Resistance and Ohm's Law

What you'll learn

This revision guide covers resistance and Ohm's Law as specified in the AQA GCSE Physics specification. You'll learn how to calculate resistance, interpret current-voltage graphs for different components, and understand the factors affecting resistance in wires. These concepts are essential for both Foundation and Higher tier papers, particularly in Paper 2.

Key terms and definitions

Resistance — the opposition to current flow in a component or wire, measured in ohms (Ω)

Ohm's Law — the relationship stating that current through a component is directly proportional to the potential difference across it (at constant temperature), expressed as V = I × R

Ohmic conductor — a component that obeys Ohm's Law, where resistance remains constant as current changes (e.g. fixed resistor at constant temperature)

Current — the rate of flow of charge, measured in amperes (A)

Potential difference — the energy transferred per unit charge between two points in a circuit, measured in volts (V)

Thermistor — a temperature-dependent resistor whose resistance decreases as temperature increases

LDR (Light-Dependent Resistor) — a component whose resistance decreases as light intensity increases

Diode — a component that allows current to flow in one direction only, with very high resistance in the reverse direction

Core concepts

The resistance equation

The fundamental equation linking potential difference, current and resistance is:

V = I × R

Where:

• V = potential difference in volts (V)
• I = current in amperes (A)
• R = resistance in ohms (Ω)

This equation can be rearranged to find any of the three quantities:

• R = V ÷ I
• I = V ÷ R

You must be able to select and apply the correct form of this equation in calculations. The equation applies to all components, whether they obey Ohm's Law or not.

Ohmic conductors and Ohm's Law

An ohmic conductor maintains constant resistance provided physical conditions (especially temperature) remain constant. For these components:

• Current is directly proportional to potential difference
• The I-V graph is a straight line through the origin
• Doubling the voltage doubles the current
• Examples include fixed resistors and metal wires at constant temperature

A resistor at constant temperature obeys Ohm's Law because the metal ions in the wire remain in fixed positions. Electrons collide with these ions at a steady rate as they flow through, maintaining constant resistance.

When temperature increases significantly:

• The metal ions vibrate more
• Electrons collide with ions more frequently
• Resistance increases
• The component no longer behaves as an ohmic conductor

Current-voltage (I-V) characteristics

You must recognise and explain the I-V graphs for different components:

Fixed resistor (at constant temperature):

• Straight line through the origin
• Constant gradient = constant resistance
• Same in both directions (symmetrical)

Filament lamp:

• Curved line (S-shape) through the origin
• Gradient decreases as voltage increases
• As current increases, the filament heats up significantly
• Higher temperature causes greater resistance
• The lamp becomes less efficient at conducting as it gets hotter

Diode:

• Flat (nearly horizontal) in reverse direction = very high resistance, virtually no current
• Sharp rise in forward direction after threshold voltage (~0.7 V for silicon)
• Only allows current in one direction
• Acts as an electrical "one-way valve"

In your exam, you may need to:

• Sketch these characteristic curves
• Identify components from their I-V graphs
• Explain the shape of the curves using resistance changes

Non-ohmic components: thermistors and LDRs

Thermistors are temperature sensors used in thermostats, fire alarms, and temperature monitoring circuits.

Key properties:

• Resistance decreases as temperature increases (for NTC thermistors - the type you study at GCSE)
• At low temperatures: high resistance, small current
• At high temperatures: low resistance, large current
• The change is non-linear

Applications include:

• Temperature-activated cooling fans in computers
• Car engine temperature sensors
• Digital thermometers

LDRs (Light-Dependent Resistors) respond to light intensity and are used in automatic lighting systems.

Key properties:

• Resistance decreases as light intensity increases
• In darkness: very high resistance (millions of ohms)
• In bright light: low resistance (hundreds of ohms)
• Used in light-sensing circuits

Applications include:

• Street lights that switch on automatically at dusk
• Camera exposure meters
• Burglar alarm systems
• Garden solar lights

Both components are used in sensing circuits where changing conditions need to trigger a response.

Factors affecting wire resistance

The resistance of a wire depends on four factors:

Length:

• Resistance is directly proportional to length
• Doubling the length doubles the resistance
• Longer wires contain more metal ions for electrons to collide with

Cross-sectional area:

• Resistance is inversely proportional to area
• Doubling the area halves the resistance
• Thicker wires provide more space for electrons to flow through

Material:

• Different materials have different resistivities
• Copper has low resistance - commonly used in wiring
• Nichrome has high resistance - used in heating elements

Temperature:

• Higher temperatures increase resistance in metals
• More vigorous ion vibrations cause more electron collisions

In practical investigations, you may measure how length affects resistance by:

1. Setting up a circuit with an ammeter, voltmeter, and test wire
2. Measuring current and voltage for different wire lengths
3. Calculating resistance using R = V ÷ I
4. Plotting resistance against length (should be a straight line through the origin)

Resistors in series and parallel circuits

Series circuits:

• Current is the same through all components
• Total resistance = R₁ + R₂ + R₃ + ...
• Adding resistors increases total resistance
• Total voltage = sum of individual voltages across each component

Parallel circuits:

• Voltage is the same across all parallel branches
• Total current = sum of branch currents
• Adding resistors in parallel decreases total resistance
• Each additional branch provides another route for current

For two resistors in parallel, total resistance is always less than the smallest individual resistor. More parallel branches mean lower total resistance because charge has more pathways to flow through.

