Resistance — OCR A-Level Physics
Test yourself on Resistance with OCR A-Level practice questions.
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Resistance explained
Resistance measures how difficult it is for current to flow through a component.
Read the full explanation
It is defined by R = V/I, where V is the potential difference across the component and I is the current through it. The unit of resistance is the ohm, symbol Ω; one ohm is one volt per ampere. For example, if a potential difference of 6.0 V drives a current of 2.0 A through a resistor, its resistance is R = 6.0 V ÷ 2.0 A = 3.0 Ω. Resistance is not a fixed property of every component: for a filament lamp it changes as the current changes, so R = V/I gives the resistance at that particular operating point. In calculations, rearrange R = V/I to V = IR or I = V/R as needed, and always use the potential difference across the component, not the e.m.f. of the whole circuit.
(b) Ohm’s law
Ohm’s law states that the current through a metallic conductor is directly proportional to the potential difference across it, provided physical conditions such as temperature remain constant. In symbols, I ∝ V, so V/I is constant. A resistor that obeys Ohm’s law is called an ohmic conductor; its current–voltage graph is a straight line through the origin. For example, if a 4.0 Ω resistor has 2.0 V across it, the current is I = V/R = 2.0 V ÷ 4.0 Ω = 0.50 A; doubling the voltage to 4.0 V doubles the current to 1.0 A. A filament lamp does not obey Ohm’s law because its temperature rises, increasing its resistance, so its I–V graph curves. Ohm’s law is a special case, not a universal rule for all components.
(c)
This topic covers the $I-V$ characteristics of specific electrical components: a resistor, filament lamp, thermistor, diode, and light-emitting diode (LED). Study the current-potential difference ($I-V$) graphs for each. For an ohmic resistor at constant temperature, the graph is a straight line through the origin. A filament lamp shows a curve with decreasing gradient as potential difference increases, because the filament heats up and its resistance increases. A thermistor (NTC) shows an increasing gradient as it warms up, meaning resistance decreases. Diodes and LEDs only allow current to flow in one direction, showing zero current until a threshold voltage is reached in forward bias, after which current increases rapidly.
(i) I – V characteristics of resistor, filament lamp, thermistor, diode and light-emitting diode (LED)
An I–V characteristic is a graph of current through a component against potential difference across it. For a fixed resistor at constant temperature, current is directly proportional to p.d., so the line is straight through the origin. A filament lamp heats as current rises, so its resistance increases and the graph curves, with a smaller gradient at higher currents. A thermistor's resistance falls as temperature rises, so its I–V curve is non-linear and depends on heating. A diode conducts only above a forward threshold, roughly 0.6 V for silicon, and blocks reverse current; an LED is a diode that emits light when forward biased. You identify a component from the shape, symmetry and threshold of its graph.
(ii) techniques and procedures used to investigate the electrical characteristics for
To investigate a component's electrical characteristic, connect it in series with an ammeter and a variable d.c. supply, and connect a voltmeter in parallel with the component. Vary the p.d. in small steps, record current and p.d. pairs, then plot current against p.d. For reverse-bias measurements on a diode or LED, reverse the supply connections and keep the current small with a protective resistor. Use a potential divider or variable resistor to control the p.d. smoothly. Take repeat readings and average them to reduce random error, and avoid overheating the component by switching off between readings.
(d) light-dependent resistor (LDR); variation of resistance with light intensity.
A light-dependent resistor, or LDR, is a semiconductor component whose resistance decreases as light intensity increases. In darkness its resistance is high, often megohms; in bright light it falls to a few hundred ohms or less. The light supplies energy that releases more charge carriers, so the current for a given p.d. rises and resistance falls. You can investigate this by placing an LDR in a circuit with an ammeter and voltmeter, varying the distance from a lamp or using different light intensities, and calculating resistance from V/I. The relationship is non-linear, so a graph of resistance against light intensity is a curve.
Your focus
- Define resistance using R = V/I and state its unit, the ohm.
- Rearrange R = V/I to calculate potential difference or current.
- Distinguish between resistance and resistivity and recognise when resistance is not constant.
Show all 18 objectives
- State Ohm’s law and the conditions under which it applies.
- Interpret current–voltage graphs for ohmic and non-ohmic conductors.
- Use Ohm’s law to calculate current, potential difference or resistance.
- Sketch and interpret $I-V$ graphs for a resistor, filament lamp, thermistor, diode, and LED.
- Explain how the resistance of a filament lamp and an NTC thermistor changes with potential difference and temperature.
- Describe the forward and reverse bias behaviour of diodes and LEDs using $I-V$ graphs.
- Identify the I–V characteristic of a fixed resistor, filament lamp, thermistor, diode and LED from its shape.
- Explain how temperature change affects the resistance of a filament lamp and a thermistor.
- Describe the forward and reverse bias behaviour of a diode and an LED.
- Draw a circuit to measure the I–V characteristic of a component.
- Describe how to vary and measure p.d. and current safely.
- Explain how to obtain and use I–V data to plot a characteristic graph.
- Describe how the resistance of an LDR changes with light intensity.
- Explain the change in resistance in terms of charge carriers.
- Calculate resistance from measured p.d. and current.
Resistance exam tips
Marking Points
- Resistance is defined as R = V/I, where V is the potential difference across the component and I is the current through it.
- The unit of resistance is the ohm (Ω), equivalent to one volt per ampere (V A⁻¹).
- Rearranging R = V/I gives V = IR and I = V/R.
- Resistance may vary with operating conditions for non-ohmic components, so R = V/I gives the resistance at a particular point.
- In circuit calculations, use the potential difference across the component, not the supply e.m.f., unless they are the same.
- Ohm’s law states that current is directly proportional to potential difference for a metallic conductor at constant temperature.
