The resistance of a wire is directly proportional to its length and inversely proportional to its cross-section, and the material is in the resistivity: rho is R times A divided by l. So a long, thin cable has more resistance, and the voltage across the cable itself never reaches your phone.
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Same charger, same phone, and yet it charges noticeably faster on one cable than on the other. The slow cable is longer and thinner, and that is no detail: that is its resistance.
The resistance of a wire depends on three things. The length: twice as long, and the electrons meet twice as many ions, so twice the resistance. The cross-section: twice as thick, and twice as many electrons can get through in the same time, so half the resistance. And the material, which you capture in one number: the resistivity, rho, in ohm metres. The rule is rho is R times A divided by l.
Copper has one of the lowest resistivities there are, seventeen times ten to the minus ninth ohm metres. That's why almost all leads are made of copper. And in metals the resistivity increases as it gets warmer: the ions vibrate harder and get in the electrons' way more.
Then with numbers. A charging cable of two metres with cores of zero point one zero square millimetres. First convert the cross-section to square metres, because that is where it most often goes wrong. The current goes out through one core and back through the other, so through four metres of copper: 0.68 ohms in total. If the charger drives two amperes through it, Ohm's law gives 1.4 volts across the cable itself. That voltage never reaches your phone.
For upper secondary physics, on electricity.
In this video
The full explanation, in writing
Two cables, one charger
0:00Your phone charges on one cable noticeably faster than on the other. Same charger, same phone. Only the slow cable is longer and thinner.
Length, cross-section and material
0:16The resistance of a wire depends on three things. The length. If the wire is twice as long, the electrons meet twice as many ions, and the resistance is twice as large. The resistance is directly proportional to the length. The cross-section. If it is twice as large, twice as many electrons can get through in the same time, and the resistance is half.
0:42The resistance is inversely proportional to the cross-section. And the material. You capture that in one number: the resistivity, symbol rho. That is the resistance of a wire one metre long with a cross-section of one square metre, and the unit is the ohm metre.
1:02The rule: rho is R times A divided by l.
Copper, and heat
1:06Copper has one of the lowest resistivities there are: seventeen times ten to the minus ninth ohm metres. That's why almost all leads are made of copper. And in metals the resistivity increases as it gets warmer. The ions vibrate harder and get in the electrons' way more.
1:26Your turn. Two copper cables, equally thick, one a metre long and the other two metres. How many times larger is the resistance of the long one?
The resistance of a charging cable
1:39Twice as large, because the length is in the numerator: R is rho times l divided by A. Now with numbers. A charging cable of two point zero metres, with copper cores of zero point one zero square millimetres. Careful: the cross-section must be in square metres, and a square millimetre is ten to the minus sixth square metres.
2:02So A is one point zero times ten to the minus seventh square metres. R is seventeen times ten to the minus ninth, times two point zero, divided by one point zero times ten to the minus seventh. That's zero point three four ohms. And the current goes out through one core and back through the other, so it runs through four metres of copper: zero point six eight ohms.
Where the voltage goes
2:31And then the phone. Say the charger delivers five point zero volts and drives two point zero amperes through that cable. With Ohm's law, across the cable itself, U is I times R: two point zero times zero point six eight, is one point four volts.
2:50That voltage is across the cable, so it doesn't reach your phone. Three point six volts are left, and on that it charges more slowly. A short, thick cable loses much less.
Three things to remember
3:03Three things. The resistance of a wire is directly proportional to the length and inversely proportional to the cross-section. The material is in the resistivity: rho is R times A divided by l, in ohm metres. Convert the cross-section to square metres first.
3:22And in metals the resistivity increases as it gets warmer.
Two questions
3:28Two questions. One. A ten-metre extension lead has copper cores of one point five square millimetres. How large is the resistance of one core? Two. Two wires of the same copper. One is twice as long as the other, and also has twice the cross-section.
3:47Which has the larger resistance?
The answers
3:53The first: one point five square millimetres is one point five times ten to the minus sixth square metres. R is seventeen times ten to the minus ninth, times ten, divided by one point five times ten to the minus sixth. That's zero point one one ohms.
4:10The second: they are equally large. Twice as long makes the resistance twice as large, and twice as thick makes it half as large again.
Resistors that change by themselves
4:20A resistor whose length you change with a knob, and resistors that change by themselves with heat or light: on the channel there's a separate video on the variable resistor, the NTC, the PTC and the LDR.
Frequently asked questions
How do you calculate the resistance of a wire?
With R is rho times l divided by A. Here rho is the resistivity of the material in ohm metres, l the length in metres and A the cross-section in square metres. So convert the cross-section first: one square millimetre is ten to the minus sixth square metres.
Why does my phone charge more slowly with a long cable?
A long, thin cable has more resistance. The current goes out and back through the cores, and part of the voltage is lost across that resistance. With a two-metre cable with thin cores that can already be 1.4 volts of the charger's 5.0 volts, and it never reaches your phone.
What is resistivity?
Resistivity is the resistance of a wire one metre long with a cross-section of one square metre. It is a property of the material, with the unit ohm metre. Copper has one of the lowest: seventeen times ten to the minus ninth ohm metres.
Does the resistance of a metal increase when it gets warm?
Yes. In metals the resistivity increases with temperature, because the ions vibrate harder and get in the electrons' way more.
Before this came Ohm's law: what resistance is, and whether it gets larger when you double the voltage. Next: resistors that change, the variable resistor, the NTC, the PTC and the LDR.
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Physics with Thomas: physics explained with pictures where they add something, and without them where they distract.
In this series
Electric current6:12
Voltage and capacity4:43
Connecting ammeter and voltmeter4:10
Resistance and Ohm's law4:21
Resistance of a wire4:40
Variable resistor, NTC, PTC and LDR3:40
Series circuit3:32
Parallel circuit3:56
Series-parallel circuit3:37
Circuits practical test5:13
Power2:58
Kilowatt-hour3:05
About me
My name is Thomas Schuurmans, and I have a passion for physics and for understanding why things work the way they do. What I want is to get young people asking “why is that?” and “how does that work?” more often, and to hand them the tools of physics in a way that is simple and that you can see.
I graduated in applied physics at Delft University of Technology in 2003. After that I spent more than twenty years outside education: first at TNO, the Dutch applied research institute, then at a design agency, and eventually founding Proportion Global, through which I work on innovation questions in Africa, Latin America and South Asia. That work resembles physics more than you would expect: don't start from a solution, first understand what is going on, try something, be wrong, and look again.
Since 2026 I have been teaching physics to both lower and upper secondary classes, and I started a master's at the University of Amsterdam for my full teaching qualification. That is where I learned that a secondary school pupil's real attention for new material lasts about seven minutes. And my own weakness happens to be telling too many side stories.
That is where the idea came from: videos that explain one topic sharply and visually, inside those seven minutes. I make them for my own pupils. Then I publish them, because good explanation should be within reach of anyone who needs it, wherever you live and whatever language you think and speak in.