.g. Vout = [R₂/(R₁ + R₂)]Vin and V₁/V₂ = R₁/R₂
A potential divider splits a supply voltage between components in series. For two resistors R₁ and R₂ in series across a supply Vin, the same current flows through both, so the voltage across each is proportional to its resistance. The output taken across R₂ is Vout = [R₂/(R₁ + R₂)]Vin, and the ratio of the voltages across the two resistors is V₁/V₂ = R₁/R₂. For example, with Vin = 12 V, R₁ = 200 Ω and R₂ = 400 Ω, Vout = [400/(200 + 400)] × 12 V = 8 V, and V₁ = 4 V so V₁/V₂ = 4/8 = 0.5 = 200/400. The equations assume ideal components and no significant load current drawn from the output.
(ii) techniques and procedures used to investigate potential divider circuits which may include a sensor such as a thermistor or an LDR.
To investigate a potential divider, build a series circuit with a fixed resistor and a sensor, such as a thermistor or a light-dependent resistor (LDR), connected across a d.c. supply. Measure the supply voltage and the output voltage across one component with a voltmeter connected in parallel. Vary the physical condition: warm or cool the thermistor, or change the light intensity on the LDR, and record how the sensor resistance and the output voltage change. For a thermistor with negative temperature coefficient, resistance falls as temperature rises, so the voltage across it falls while the voltage across the fixed resistor rises. Plot a graph of output voltage against temperature or light intensity and compare with the predicted divider equation.
Your focus
- Apply the potential divider equation to series circuits.
- Explain how p.d. is shared in proportion to resistance.
- Predict how a load affects the output p.d. of a divider.
Show all 15 objectives
- Describe how LDR and thermistor resistance varies with light intensity and temperature.
- Apply the potential divider equation to circuits containing variable components.
- Predict and explain changes in output p.d. as conditions change.
- Identify that sub-heading (c) introduces the potential divider content in section 4.3.3.
- List the following statements about divider equations and practical investigation as revision targets.
- Plan study of divider circuits by linking each statement to a worked example or practical activity.
- Apply Vout = [R₂/(R₁ + R₂)]Vin to calculate an output voltage.
- Use V₁/V₂ = R₁/R₂ to compare potential differences across series resistors.
- Explain why the simple divider equations assume negligible output current.
- Describe a procedure to investigate a potential divider containing a thermistor or an LDR.
- Explain how changing temperature or light intensity changes the output voltage.
- Interpret a graph of output voltage against the physical condition using the divider equation.
Potential dividers exam tips
Marking Points
- States that components in a potential divider are connected in series across a supply.
- Explains that the supply p.d. is divided in proportion to the resistances of the components.
- Applies V_out = V_in × R₂/(R₁ + R₂) to a two-resistor divider.
- Explains that the same current flows through each series component.
- Explains that connecting a load across the output reduces the output p.d. because the effective resistance changes.
- States that an LDR resistance decreases as light intensity increases.
- States that an NTC thermistor resistance decreases as temperature increases.
- Explains that changing the resistance of one component changes the p.d. across both components in the divider.
- Applies V_out = V_in × R₂/(R₁ + R₂) with the variable resistance substituted appropriately.
- Explains a sensing application, such as a light- or temperature-sensitive output p.d.
- State that in a series divider the current is the same through each resistor, so the potential difference across each resistor is proportional to its resistance.
- Apply Vout = [R₂/(R₁ + R₂)]Vin to find the output voltage across the lower resistor R₂.
- Apply V₁/V₂ = R₁/R₂ to compare the potential differences across two series resistors.
- Substitute values with consistent units and calculate the output voltage or voltage ratio correctly.
- Recognise that the simple divider equations assume negligible current is drawn from the output, so a connected load changes the output voltage.
- Set up a series divider with a fixed resistor and a sensor such as a thermistor or an LDR across a d.c. supply.
- Connect a voltmeter in parallel with the component whose output voltage is being measured.