- For an ohmic conductor, V/I is constant and the I–V graph is a straight line through the origin.
- Ohm’s law applies only when physical conditions, especially temperature, remain constant.
- Components such as filament lamps and diodes are non-ohmic because their resistance changes with current or voltage.
- The law can be used to calculate current, potential difference or resistance for an ohmic conductor.
- Fixed resistor: straight line through the origin, because current is proportional to p.d. when temperature is constant.
- Filament lamp: curve through the origin whose gradient decreases as current increases, because the filament temperature and resistance rise.
- Thermistor: non-linear curve; resistance decreases as temperature increases, so the graph is not a straight line.
- Diode: negligible current in reverse bias and a forward threshold near 0.6 V for silicon before current rises steeply.
- LED: forward-biased diode characteristic that emits light; it also has a threshold and blocks reverse current.
- Ammeter in series with the component to measure current.
- Voltmeter in parallel with the component to measure potential difference.
- Variable d.c. supply or potential divider to change the p.d. in controlled steps.
- Protective resistor or current limit to prevent damage to diode, LED or filament lamp.
- Record multiple I–V pairs, repeat and average, then plot a graph of current against p.d.
- LDR resistance decreases as light intensity increases.
- In darkness the resistance is high; in bright light it is much lower.
- Light energy releases more charge carriers in the semiconductor, increasing current for a given p.d.
- Resistance is calculated from R = V/I using measured p.d. and current.
- The variation of resistance with light intensity is non-linear.
Examiner Tips
- 💡Write down R = V/I before substituting values so the rearrangement is clear.
- 💡Check that the current is in amperes and the potential difference in volts before dividing.
- 💡If a graph of V against I is given, the resistance at a point is V/I, not the gradient unless the graph is linear through the origin.
- 💡Give the unit with the numerical answer, for example 3.0 Ω.
- 💡Quote Ohm’s law with the condition of constant temperature to gain full credit.
- 💡When interpreting an I–V graph, check whether it is a straight line through the origin before calling the component ohmic.
- 💡Use the gradient of a V–I graph to find resistance only if the graph is linear through the origin.
- 💡For non-ohmic components, describe how resistance changes rather than saying the component has no resistance.
- 💡Practice sketching the $I-V$ graphs for all five named components, ensuring axes are clearly labelled with $I$ on the y-axis and $V$ on the x-axis.
- 💡Be prepared to explain the physical reasons for the shape of the filament lamp and thermistor graphs in terms of temperature and charge carrier density.
- 💡Note the threshold voltage on a diode or LED graph and ensure the curve is flat along the x-axis for negative voltages.
- 💡Label axes with current I and potential difference V, and state the component before describing the shape.
- 💡Use the gradient or the ratio V/I to explain resistance changes rather than just saying 'the graph curves'.
- 💡For diode and LED questions, quote the forward threshold and the reverse-bias behaviour.
- 💡Sketch the circuit clearly and label the ammeter, voltmeter, component and variable supply.
- 💡State that you change the p.d. in small steps and record corresponding current values.
- 💡Mention a protective resistor or limiting current when testing diodes and LEDs.
- 💡State the direction of change clearly: more light means less resistance.
- 💡Use the equation R = V/I when calculating resistance from measurements.
- 💡Describe the graph as a curve showing a non-linear decrease.
Common Mistakes
- Using the e.m.f. of the supply instead of the potential difference across the component. Correction: identify the voltage across the component itself.
- Writing the unit as V A instead of V A⁻¹. Correction: the ohm is volts per ampere, so the unit is V A⁻¹.
- Assuming resistance is always constant for every component. Correction: for a filament lamp or diode, resistance changes with current or voltage.
- Confusing resistance with resistivity. Correction: resistance depends on the component and its dimensions, while resistivity is a property of the material.
- Stating that all conductors obey Ohm’s law. Correction: only ohmic conductors at constant temperature obey it; filament lamps and diodes do not.
- Saying that V is proportional to I without specifying constant temperature. Correction: include the condition of constant physical conditions, especially temperature.
- Treating a curved I–V graph as ohmic. Correction: a straight line through the origin is required for ohmic behaviour.
- Confusing Ohm’s law with the definition of resistance. Correction: R = V/I defines resistance for any component, while Ohm’s law is the statement that V/I is constant for an ohmic conductor.
- Assuming the gradient of an $I-V$ graph is exactly equal to resistance; resistance is $R = \frac{V}{I}$, which only equals $\frac{1}{\text{gradient}}$ if the graph is a straight line through the origin.
- Drawing the diode $I-V$ graph symmetrically; it must show zero current in the reverse bias direction.
- Confusing the $I-V$ curve of a filament lamp with that of a thermistor; the lamp's resistance increases with voltage, while an NTC thermistor's resistance decreases.
- Thinking a filament lamp obeys Ohm's law at all currents. Correction: it is non-ohmic because its resistance changes with temperature.
- Drawing a diode as a straight line through the origin. Correction: a diode has a forward threshold and blocks reverse current.
- Confusing thermistor and filament lamp curves. Correction: a thermistor's resistance falls with temperature, while a filament lamp's resistance rises with temperature.
- Connecting the ammeter in parallel with the component. Correction: the ammeter must be in series so that the component's current passes through it.
- Connecting the voltmeter in series. Correction: the voltmeter must be in parallel with the component to measure the p.d. across it.
- Forgetting to reverse the supply for reverse-bias readings. Correction: reverse the connections to obtain negative p.d. and current values.
- Saying LDR resistance increases with light intensity. Correction: resistance decreases as light intensity increases.
- Treating the LDR as ohmic with constant resistance. Correction: its resistance changes with light intensity, so it is non-ohmic.
- Assuming a directly proportional relationship between resistance and light intensity. Correction: the graph is a curve, not a straight line.