OxfordAQA International GCSE Physics: Resistance, I-V graphs and components (9203) – Revision Notes

These notes recap resistance and components for the OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards, section 3.5.1 Electrical circuits, statements h to o. For full explanations and worked examples, read the study guide. Then test yourself with the practice questions. Related pages: the OxfordAQA Physics hub, the printable checklist and the free diagnostics.

Key definitions and equation

Term	Meaning
Resistance	How strongly a component opposes the flow of charge. Greater resistance means smaller current for the same p.d.
Ohmic conductor	A resistor at constant temperature: current is directly proportional to p.d., so resistance is constant
Non-ohmic	Resistance changes with current: filament lamp, diode, thermistor, LDR

Quantity	Symbol	Unit
Potential difference	V	volt (V)
Current	I	ampere (A)
Resistance	R	ohm (Ω)

V = I × R, so R = V ÷ I and I = V ÷ R.

Method in steps: any V = IR calculation

1. Write the quantity you want and the two you know.
2. Convert units: mA to A (÷ 1000), kΩ to Ω (× 1000), MΩ to Ω (× 1 000 000).
3. Rearrange, then substitute.
4. Give the answer with a unit and a sensible number of significant figures.

Small reminder

A heater element has 12 V across it and carries 0.50 A: R = 12 ÷ 0.50 = 24 Ω. If the p.d. were raised to 18 V and the resistance stayed fixed, the current would be 18 ÷ 24 = 0.75 A. Check: 0.75 ÷ 0.50 = 1.5 = 18 ÷ 12, so the current rose in proportion.

I-V graphs at a glance

In the specification, current is on the vertical axis and p.d. on the horizontal axis.

Component	Shape of the I-V graph	Resistance
Resistor kept at a steady temperature	Straight line passing through the origin	Does not change
Filament lamp	Curve through the origin that flattens as p.d. rises; symmetrical for negative values	Increases as the filament gets hotter
Diode	Flat along the axis for reverse p.d. and small forward p.d., then rises steeply	Low forward, very high reverse; not constant

A rough sketch in words of the diode graph:

Reverse p.d.: I is about 0. Small forward p.d.: I is about 0. Then a steep rise.

• On a straight-line graph, steeper means smaller resistance.
• On a curve, find resistance at a point from V ÷ I at that point. Not from the gradient.
• A graph that goes through the origin is not enough to prove ohmic behaviour. It must also be a straight line.

Filament lamp: the ion and electron explanation

1. The current heats the metal filament.
2. Positive ions in the lattice vibrate with larger amplitude.
3. Free electrons collide with the ions more often.
4. The flow of charge is hindered more, so the resistance rises.
5. For each extra volt, the current rises by less.

Write “ions vibrate more” and “more frequent collisions with electrons”. Do not write “the electrons vibrate more” or “the filament has more resistance because it is hot” without saying why.

Thermistor, LDR and applications

Component	Resistance changes with	Direction	Typical application
Thermistor	Temperature	Decreases as temperature increases	Thermostat, fire alarm, temperature sensor
LDR	Light intensity	Decreases as light intensity increases	Switching lights on when it gets dark

How to describe an application

1. Name the component and the quantity that changes (temperature or light intensity).
2. State how its resistance changes.
3. State the effect on current or p.d. in the circuit.
4. State what the circuit then does: switch a heater or lamp on or off.

Example for a thermostat: when the room cools, the thermistor’s resistance increases, which changes the current or p.d. in the control circuit, and the heater is switched on. When the room warms up, the resistance falls and the heater is switched off.

Small reminder: LDR currents

An LDR on a 6.0 V supply has a resistance of 400 kΩ in the dark and 800 Ω in daylight. Dark: 6.0 ÷ 400 000 = 0.000 015 A = 15 µA. Daylight: 6.0 ÷ 800 = 0.0075 A = 7.5 mA. The current is 500 times larger in daylight (400 000 ÷ 800 = 500).

Small reminder: thermistor currents

A thermistor on a 9.0 V supply has a resistance of 3000 Ω at 15 °C and 450 Ω at 55 °C. At 15 °C: 9.0 ÷ 3000 = 0.0030 A = 3.0 mA. At 55 °C: 9.0 ÷ 450 = 0.020 A = 20 mA. The current is larger when the thermistor is warmer, which is the change a thermostat circuit uses.