- Vary the physical condition, for example temperature for a thermistor or light intensity for an LDR, and record the output voltage.
- Relate the measured output voltage to the changing resistance of the sensor using the divider equation.
- Plot a suitable graph, such as output voltage against temperature or light intensity, and describe the trend.
Examiner Tips
- 💡Identify which resistor the output is taken across before substituting into the ratio.
- 💡Check that the two fractions for the two resistors sum to 1.
- 💡Consider whether a connected load changes the effective resistance of the output section.
- 💡State the direction of resistance change for the sensor before working out the effect on output p.d.
- 💡Use the ratio with the resistance across which the output is measured in the numerator.
- 💡Check the answer against the limiting cases of very high and very low sensor resistance.
- 💡Turn each sub-heading into a short checklist and tick off the statements beneath it once you can explain and use them.
- 💡For every divider statement, write one worked calculation and one practical description so you can handle both calculation and practical questions.
- 💡When revising sensors, sketch the divider circuit and state how the output voltage changes as the sensor's resistance changes.
- 💡Write down the equation before substituting so the numerator and denominator are clearly assigned to the correct resistors.
- 💡Check the ratio answer by seeing whether the larger resistor has the larger share of the supply voltage.
- 💡Keep units consistent, converting kΩ to Ω only if the question requires it, and state the unit with the final answer.
- 💡State clearly which component the output voltage is measured across, because the direction of the voltage change depends on this choice.
- 💡Describe the control of variables, such as keeping the supply voltage constant while changing temperature or light intensity.
- 💡Use a graph or table to show the trend and link it back to the divider equation rather than listing readings alone.
Common Mistakes
- Assuming the p.d. divides equally regardless of resistance: the correction is that the p.d. across each component is proportional to its resistance.
- Using the ratio R₁/(R₁ + R₂) for the p.d. across R₂: the correction is that the numerator must be the resistance across which the output is taken.
- Ignoring the effect of a load: the correction is that a load in parallel with the output reduces the effective resistance and the output p.d.
- Treating the supply p.d. as the p.d. across only one component: the correction is that the supply p.d. is shared across all series components.
- Stating that LDR resistance increases with light intensity: the correction is that LDR resistance decreases as light intensity increases.
- Stating that an NTC thermistor resistance increases with temperature: the correction is that its resistance decreases as temperature increases.
- Assuming the output p.d. stays constant when one resistance changes: the correction is that the p.d.s redistribute as the resistance ratio changes.
- Placing the variable component in parallel with the supply: the correction is that it must be in series with the other divider component for the ratio to operate.
- Treating a sub-heading such as (c) as a fact to memorise. Correction: it is a signpost; the examinable content is in the statements that follow it.
- Skipping the practical statements because they look less mathematical. Correction: techniques and procedures for investigating divider circuits, including sensor-based dividers, are part of the specification and can be assessed.
- Reading only the equation statements and ignoring the sensor context. Correction: the specification explicitly mentions a thermistor or an LDR, so link the divider equation to how sensor resistance changes with temperature or light.
- Swapping the numerator so the output is taken across the wrong resistor. Correction: Vout across R₂ uses R₂ in the numerator, Vout = [R₂/(R₁ + R₂)]Vin.
- Adding resistances in parallel when the divider resistors are in series. Correction: the denominator is the series sum R₁ + R₂.
- Assuming the output voltage is unchanged when a load is connected. Correction: a load draws current and reduces the output voltage unless its resistance is much larger than the divider resistances.
- Connecting the voltmeter in series with the divider. Correction: a voltmeter is connected in parallel with the component across which the potential difference is measured.
- Assuming the sensor resistance is constant while the temperature or light intensity changes. Correction: the sensor resistance changes, and that change is what alters the output voltage.
- Recording only the output voltage without noting the physical condition. Correction: record temperature or light intensity alongside each voltage so the relationship can be analysed.