Resistance and Ohm's Law

This lesson covers resistance, Ohm's law and the factors affecting resistance, as required by AQA GCSE Combined Science Trilogy (8464, section 6.2.1). Understanding resistance and how it relates to current and potential difference is essential for circuit calculations.

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What Is Resistance?

Resistance is a measure of how difficult it is for current to flow through a component. The greater the resistance, the smaller the current for a given potential difference.

Resistance is measured in ohms (Ω).

The Resistance Equation

$V = I \times R$V=I×R

Where:

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

Rearranging: $R = \dfrac{V}{I}$R=IV​ and $I = \dfrac{V}{R}$I=RV​

Quantity	Symbol	Unit	Unit Symbol
Potential difference	V	Volts	V
Current	I	Amperes	A
Resistance	R	Ohms	Ω

Exam Tip (AQA 8464): You must be able to rearrange $V = IR$V=IR confidently. Cover the quantity you want in the formula triangle: V at the top, I and R at the bottom.

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What Causes Resistance?

In a metal conductor, free electrons (delocalised electrons) carry the current. As these electrons move through the metal, they collide with the vibrating metal ions in the lattice structure. Each collision:

• Transfers energy from the electrons to the ions.
• Causes the metal to heat up.
• Slows the electrons down.

The more collisions that occur, the greater the resistance.

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Ohm's Law

Ohm's law states:

The current through an ohmic conductor is directly proportional to the potential difference across it, provided the temperature remains constant.

This means that if you double the voltage across an ohmic conductor, the current doubles — and the resistance stays constant.

A component that obeys Ohm's law is called an ohmic conductor. Its V–I graph is a straight line through the origin.

Ohmic vs Non-Ohmic Components

Component	Obeys Ohm's Law?	V–I Graph Shape
Fixed resistor (constant temp.)	Yes	Straight line through origin
Wire (constant temp.)	Yes	Straight line through origin
Filament lamp	No	Curve — steeper at low current
Diode	No	Current in one direction only

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Factors Affecting the Resistance of a Wire

The resistance of a wire depends on four factors:

Factor	Effect on Resistance	Explanation
Length	Longer wire → higher resistance	More metal ions for electrons to collide with
Cross-sectional area	Thicker wire → lower resistance	More space for electrons to flow through — fewer collisions per unit length
Material (resistivity)	Different materials → different resistance	Each material has a different lattice structure
Temperature	Higher temp. → higher resistance (for metals)	Ions vibrate more → more collisions

The equation linking these factors is:

$R = \frac{\rho \times L}{A}$R=Aρ×L​

Where $\rho$ρ (rho) is the resistivity of the material, $L$L is the length and $A$A is the cross-sectional area. (This equation is provided for reference — AQA Combined Science does not typically require direct use of this formula, but you must understand the proportional relationships.)

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Special Components — Thermistors and LDRs

Thermistor (NTC — Negative Temperature Coefficient)

Temperature	Resistance	Explanation
Increases	Decreases	At higher temperatures, more charge carriers are released, so current flows more easily

Application: Temperature sensors, thermostats, fire alarms.

LDR (Light-Dependent Resistor)

Light Intensity	Resistance	Explanation
Increases	Decreases	More light releases more charge carriers, allowing current to flow more easily

Application: Automatic streetlights, camera light meters, burglar alarms.

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Worked Examples

Worked Example 1

A 12 V battery is connected to a resistor. The current is 2 A. Calculate the resistance.

$R = \frac{V}{I} = \frac{12}{2} = 6 \text{ Ω}$R=IV​=212​=6 Ω

Worked Example 2

A current of 0.5 A flows through a 20 Ω resistor. Calculate the potential difference.

$V = I \times R = 0.5 \times 20 = 10 \text{ V}$V=I×R=0.5×20=10 V

Worked Example 3

A 9 V battery is connected to a resistor with a resistance of 45 Ω. Calculate the current.

$I = \frac{V}{R} = \frac{9}{45} = 0.2 \text{ A}$I=RV​=459​=0.2 A

Worked Example 4

A wire is 50 cm long and has a resistance of 4 Ω. If the wire is replaced with one that is 1 m long (same material and thickness), what is the new resistance?

Length doubles (50 cm → 100 cm), so resistance doubles:

$R = 2 \times 4 = 8 \text{ Ω}$R=2×4=8 Ω

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Common Mistakes

Mistake	Correction
Saying "Ohm's law always applies"	Ohm's law only applies to ohmic conductors at constant temperature
Confusing a thermistor with an LDR	Thermistor: resistance changes with temperature; LDR: resistance changes with light
Forgetting that $V = IR$V=IR is the definition of resistance	$V = IR$V=IR applies to all components; Ohm's law is the additional statement that R is constant

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Summary

• Resistance opposes the flow of current and is measured in ohms (Ω).
• $V = I \times R$V=I×R — this is the key equation linking potential difference, current and resistance.
• Ohm's law states that current is proportional to p.d. at constant temperature (straight-line V–I graph through the origin).
• Resistance of a wire depends on length, cross-sectional area, material and temperature.
• A thermistor has resistance that decreases as temperature increases.
• An LDR has resistance that decreases as light intensity increases.

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Extended Worked Examples

Worked Example 1 — Ohmic Conductor

A fixed resistor has 12 V across it and a current of 3.0 A flows through it. Calculate the resistance.

Using $V = IR$V=IR, rearrange to $R = V/I = 12 \div 3.0 = 4.0$R=V/I=12÷3.0=4.0 Ω.

If the voltage were doubled to 24 V (and the resistor stayed at the same temperature), the current would also double to 6.0 A — confirming the resistor is an ohmic conductor because the ratio $V/I$V/I stays constant at 4.0 Ω.

Worked Example 2 — Non-Ohmic Conductor (Filament Lamp)

A filament lamp shows these readings:

p.d. / V	Current / A	Resistance / Ω
1.0	0.50	2.0
2.0	0.80	2.5
4.0	1.20	3.33
6.0	1.50	4.0

Comment on the data.