Resistors I–V characteristics, thermistors and LDRs & RP4

SPEC 8463 • MODULE 2 • LESSON 2.04 • RP4

I–V Characteristics

Three components, three different graph shapes — and the practical that produces each one. Plus the thermistor and LDR your spec specifically requires you to know.

Building on Lesson 2.02

In 2.02 we met the ohmic conductor — a special case where current is directly proportional to pd at constant temperature. Most of GCSE-level circuit physics deals with the four non-ohmic components in this spec: the filament lamp, the diode, the thermistor, and the LDR.

What's Coming Up In This Lesson

Required Practical 4 (RP4) — the experiment that produces the I–V graphs for a fixed resistor, a filament lamp, and a diode.

Three I–V shapes you must recognise, draw, and explain.

The thermistor and LDR — what changes their resistance, and the spec-required applications.

Calculating R at any point on an I–V graph.

Spec Reference

This whole lesson is spec 4.2.1.4. The exact wording in the spec — "the resistance of components such as lamps, diodes, thermistors and LDRs is not constant; it changes with the current through the component" — is the headline takeaway.

RP4 Apparatus

One circuit. The component under test changes (resistor, lamp, or diode), but the rest of the circuit stays the same.

RP4 — variable resistor varies the pd; voltmeter parallel across the component under test; ammeter in series

What Each Part Does

Cell + switch: source of pd; switch lets you disconnect.

Variable resistor: changes the current in the circuit, which changes the pd across the component. This is how you vary the IV.

Component under test: the resistor, lamp, or diode you're characterising.

Ammeter (series): measures current through the component.

Voltmeter (parallel): measures pd across the component.

IV / DV / Controls

The variable structure for RP4 is slightly different from RP3. Pd is now the IV — and the component itself is what's being characterised, not changed.

Variable TypeWhat It IsHow It's Set / Measured

Independent VariablePotential difference ( V ) across the componentSet by adjusting the variable resistor — controls how much of the cell's pd drops across the component

Dependent VariableCurrent ( I ) through the componentRead directly from the ammeter

Control VariablesThe component itself; temperature; the rest of the circuitUse the same component throughout one set of readings; allow it to cool between readings if heating is a factor; don't change the wiring

The Ohmic-Conductor Catch

The fixed resistor in RP4 must be tested at constant temperature — that's the spec wording. If it heats up during the experiment, its straight-line behaviour will start to curve. Take readings quickly and don't leave the circuit on between readings.

The RP4 Method

The same method works for all three components — only the component under test changes. The trick is getting both positive and negative pd readings, which is how you build the full I–V curve.

1

Build the circuit : cell, switch, variable resistor, ammeter, and component under test in series. Voltmeter in parallel across the component.

2

Set the variable resistor to its maximum resistance (so initial current is small).

3

Close the switch briefly ; record V (voltmeter) and I (ammeter).

4

Reduce the variable resistor in steps to give around 6–8 different pd values; record V and I at each step.

5

Reverse the cell connections to record the negative-V part of the curve. For the resistor and lamp this gives negative I values; for the diode you'll see I ≈ 0 throughout the reverse region.

6

Plot I (y-axis) against V (x-axis) . Both positive and negative quadrants — that's how the full I–V characteristic appears.

Why Reverse The Connections?

Because the diode behaves completely differently in reverse — and you can't see that without negative-pd readings. The lamp's full S-curve also requires both quadrants to be visible. The fixed resistor still gives a straight line, but now passing through both quadrants.

Three Shapes — One Glance

Match the component to the shape. These three are the headline I–V graphs of the spec.

Diode

The One-Sentence Summary For Each

Resistor: straight line through the origin — I directly proportional to V (ohmic, at constant temperature).

Lamp: S-curve through the origin — gradient gets shallower as V increases (lamp heats up, R rises).

Diode: essentially zero current in reverse, then a sharp rise once forward pd is high enough.

The Filament Lamp — Full I–V

The lamp's curve is symmetric through the origin. The S-shape is the headline feature; if you draw it as a straight line, you've got the physics wrong.

Filament lamp I–V — S-shaped, symmetric through origin

Reading the S-Curve

Near the origin: line is steep — at low pd, the filament is cool, resistance is low, so current rises quickly with V.

Further from origin: line flattens — as more current flows, the filament heats up, resistance rises, and so for the same increase in pd, the increase in current is smaller.

The curve is symmetric because reversing the pd reverses the current — the heating effect doesn't depend on direction.

Why The Lamp Is Non-Ohmic

The whole point of an ohmic conductor is constant temperature. A filament lamp cannot stay at constant temperature when current flows — its job is to get hot enough to glow.

Spec Statement (4.2.1.4)

The resistance of a filament lamp increases as the temperature of the filament increases.

