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Orient and predict
Before You Read
warm-upYou have two wires of the same metal: one long and thin, one short and thick.
Before reading: which do you think has the higher resistance, and why? Write your prediction.
Year 11 Physics
Electricity and magnetism
⏱ ~60 min
5 MC · 3 Short Answer
Lesson 13 of 26
Resistance and Its Factors
If voltage pushes charge forward, resistance is what pushes back. As electrons drift through a wire they keep colliding with the vibrating metal lattice, and those collisions are resistance. Four things change how often they happen, the material, the length, the thickness and the temperature of the conductor. Understand these and you can design a wire to carry exactly the current you want.
Today's hook: A long thin wire glows and gets hot, while a short fat wire of the same metal barely warms up. What is it about the wire's shape and material that decides how much it resists the current?
0/5TASKS
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Intentions and key terms
Learning Intentions
goalsKnow
- That resistance opposes the flow of current, measured in ohms (Ω)
- The four factors: material, length, cross-sectional area, temperature
- The direction each factor pushes resistance
Understand
- Why collisions of electrons with the lattice cause resistance
- Why a longer or thinner wire resists more
- Why heating most metals raises their resistance
Can Do
- Predict how resistance changes when a factor is altered
- Explain each factor in terms of electron collisions
- Choose a wire's properties to give a desired resistance
Scan these before reading
vocabResistance ($R$)A measure of how strongly a conductor opposes the flow of current, measured in ohms (Ω).
ResistivityA property of the material itself that sets how strongly it resists current, independent of the wire's shape.
Cross-sectional areaThe area of the wire's circular end face, a thicker wire has a larger cross-sectional area.
LatticeThe regular array of metal ions through which the free electrons drift, colliding as they go.
Where this sits in the course: L12 showed that voltage drives current. This lesson explains what opposes the current, resistance, and the four factors that set it. The next lesson (L14, already built) makes the link quantitative with Ohm's law, $V = IR$.
Misconceptions To Fix
watch out✗ Wrong: A thicker wire has more resistance because there is more metal in the way.
✓ Right: A thicker wire has a larger cross-sectional area, giving the electrons more paths, so resistance decreases. Area and resistance are inversely related.
✗ Wrong: Cooling a metal always increases its resistance.
✓ Right: For most metals, heating increases resistance (the lattice vibrates more) and cooling decreases it.
Core Content
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Resistance as Electron Collisions
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Resistance as Electron Collisions
+5 XPResistance is the drifting electrons bumping into the lattice
Resistance is just how often the drifting electrons collide with the metal ions, more collisions means more opposition to the current.
As free electrons drift through a conductor under an applied voltage, they repeatedly collide with the vibrating ions of the metal lattice. Each collision transfers some of the electrons' energy to the lattice (which is why a resistor heats up) and slows their progress. Resistance is a measure of how strongly the conductor opposes this flow:
- more frequent collisions → higher resistance;
- resistance is measured in ohms (Ω);
- anything that increases collisions (or reduces the number of available paths) raises the resistance.
Resistance arises because drifting electrons collide with the vibrating ions of the metal lattice, losing energy and being slowed. More frequent collisions mean higher resistance, measured in ohms (Ω).
Pause, copy the highlighted definition into your book before moving on.
Did you get this? True or false: resistance arises because drifting electrons collide with the ions of the metal lattice.
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The Four Factors
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The Four Factors
+5 XPMaterial, length, area and temperature each change the resistance
We just saw that resistance comes from collisions. That raises a question: what makes those collisions more or less frequent? This card answers it → four properties of the conductor, material, length, cross-sectional area and temperature.
Each of the four factors changes either how often the electrons collide or how many paths they have to flow through.
The resistance of a conductor depends on:
- Material: different metals have different resistivities, copper conducts better (lower resistance) than nichrome, because of how its electrons interact with the lattice.
- Length: a longer wire means more lattice to drift through and more collisions, so resistance increases with length.
- Cross-sectional area: a thicker wire gives the electrons more parallel paths, so resistance decreases as area increases.
