Current–voltage characteristics — AQA A-Level Physics

This topic explores how the current through electrical components varies with the potential difference across them. You will study the I-V characteristics of an ohmic resistor, a filament lamp, and a semiconductor diode, and relate their shapes to the microscopic behaviour of charge carriers. Understanding these characteristics is fundamental to circuit analysis and explains why components behave differently under varying voltages.

The topic builds on Ohm's law and resistance, extending them to non-ohmic devices. It is essential for later work on electrical power, resistivity, and semiconductor physics. In AQA A-Level exams, you are expected to describe, explain, and analyse these graphs, often linking them to temperature changes and material properties.

• →Ohm's law states that for an ohmic conductor at constant temperature, the current is directly proportional to the potential difference (I proportional to V), so the I-V graph is a straight line through the origin.
• →The resistance of a filament lamp increases as the potential difference increases because the temperature of the filament rises, causing increased lattice vibrations and more frequent electron-ion collisions.
• →A silicon diode has a forward threshold voltage of about 0.6 V; below this, it has a very high resistance. In reverse bias, it has an extremely high resistance with only a tiny leakage current until breakdown.
• →The I-V characteristic of a component can be investigated using a variable resistor, ammeter, voltmeter, and a suitable power supply, taking care to reverse the connections for negative values.
• →Resistance is defined as R = V / I and can be found at any point on a non-linear I-V graph by reading the coordinates, not by taking the gradient.

• Describes the I–V graph for an ohmic conductor as a straight line through the origin, showing I ∝ V at constant temperature.
• States that resistance is constant for an ohmic conductor and calculates it from the gradient or from V/I.
• Describes the forward and reverse bias behaviour of a semiconductor diode, including the threshold voltage and very high reverse resistance.
• Explains that a diode conducts when forward biased above about 0.6 V and does not conduct significantly in reverse bias.
• Describes the I–V graph for a filament lamp as a curve that flattens as current increases.
• Explains that the resistance of a filament lamp increases because the filament temperature rises, increasing lattice vibrations and reducing electron drift.
• Compares the three characteristics and identifies which is ohmic and which are non-ohmic.
• Ohm’s law applies only when current is directly proportional to potential difference, so I/V is constant.
• The constant of proportionality is 1/R, giving V = IR and R = V/I.
• An ohmic conductor at constant temperature gives a straight-line I–V graph passing through the origin.
• Changing physical conditions, especially temperature, changes resistance and breaks the proportionality.
• A filament lamp is non-ohmic because increasing current heats the filament and raises its resistance.
• Proportionality requires a straight line through the origin; a straight line with a non-zero intercept is not proportional.
• An ideal ammeter has zero resistance and is connected in series with the component.
• An ideal voltmeter has infinite resistance and is connected in parallel with the component.
• Zero resistance means no p.d. is dropped across an ideal ammeter, so it does not change the current.
• Infinite resistance means no current flows through an ideal voltmeter, so it does not change the p.d. across the component.
• Real meters have small but non-zero ammeter resistance and large but finite voltmeter resistance, which cause small measurement errors.
• Unless a question specifies non-ideal meters, use the ideal assumption in calculations and circuit analysis.
• Identifies which quantity is plotted on each axis before attempting any calculation from the characteristic graph.
• Calculates resistance at any given point on the graph by reading the coordinates and using the equation R = V/I.
• Recognises that for an ohmic conductor, the graph is a straight line through the origin, meaning resistance is constant and equals the inverse gradient of an I–V graph.
• Describes the diode characteristic as having negligible reverse current and a forward threshold voltage before conduction becomes significant.
• Explains the filament lamp curve in terms of increasing temperature raising the lattice vibration and so increasing resistance.