The Causal Chain

Higher pd across the lamp

→ Higher current through the filament

→ More energy transferred to thermal store of filament (P = I²R, lesson 2.07)

→ Higher temperature of the filament

→ Higher resistance (metal ions vibrate more, more collisions with charge carriers)

→ For each further increase in V, the increase in I is smaller

→ Curve flattens — that's the S-shape.

"Filament Lamp Is Ohmic" — Wrong

This is one of the most common misconceptions in Module 2. Filament lamps are not ohmic — at any reasonable operating pd, the filament is hot, and its resistance is changing. Saying "lamps are ohmic" loses recall marks straight away.

The Diode — Full I–V

A diode's defining property: it lets current flow in one direction only. Its I–V graph reflects that asymmetry exactly.

Diode I–V — zero in reverse direction, sharp rise in forward direction

Reading the Diode Curve

Negative pd (reverse): the line lies on the V-axis — current is essentially zero, no matter how large V becomes. Resistance is very high.

Positive pd (forward): current is also essentially zero until the pd is high enough, then the curve rises sharply. Resistance is very low at higher forward pd.

Why The Diode Is One-Way

The spec gives you the two-sentence description. Memorise both — both are mark-scheme statements.

Spec Statement (4.2.1.4)

The current through a diode flows in one direction only. The diode has a very high resistance in the reverse direction.

Why The Reverse-Direction Resistance Matters

"Very high resistance in reverse" is the key phrase. It means the diode acts as an open circuit for reverse current — almost no current flows even with a large reverse pd. This is why diodes are used to protect circuits from accidental reverse polarity, and to convert AC to DC (rectification — beyond GCSE but relevant context).

Out Of Spec

The exact forward threshold pd (≈0.7 V for a silicon diode) is not on the AQA spec. Don't quote it as if it were a required fact. The spec just expects you to describe the shape: zero in reverse, sharp rise in forward.

Calculating R Anywhere On An I–V Curve

For non-ohmic components, R changes from point to point. To find R at a particular pd, you read off (V, I) from the graph and apply V = IR.

The Method

1. Pick a point on the curve at the required pd.

2. Read off V and I from the axes.

3. Calculate R = V / I.

4. The result is the resistance at that specific point — not a property of the whole curve.

Don't Confuse This With "Gradient = 1/R"

The gradient of the line at a point gives 1/R only for a straight line through the origin (ohmic). For a curved I–V graph, the gradient at a point is not the same as V/I at that point. For non-ohmic components, always use R = V / I directly — read off the values, divide, done.

What This Tells You About The Lamp

Pick two points on a lamp's I–V curve, one near the origin and one far from it. R = V/I at the far point will be larger than at the near point. The difference is the temperature effect — proven by the data, not just claimed.

Thermistor

A thermistor is a resistor whose resistance depends on temperature. Specifically — and this is the verbatim spec wording:

Spec Statement (4.2.1.4)

The resistance of a thermistor decreases as the temperature increases.

Required Application: Thermostat

The spec specifically requires you to know an application. The standard one is a thermostat:

In a heating system, a thermistor is part of the control circuit. As the room cools down, the thermistor's resistance increases. The control circuit detects this change and switches the heater on. As the room warms back up, the thermistor's resistance falls, and the heater switches off. The thermistor is the temperature sensor that makes the system self-regulating.

Direction Memory Aid

Thermistor: T up → R down. Opposite to a normal metal wire (where heating raises R). This is because thermistors are typically made from semiconductor materials, where heat actually frees more charge carriers — the opposite of what happens in a metal.

LDR — Light-Dependent Resistor

An LDR is the optical cousin of the thermistor. Its resistance depends on light intensity instead of temperature.

Spec Statement (4.2.1.4)

The resistance of an LDR decreases as light intensity increases.

Required Application: Switching Lights On In The Dark

The spec specifically requires this application. Automatic street lighting is the standard example:

An LDR is part of the street lamp's control circuit. In bright daylight, the LDR's resistance is low, and the control circuit keeps the lamp off. As dusk falls and light intensity drops, the LDR's resistance rises. Once it crosses a threshold, the control circuit switches the lamp on. The light stays on through the night and switches off again at dawn — automatically.

Direction Memory Aid

LDR: Light up → R down. Same direction as the thermistor's relationship — both are "increase the input → decrease the resistance".

Examiner Alert — The Milliwatt Trap

RP4 questions often combine I–V graph reading with a power calculation. AQA examiner reports flag one specific unit-conversion error every year.

The Trap

Questions sometimes give component power in milliwatts (mW). To use power in any equation involving SI units (P = VI, P = I²R), you must convert to watts first.

1 mW = 1 × 10⁻³ W = 0.001 W

What AQA Examiner Reports Have Said

Recent examiner reports on Paper 1 have flagged the milliwatt → watt conversion as one of the most reliably-missed unit conversions in calculation questions. Students who don't convert produce answers wrong by a factor of 1000 — a clear power-of-ten error.