- Temperature: heating most metals makes the lattice ions vibrate more, increasing collisions, so resistance increases with temperature.
Text description
- Two wires of the same metal at the same temperature.
- Long and thin: high resistance, because a longer path means more collisions and a thin wire gives fewer paths side by side.
- Short and thick: low resistance.
WORKED EXAMPLE · COMPARING TWO WIRES
Two copper wires are held at the same temperature. Wire B is longer than wire A and also thinner. State which wire has the greater resistance, and explain the comparison in terms of what the drifting electrons actually encounter.
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GIVEN: same material (copper), same temperature; wire B is longer and thinner than wire A.
Two of the four factors are held fixed, which is what makes a clean comparison possible.
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METHOD: take the two changed factors one at a time. A longer wire gives electrons a longer path, so more collisions with vibrating lattice ions.
Length and cross-sectional area act in opposite senses, so separating them keeps the reasoning straight.
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METHOD: a thinner wire has a smaller cross-sectional area, so the electrons have fewer parallel paths and the same current is carried by a narrower cross-section.
This one is geometric, not a change in how often each electron collides: same material and temperature means the collision rate per electron is unchanged. A thicker wire simply offers more paths, which is why it resists less.
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ANSWER: both changes push the same way, so wire B has the greater resistance. ✓
Because the two effects agree here, no numerical comparison is needed. Had one wire been longer but thicker, the answer would depend on which change dominated.
Resistance depends on four factors: material (resistivity), length (longer → more resistance), cross-sectional area (thicker → less resistance), and temperature (hotter metal → more resistance). Length and temperature raise it; greater area lowers it.
Add the highlighted four factors to your notes before the check below.
Quick check: Which change to a wire would decrease its resistance?
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Apply it yourself
Activity 1
AnalyseBand 5
Predict the Effect of Each Factor
Pattern B, Reason factor by factor
In your book, make a four-row table. For each factor (material, length, cross-sectional area, temperature), state (1) the change you would make to increase the resistance, and (2) a one-line explanation in terms of electron collisions or available paths.
Two truths, one lie: three of these statements about resistance are correct. Which one is the lie?
Dot point: Explain why the resistance of a conductor can be affected by its material, length, cross-sectional area and temperature
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Why Temperature Matters
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Why Temperature Matters
+5 XPHotter lattice ions vibrate more and get in the way
We just learned the four factors. That raises a question: why does simply heating a metal make it resist more? This card answers it → hotter ions vibrate more, so the drifting electrons collide with them more often.
Temperature is special because it is the one factor you can change without altering the wire itself, and it works by making the lattice a bigger obstacle.
In a metal, raising the temperature gives the lattice ions more thermal energy, so they vibrate with larger amplitude about their fixed positions. A drifting electron then finds the ions sweeping through a bigger volume of space, so it collides with them more frequently. More collisions means more opposition to the flow, a higher resistance. This is why a globe's filament has a much higher resistance when it is hot and glowing than when it is cold, and why electrical components are often rated for a particular operating temperature.
Heating a metal makes its lattice ions vibrate more, so drifting electrons collide with them more frequently, increasing the resistance. For most metals, resistance rises with temperature and falls as the metal cools.
Pause, copy the highlighted temperature explanation into your book before the check below.
Last check: Decide if the statement is true or false.
Heating most metals raises their resistance because the lattice ions vibrate more and the electrons collide with them more often.
Fill the blanks: Complete the factor summary.
Resistance increases with the of a conductor and decreases as its cross-sectional area increases. For a metal, raising the temperature makes the lattice ions vibrate more, which the resistance.
Dot point: Explain why the resistance of a conductor can be affected by its material, length, cross-sectional area and temperature
✓
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Show what you have learned
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Multiple Choice
+5 XPA fresh set drawn from this lesson's question bank, feedback shown immediately. +5 XP per correct · +25 XP all correct
Pick your answer, then rate your confidence, that tells the system what to drill next.
