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

This guide is aligned to the OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards (Version 5.2). It covers the resistance part of specification section 3.5.1 Electrical circuits, statements h to o, including the required practical on V-I characteristics. The qualification is untiered.

Charge, current and potential difference, circuit symbols, and series and parallel circuits are covered elsewhere. Here the focus is what resistance is, how to read an I-V graph, and what each component does. Use the revision notes for a short recap and the practice questions to test yourself. Course pages: the OxfordAQA Physics hub and the printable checklist. To find weak spots first, try the free diagnostics.

What this guide covers

Statement	What you must be able to do
h	Explain resistance and use V = I × R
i	Describe an ohmic resistor: I directly proportional to V at constant temperature
j	Know that resistance of lamps, diodes, thermistors and LDRs changes with current
k	Thermistor resistance falls as temperature rises; describe uses such as a thermostat
l	LDR resistance falls as light intensity rises; describe uses such as switching lights on in the dark
m	Filament lamp resistance rises with temperature; explain using ions and electrons
n	Diode: low forward resistance, very high reverse resistance, current in one direction only; required practical
o	LED emits light when forward current flows; LEDs use much smaller current than other lighting

Resistance and V = I × R (statement h)

Components resist the flow of charge through them. The greater the resistance, the smaller the current for a given potential difference across the component.

The resistance of a component is found by measuring the current through it and the potential difference across it:

V = I × R

where V is potential difference in volts (V), I is current in amperes (A) and R is resistance in ohms (Ω). Rearranged: R = V ÷ I and I = V ÷ R.

Resistance is not the same as current or p.d. Two components with the same p.d. across them carry different currents if their resistances differ.

Worked example 1: finding resistance

A small lamp has 6.0 V across it and carries 0.40 A.

1. R = V ÷ I
2. R = 6.0 ÷ 0.40 = 15 Ω

Worked example 2: rearranging

(a) A fixed resistor of 450 Ω has 9.0 V across it. I = V ÷ R = 9.0 ÷ 450 = 0.020 A, which is 20 mA.

(b) A current of 35 mA flows through a 120 Ω resistor. Convert first: 35 mA = 0.035 A. V = I × R = 0.035 × 120 = 4.2 V.

Always change milliamps to amps (divide by 1000) and kilohms or megohms to ohms before substituting.

Ohmic resistors (statement i)

The current through a resistor at constant temperature is directly proportional to the potential difference across it. This means its resistance stays constant as the current changes. Its I-V graph (current on the vertical axis, p.d. on the horizontal axis, as in the specification) is a straight line through the origin.

If you reverse the connections, the line continues through the origin into negative values: the same resistance, with the current flowing the other way.

Reading the graph

• A steeper line means a lower resistance, because more current flows for each volt.
• For an ohmic resistor with I on the vertical axis, the gradient is 1 ÷ R.
• If you plot V on the vertical axis instead, the gradient is R.

Worked example 3: testing whether a resistor is ohmic

V (V)	1.0	2.0	3.0	4.0	5.0
I (mA)	15	29	44	59	74
V ÷ I (Ω)	66.7	69.0	68.2	67.8	67.6

Each current was converted to amps before dividing (for example 1.0 ÷ 0.015 = 66.7 Ω). V ÷ I is the same within the scatter of the readings, so the resistance is constant: about 68 Ω. The component behaves as an ohmic resistor.

Components whose resistance changes (statement j)

For lamps, diodes, thermistors and LDRs the resistance is not constant. It changes with the current through the component. Their I-V graphs are curves, not straight lines through the origin. They are called non-ohmic.

To find the resistance at one point on a curved graph, read V and I at that point and calculate V ÷ I. Do not use the gradient of the curve at that point: for a curve, the gradient is not the resistance.

Filament lamp (statement m)

The resistance of a filament lamp increases as the temperature of the filament increases. On an I-V graph the line starts steep and bends over: the current rises more slowly than the p.d. The graph is symmetrical, passing through the origin in both directions.

Explaining it with ions and electrons

A metal filament is a lattice of positive ions with free electrons moving among them.

1. As current flows, the filament gets hotter.
2. The ions in the lattice vibrate with larger amplitude.
3. The moving electrons collide with the ions more often.
4. Each electron is slowed more, so the flow of charge is harder to maintain.
5. The resistance is greater, so the current is smaller for each volt.

Worked example 4: lamp data

V (V)	1	2	3	4	5	6
I (A)	0.18	0.28	0.35	0.41	0.46	0.50
R = V ÷ I (Ω)	5.6	7.1	8.6	9.8	10.9	12.0

The resistance more than doubles. The current did not double when the p.d. doubled (0.18 A at 1 V, 0.28 A at 2 V), so the lamp is non-ohmic.