• 💡Label axes with quantity and unit, and mark the origin clearly when sketching characteristics.
• 💡For the diode, indicate the forward threshold voltage and the reverse breakdown region if shown.
• 💡When explaining the filament lamp, link temperature rise to increased lattice vibrations and reduced electron drift, not just 'more resistance'.
• 💡Use the phrase 'at constant temperature' when describing ohmic behaviour.
• 💡State explicitly that temperature and other physical conditions must remain constant when quoting Ohm’s law.
• 💡When describing a graph, quote the gradient or ratio rather than saying only that the line goes up.
• 💡Link any non-ohmic behaviour to a named physical change, such as heating of the filament, rather than calling the component faulty.
• 💡Check meter positions before calculating: ammeter in series, voltmeter in parallel.
• 💡If a question gives a meter resistance, treat the meter as a real component in the circuit rather than as ideal.
• 💡Explain meter effects in terms of resistance changing current or potential difference, not merely as vague ‘errors’.
• 💡Always read the coordinates for V and I at the specific point in question to calculate resistance using R = V/I.
• 💡Pay close attention to the axis labels and units, especially checking for milliamperes (mA) which must be converted to amperes (A).
• 💡When explaining the shape of an I-V graph, always link the macroscopic observation (current, voltage) to microscopic behaviour (electron collisions, lattice vibrations, temperature).
• 💡For calculation questions, show the formula R = V / I, substitute values with units, and give your answer to an appropriate number of significant figures. Do not simply read the gradient unless the graph is linear.
• 💡When sketching I-V characteristics, label axes with quantity and unit (e.g., I / A, V / V), and indicate the scale or key values such as the threshold voltage for a diode.

• Treating the filament lamp as ohmic and drawing a straight line. Correct by drawing a curve that flattens as current increases.
• Drawing the diode as a symmetric curve. Correct by showing negligible current in reverse bias and a sharp increase in forward bias above the threshold.
• Saying resistance decreases as temperature increases for a filament lamp. Correct by explaining that increased temperature increases resistance.
• Confusing the gradient of an I–V graph with resistance. Correct by using R = V/I for a point on the graph, not the gradient.
• Treating Ohm’s law as true for all components; correct this by restricting it to ohmic conductors under constant physical conditions.
• Reading a curved I–V graph as proportional because current still rises with p.d.; correct this by checking that the ratio I/V stays constant.
• Assuming a straight-line graph proves proportionality even when it does not pass through the origin; correct this by checking the origin intercept.
• Connecting a voltmeter in series or an ammeter in parallel; correct this by placing the voltmeter in parallel and the ammeter in series.
• Assuming an ideal voltmeter carries a small current; correct this by treating its resistance as infinite so no current passes through it.
• Including the ammeter’s resistance in series calculations when the question assumes ideal meters; correct this by using zero resistance unless told otherwise.
• Assuming the horizontal axis is always voltage; the correction is to read the axis labels first to correctly identify V and I values.
• Calculating resistance of a non-ohmic component by taking the gradient of a tangent; the correction is that resistance at a point is always V/I using the coordinates, not the gradient.
• Stating that a decreasing gradient on an I–V graph means resistance is decreasing; the correction is that a decreasing gradient on an I–V graph (like a filament lamp) indicates that V/I is increasing, so resistance is increasing.
• Students often think that a curved I-V graph means the component does not obey Ohm's law at all. In fact, Ohm's law is only defined for constant temperature; the filament lamp is non-ohmic because its temperature changes, but it may still follow Ohm's law at a fixed temperature.
• Many students believe that resistance is the gradient of an I-V graph. This is only true for a straight line through the origin; for non-linear graphs, resistance must be calculated using R = V / I at a specific point.
• Students frequently forget that the diode's threshold voltage is about 0.6 V for silicon and 0.3 V for germanium, and they may omit the reverse bias region entirely when sketching.

1. 1Day 1-2: Revise the definitions of current, potential difference, resistance, and Ohm's law. Practice calculations using V = IR and R = V / I.
2. 2Day 3-4: Study the I-V characteristics of an ohmic resistor, filament lamp, and diode. For each, draw the graph and write a detailed explanation linking shape to physical mechanisms.
3. 3Day 5-6: Work through exam-style questions, including those requiring graph interpretation, calculations, and 6-mark explanations. Focus on using precise terminology.
4. 4Day 7-8: Create flashcards for key facts (threshold voltage, shape of graphs, reasons for non-ohmic behaviour) and test yourself using active recall.
5. 5Day 9-10: Complete a past paper section on this topic under timed conditions, then review your answers against the mark scheme to identify gaps.

• 📋Graph sketching and interpretation: You may be asked to sketch the I-V characteristic for a given component and explain its shape. Practice drawing accurate graphs with correct axes and key features.
• 📋Calculation of resistance from I-V data: Given a set of current and voltage readings, calculate resistance at different points and explain any variation. Remember to use R = V / I and comment on temperature effects.
• 📋Explanation of non-ohmic behaviour: A 4-6 mark question may ask you to explain why a filament lamp is non-ohmic. Structure your answer to include the effect of temperature on lattice vibrations and electron collisions.
• 📋Experimental design: You might be asked to describe an experiment to obtain the I-V characteristic of a component, including circuit diagram, method, and safety precautions.