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Short Answer
+5 XPUnderstandBand 5(4 marks) 1. Explain how the length, cross-sectional area and temperature of a metal conductor each affect its resistance. Refer to electron collisions with the lattice in your answer.
1 mark: longer wire → more collisions → higher resistance · 1 mark: larger cross-sectional area → more paths → lower resistance · 1 mark: higher temperature → ions vibrate more → more collisions → higher resistance · 1 mark: links all three to the rate of electron–lattice collisions
AnalyseBand 5(3 marks) 2. A filament lamp draws a noticeably larger current in the first instant after it is switched on than it does a second later, even though the supply voltage is unchanged. Explain this using the effect of temperature on the resistance of a metal.
1 mark: when cold the filament has a comparatively low resistance · 1 mark: current heats the filament, the lattice ions vibrate more and collide with the drifting electrons more often, so resistance rises · 1 mark: with $V$ fixed, $I = V/R$ means the rising resistance reduces the current to a steady lower value
Dot point: Explain why the resistance of a conductor can be affected by its material, length, cross-sectional area and temperature
ApplyBand 5(3 marks) 3. A wire has resistance $R$. A second wire of the same material has twice the length and twice the diameter. Determine the resistance of the second wire, showing your reasoning.
1 mark: resistance is proportional to length, so doubling length doubles it · 1 mark: doubling the diameter multiplies the area by 4, dividing resistance by 4 · 1 mark: net resistance is $R/2$
Dot point: Explain why the resistance of a conductor can be affected by its material, length, cross-sectional area and temperature
Show all answers
Multiple choice
MC answers and full explanations are shown inline as you complete each question. Use the retry button to attempt a fresh set from the lesson bank.
Short Answer Model Answer
Q1 (4 marks): A longer wire gives the drifting electrons more lattice to travel through, so they undergo more collisions with the lattice ions, increasing the resistance. A larger cross-sectional area (thicker wire) provides more parallel paths for the electrons, so for the same current there are fewer collisions per electron and the resistance is lower. A higher temperature gives the lattice ions more thermal energy so they vibrate with larger amplitude; the electrons then collide with them more frequently, raising the resistance. In every case the resistance is governed by how often the drifting electrons collide with the vibrating ions of the metal lattice, more frequent collisions mean greater resistance.
Q2 (3 marks): At the instant of switch-on the filament is at room temperature, and a cold metal has a comparatively low resistance, so the initial current is large. That current immediately dissipates power in the filament and its temperature climbs very rapidly to operating temperature. As the metal heats, its lattice ions vibrate with greater amplitude, so the drifting electrons collide with them far more frequently, and each collision impedes the drift. The resistance of the filament therefore rises substantially. The supply voltage has not changed, so by $I = V/R$ the increasing denominator reduces the current, which settles at a steady, smaller value once the filament reaches its working temperature. This is also why filament lamps most often fail at the moment of switch-on.
Q3 (3 marks): Resistance is directly proportional to length and inversely proportional to cross-sectional area. Doubling the length on its own would double the resistance, giving a factor of $2$. Doubling the diameter multiplies the cross-sectional area by $2^2 = 4$, because area depends on the square of the diameter, and that on its own divides the resistance by $4$. Combining the two effects, the resistance changes by a factor of $2/4 = \tfrac{1}{2}$, so the second wire has resistance $R/2$. The common error is to treat doubling the diameter as halving the resistance, which forgets that area depends on the square of the diameter.
✓
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Retrieve, reflect and finish
Lock it in
bossYou can now explain resistance as electron–lattice collisions and predict how material, length, area and temperature change it. Next lesson makes the relationship between voltage, current and resistance quantitative with Ohm's law, $V = IR$.
↩ Back to focus-area hubHow did your thinking change?
At the start you compared a long thin wire with a short thick one. The long thin wire has the higher resistance: greater length means more electron–lattice collisions, and a smaller cross-sectional area means fewer paths for the electrons. Both effects oppose the current more strongly.
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Check what actually stuck
A short spaced-retrieval set, mixing this lesson with earlier ones. It gets harder to guess and easier to remember.