Describing a lamp, resistor and diode graph in an answer

Use this order: shape, behaviour near the origin, behaviour at larger p.d., then what it means for resistance.

• Resistor: straight line, through the origin, constant gradient, so constant resistance.
• Lamp: curve through the origin, steep at first then flatter, so resistance increases with p.d. and temperature.
• Diode: almost no current in reverse and for small forward p.d., then a steep rise, so very high reverse resistance and low forward resistance.

Diode and LED

• A diode conducts in one direction only.
• Forward resistance is low; reverse resistance is very high.
• An LED is a diode that emits light when current flows in the forward direction.
• LEDs are increasingly used for lighting because they use a much smaller current than other forms of lighting.

Small reminder: diode resistance

A diode has 0.75 V across it, forward, and carries 25 mA. R = 0.75 ÷ 0.025 = 30 Ω. In reverse, 4.0 V gives 0.50 µA, so R = 4.0 ÷ 0.00000050 = 8 000 000 Ω = 8.0 MΩ. The reverse resistance is about 270 000 times larger.

Required practical: V-I characteristics

Aim: investigate the V-I characteristics of a filament lamp, a diode and a resistor at constant temperature.

• Circuit: variable supply, component and ammeter in series; voltmeter in parallel across the component only.
• Method: increase p.d. in equal steps from zero; record V and I each time; reverse the connections and repeat.
• Diode: include a protective resistor in series.
• Constant temperature: use small currents and let the resistor cool between readings.
• Graph: I vertical, V horizontal, smooth curve or line through the points.
• Conclusion: use V ÷ I to comment on how resistance changes.

Must-know distinctions

• Thermistor: temperature. LDR: light. Both have resistance that falls as the stimulus increases.
• Ohmic resistor: constant resistance. Filament lamp: resistance rises with temperature. Diode: resistance very high in reverse.
• Forward resistance: low. Reverse resistance: very high.
• Ions vibrate; electrons collide with the ions.
• Resistance at a point: V ÷ I. Not the gradient of a curve.

Quick self-test

1. A component has 3.0 V across it and 0.020 A through it. What is its resistance?
2. A lamp has a resistance of 24 Ω when 0.50 A flows. What is the p.d. across it?
3. A 250 Ω resistor carries 80 mA. Calculate the p.d. across it.
4. A 2200 Ω resistor has 10 V across it. What is the current in mA, to 2 significant figures?
5. Describe the I-V graph of a resistor at constant temperature.
6. Why does the resistance of a filament lamp increase as the current increases?
7. What happens to the resistance of a thermistor when the temperature rises?
8. What happens to the resistance of an LDR when the light gets brighter?
9. State two facts about the resistance of a diode.
10. Give one reason why LEDs are replacing other forms of lighting.

Answers

1. R = 3.0 ÷ 0.020 = 150 Ω.
2. V = 24 × 0.50 = 12 V.
3. 80 mA = 0.080 A. V = 250 × 0.080 = 20 V.
4. I = 10 ÷ 2200 = 0.004 545 A = 4.5 mA.
5. A straight line passing through the origin. Current is directly proportional to p.d.
6. The filament gets hotter, the ions vibrate more, and electrons collide with them more often.
7. It decreases.
8. It decreases.
9. Low resistance in the forward direction; very high resistance in the reverse direction (current flows in one direction only).
10. They use a much smaller current than other forms of lighting.

Where marks are usually lost

• Substituting milliamps or kilohms directly into V = IR without converting them.
• Writing the answer without a unit, or with the wrong one.
• Stating that the lamp’s resistance increases “because the current is higher” with no mention of temperature, ions and electrons.
• Saying the electrons, not the ions, vibrate more.
• Giving the thermistor’s response to light, or the LDR’s response to temperature.
• Drawing an I-V graph for a lamp or diode as a straight line.
• Using a graph’s gradient as the resistance for a curve.
• Describing the practical with the voltmeter in series, or leaving out the reversed readings.
• Forgetting that the diode conducts in the forward direction only.

Official syllabus

This page follows the OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards, Version 5.2, published by OxfordAQA, section 3.5.1 Electrical circuits, statements h to o.