Required practical: investigating resistance

AQA requires you to investigate how length of wire affects resistance. You must know:

Method:

1. Set up a circuit with a power supply, ammeter (in series), test wire, and voltmeter (in parallel across the wire)
2. Use a metre ruler to measure precise lengths of wire
3. Record current and voltage for each length
4. Calculate resistance using R = V ÷ I
5. Repeat readings and calculate means to improve accuracy
6. Plot a graph of resistance against length

Variables:

• Independent variable: length of wire
• Dependent variable: resistance
• Control variables: wire material, cross-sectional area, temperature, current

Safety considerations:

• Low voltage supply to prevent overheating
• Switch off between readings to prevent temperature rise
• Ensure connections are secure to avoid sparking

Expected results:

• Resistance increases linearly with length
• Graph should be a straight line through the origin
• Gradient represents resistance per unit length

Worked examples

Example 1: Basic resistance calculation

Question: A 6 V battery is connected to a resistor. An ammeter measures a current of 0.5 A flowing through the resistor. Calculate the resistance of the resistor. [3 marks]

Solution:

Write down the equation: R = V ÷ I [1 mark]

Substitute values: R = 6 ÷ 0.5 [1 mark]

R = 12 Ω [1 mark]

Examiner tip: Always show the equation, substitution, and answer with units for full marks.

Example 2: Using Ohm's Law with unit conversion

Question: A lamp has a resistance of 480 Ω. It is connected to a 12 V power supply. Calculate the current flowing through the lamp in milliamps (mA). [4 marks]

Solution:

Write down the equation: I = V ÷ R [1 mark]

Substitute values: I = 12 ÷ 480 [1 mark]

I = 0.025 A [1 mark]

Convert to mA: 0.025 × 1000 = 25 mA [1 mark]

Examiner tip: Read the question carefully for required units. Standard formula gives amperes, but the question asks for milliamps.

Example 3: Interpreting I-V characteristics (Higher tier)

Question: A student investigates the I-V characteristics of a filament lamp. As the voltage across the lamp increases from 0 V to 6 V, the current increases from 0 A to 0.5 A, but the I-V graph curves rather than being a straight line.

(a) Calculate the resistance of the lamp at 6 V. [2 marks] (b) Explain why the I-V graph for the filament lamp is not a straight line. [3 marks]

Solution:

(a) R = V ÷ I = 6 ÷ 0.5 [1 mark] R = 12 Ω [1 mark]

(b) As current increases, the filament heats up / temperature increases [1 mark]

The resistance of the filament increases with temperature [1 mark]

This is because ions vibrate more, causing more collisions with electrons / making it harder for current to flow [1 mark]

Examiner tip: For explanation questions, use because/therefore to show causation clearly. Link current → temperature → resistance → I-V graph shape.

Common mistakes and how to avoid them

• Confusing current and voltage in the resistance formula. Remember: V = I × R (Voltage = Current × Resistance). Use the triangle method or write out what each letter represents before substituting numbers.

• Getting resistance calculations backwards with thermistors and LDRs. Thermistor resistance decreases with increasing temperature; LDR resistance decreases with increasing light. Many students reverse these relationships.

• Forgetting units or using incorrect units. Resistance must be in ohms (Ω), current in amperes (A), and voltage in volts (V). Convert milliamps to amps (÷1000) or kiloohms to ohms (×1000) before calculating.

• Thinking all conductors obey Ohm's Law. Only ohmic conductors (those with constant resistance) obey Ohm's Law. Filament lamps, diodes, thermistors and LDRs do not obey Ohm's Law because their resistance changes.

• Drawing I-V graphs with axes reversed. Convention is current (I) on the y-axis and voltage (V) on the x-axis. Mark clearly which axis is which and include units.

• Not explaining temperature effects on resistance sufficiently. Don't just state "resistance increases with temperature." Explain that ions vibrate more, causing more frequent electron collisions, which increases resistance.

Exam technique for "Resistance and Ohm's Law"

• Command word "calculate" means show working clearly. Always write the formula, substitute values with units, then give your answer. Each step typically earns one mark. Not showing working loses marks even with correct answers.

• Describing I-V graphs requires both shape and explanation. State whether the line is straight/curved, mention if it passes through the origin, and explain the shape using physics (temperature effects, resistance changes). Aim for 3-4 sentences for a 3-mark question.

• "State the relationship" questions need precise language. Use "directly proportional," "inversely proportional," "increases," "decreases" - not vague terms like "changes" or "affects." For example: "Resistance is directly proportional to length."

• Read scales carefully on given I-V graphs. Axes may not start at zero or may use unusual scales. Check intervals between gridlines before reading values. Work out resistance by selecting a clear point and using R = V ÷ I.

Quick revision summary

Resistance opposes current flow and is calculated using R = V ÷ I. Ohmic conductors maintain constant resistance and produce straight-line I-V graphs. Filament lamps show increasing resistance due to heating. Diodes allow current in one direction only. Thermistors decrease resistance with temperature; LDRs decrease resistance with light. Wire resistance increases with length and temperature but decreases with cross-sectional area. Always show formula, substitution, and units in calculations for full marks.