Thermistor (statement k)

The resistance of a thermistor decreases as the temperature increases. Applications use a circuit where the change in resistance alters the current or the p.d. in part of the circuit. In a thermostat, a falling room temperature raises the thermistor’s resistance and a rising temperature lowers it. The change is detected and used to switch a heater on or off. The same idea works in a fire alarm or a temperature sensor.

Worked example 5: thermistor current

A thermistor is connected to a 6.0 V supply. At 20 °C its resistance is 2500 Ω; at 60 °C it is 300 Ω.

• At 20 °C: I = 6.0 ÷ 2500 = 0.0024 A = 2.4 mA
• At 60 °C: I = 6.0 ÷ 300 = 0.020 A = 20 mA

The warmer thermistor lets about 8 times as much current flow (2500 ÷ 300 = 8.3). A circuit can respond to that change.

Light-dependent resistor, LDR (statement l)

The resistance of an LDR decreases as light intensity increases. In the dark its resistance is very large, so little current flows. In bright light it is much smaller.

Application: automatic lights. In the dark the LDR’s resistance is high; the circuit responds to that change and switches the lamp on. When it becomes light the resistance falls and the lamp is switched off.

Worked example 6: LDR current

An LDR is across a 9.0 V supply. In the dark it is 750 kΩ; in bright light it is 1.5 kΩ.

• Dark: I = 9.0 ÷ 750 000 = 0.000 012 A = 12 µA
• Bright: I = 9.0 ÷ 1500 = 0.0060 A = 6.0 mA

Diode (statement n)

A diode lets current flow in one direction only. Its forward resistance is low and its reverse resistance is very high.

On the I-V graph, a small p.d. in the forward direction gives almost no current. Once the p.d. reaches about 0.6 to 0.7 V (typical for a silicon diode) the current rises very steeply. In the reverse direction the current is almost zero.

The resistance of a diode is not constant. It falls as the forward current increases.

Worked example 7: diode resistance

Data supplied: forward, 0.50 V gives 0.10 mA; 0.70 V gives 12 mA; 0.80 V gives 60 mA. Reverse, 5.0 V gives 1.0 µA.

• 0.50 V: R = 0.50 ÷ 0.00010 = 5000 Ω
• 0.70 V: R = 0.70 ÷ 0.012 = 58 Ω
• 0.80 V: R = 0.80 ÷ 0.060 = 13 Ω
• Reverse 5.0 V: R = 5.0 ÷ 0.000 001 = 5 000 000 Ω = 5.0 MΩ

Forward resistance drops from kilohms to about ten ohms. Reverse resistance is millions of ohms.

Light-emitting diode, LED (statement o)

An LED emits light when a current flows through it in the forward direction. It is a diode, so it conducts in one direction only; connected the wrong way round, no current flows and no light is emitted.

The use of LEDs for lighting is increasing because they use a much smaller current than other forms of lighting. For the same p.d., a smaller current means less energy is transferred each second.

Required practical: V-I characteristics

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

Method

1. Connect the component in series with a variable power supply (or a variable resistor) and an ammeter.
2. Connect a voltmeter in parallel across the component only.
3. Increase the p.d. from zero in equal steps (at least six). At each step record V and I.
4. Reverse the connections to the component and repeat to get readings in the opposite direction. For a diode, keep a protective resistor in series so the forward current stays within its rating.
5. Plot I (vertical axis) against V (horizontal axis) for each component and draw a smooth line or curve.

Controlling temperature

Keep the currents through the resistor small and switch off between readings so it does not warm up. If it did, its resistance would change and you would not be testing at constant temperature. A filament necessarily gets hotter as current rises; that is the effect you are investigating.

Expected results

Component	Graph shape	Meaning
Resistor	Straight line through the origin	Constant resistance
Filament lamp	S-shaped curve, steepest at the origin	Resistance increases with temperature
Diode	Almost flat for reverse and small forward p.d., then steep	Low forward and very high reverse resistance

Common errors

• Writing “the lamp breaks Ohm’s law”. Say the lamp’s resistance is not constant because its temperature changes.
• Saying “the electrons get hot”. It is the ions that vibrate more; the electrons collide with them more often.
• Using the gradient to find resistance on a curve. Use V ÷ I at the point.
• Substituting mA, kΩ or MΩ values without converting them first.
• Saying a thermistor and an LDR both react to light. A thermistor responds to temperature; an LDR to light intensity.
• Connecting the voltmeter in series or the ammeter across the component in the practical.

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.