The Habit

Whenever a power, current, voltage or resistance is given with a prefix (m, μ, k), convert at the substitution step — not at the end. Show the conversion as a separate line of working: "P = 200 mW = 0.200 W". The conversion is visible, the working is markable, and the final answer is in SI units.

Weak vs Strong — Drawing The Lamp Curve

"Sketch the I–V graph for a filament lamp" is a recurring exam question. The marks come from shape accuracy, not just having a line through the origin.

✗ Loses 2 marks

Drawing a straight line through the origin for a filament lamp.

Wrong physics: a straight line says R is constant, which would make the lamp ohmic — but the spec says it isn't. Mark scheme rejects.

✓ Full marks

Drawing an S-curve through the origin: steep near origin, flattening as |V| increases. Symmetric in both quadrants.

Correct shape — line through origin (1 mark), S-shape with shallowing gradient (2nd mark), often a third mark for symmetry across both quadrants.

✗ Loses 1 mark

"The diode allows current in both directions if the voltage is high enough."

Incorrect physics. The diode's reverse resistance is very high — current is essentially zero in reverse no matter how large the pd.

✓ Full marks

"The current through a diode flows in one direction only. The diode has a very high resistance in the reverse direction."

Verbatim spec wording — both clauses present and correct.

Common Errors

Students often writeCorrect versionWhy it matters

"Filament lamp is ohmic"Lamp is not ohmic — R rises with temperatureWrong characterisation; loses recall marks

Lamp I–V drawn as a straight lineS-curve through originWrong shape = wrong physics

"Diode allows current both ways at high V"Diode allows current one way only ; very high resistance in reverseSpec wording is explicit

Power left in mW in calculationConvert mW → W (÷ 1000) before substitutingAnswer wrong by factor of 1000

"Thermistor: T up → R up"Thermistor: T up → R downDirection reversed — both letter recall marks lost

"LDR: light up → R up"LDR: light up → R downSame direction as thermistor (input up → R down)

Calculating R from gradient on a curved I–VUse R = V/I at a point — read coords, divideGradient of curve ≠ V/I except at origin

Practice Question

A filament lamp is being tested in a circuit. The student records the following readings at two different points on the lamp's I–V curve:

Point A: V = 1.0 V, I = 0.20 A

Point B: V = 4.0 V, I = 0.40 A

(a) Calculate the resistance of the lamp at Point A and at Point B.

(b) Explain why the resistance has changed. 5 MARKS

a-A

Point A: R = V / I = 1.0 / 0.20 = 5.0 Ω

a-B

Point B: R = V / I = 4.0 / 0.40 = 10 Ω

b-1

Observation: The resistance has doubled — from 5.0 Ω to 10 Ω.

b-2

Cause: At Point B the current is higher than at Point A, so the filament transfers more energy and heats up to a higher temperature.

b-3

Link: The resistance of a filament lamp increases as the temperature of the filament increases (spec wording). So a higher temperature at Point B gives a higher resistance.

✓

Mark scheme: M1, M2 for each correct R calculation. M3 for noting R has changed/doubled. M4 for naming the temperature increase. M5 for stating R rises with T.

Three Things to Remember

1. Three Shapes, Three Reasons

Resistor: straight line — constant R (ohmic). Lamp: S-curve — heating raises R. Diode: zero in reverse, sharp rise in forward — current flows one way only. The shape is the physics.

2. Thermistor & LDR — Direction + Application

Thermistor: T up → R down; application thermostat. LDR: light up → R down; application switching lights on at dark. Both directions and both applications are spec-required.

3. Convert mW Before Calculating

Whenever power is given in milliwatts, your first step is the conversion: P = 200 mW = 0.200 W. Show it as a separate line of working. Power-of-ten errors here cost the entire answer mark — and they're the single most common slip on RP4 calculation questions.

Summary & Checkpoint

The Three I–V Shapes

Fixed resistor (constant T): straight line through origin · ohmic · gradient = 1/R

Filament lamp : S-curve through origin · gradient flattens as |V| rises · R rises with T

Diode : zero in reverse direction (very high R) · sharp rise in forward · one-way current

Thermistor & LDR (Spec-Required)

Thermistor : R decreases as temperature increases · application: thermostat

LDR : R decreases as light intensity increases · application: switching lights on when it gets dark

RP4 — IV Characteristics

IV : pd across component · DV : current through component · controls : same component, temperature

Vary pd with the variable resistor; reverse cell to get negative readings

Plot I (y) against V (x) — both quadrants for full curve

Calculate R at any point as R = V / I

Next Lesson

2.05 — Series circuits. Three rules govern current, pd, and resistance in series: same current everywhere, pds add up, resistances add up. Then in 2.06 we'll cover the parallel-circuit equivalents — and how the two combine.