Voltage is energy per charge: U is delta E divided by Q, and a volt is a joule per coulomb. One and a half volts means that each coulomb takes one and a half joules along; it says nothing about how much charge the source holds. That is the capacity. Two batteries with the same voltage can last very differently.
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Two batteries, both one and a half volts. Both carry the same number, but one is almost twice as thick. Nobody ever buys the small one because it has just as many volts. Why not?
Because volts do not tell you how much is inside. Voltage is the measure of how much energy the source gives to each coulomb that leaves it: U is delta E divided by Q. A volt is nothing other than a joule per coulomb, so one and a half volts means that each coulomb takes one and a half joules with it. How many coulombs come out is a separate matter.
You see that difference in the two batteries. The big one delivers about nine thousand coulombs before it is empty, the small one about three thousand six hundred. At one and a half volts that is 1.4 times ten to the fourth joules against 5.4 times ten to the third: two and a half times as much energy, with exactly the same number on the label. The amount of charge a source can deliver is called the capacity. Volts are how hard it pushes, capacity is how much is inside.
Then the nine-volt battery, where the mix-up becomes clearest. Nine volts is six times as much as one and a half, so does it last six times as long? No, quite the opposite: it holds about two thousand coulombs against nine thousand for the big one. Less charge, not more. If you count with six times nine thousand, you end up with more than a hundred thousand joules and you have confused voltage with quantity.
Finally, combining sources. In series, plus to minus, the voltages add up: two of one and a half make three volts. Put them the wrong way round, plus against plus, and they work against each other. In parallel the voltage stays one and a half and you gain running time.
For upper secondary physics, in the electricity topic.
In this video
The full explanation, in writing
Two sizes, the same number
0:00These two are both one and a half volts. Both carry the same number. One is almost twice as thick as the other. And yet nobody ever buys the small one because it has the same voltage.
Voltage is energy per charge
0:18Pumping charge around takes energy, and that comes from the voltage source. A battery gets it from a chemical reaction, a solar cell from the light of the sun. Voltage is the measure of how much energy the source gives to each coulomb that leaves it. As a formula: U is delta E divided by Q.
0:39U is the voltage in volts, delta E the energy given, in joules, Q the charge in coulombs. And so a volt is nothing other than a joule per coulomb. One and a half volts means: each coulomb that leaves this battery takes one and a half joules with it.
0:59So volts say nothing about how much charge is inside. Only how much energy each bit takes along.
Why the big one lasts longer
1:06Back to those two batteries. The big one delivers about nine thousand coulombs before it is empty, the small one about three thousand six hundred. At one and a half volts the energy so delta E is U times Q: one and a half times nine thousand, is one point four times ten to the fourth joules for the big one, against five point four times ten to the third joules for the small one.
1:32Two and a half times as much energy, with exactly the same number on the label. And there is a separate name for that: the amount of charge a source can deliver is called the capacity. Volts are how hard it pushes; capacity is how much is inside.
1:52This one is nine volts, six times as much as that one and a half. So does it last six times as long in the same device?
The answer, with the wrong number next to it
2:02No, quite the opposite. This nine-volt battery delivers about two thousand coulombs, against nine thousand for the big one. There is less charge in it, not more. The energy: nine times two thousand is one point eight times ten to the fourth joules.
2:18So in energy it and the big one are close together, while one has six times as many volts. If you think nine volts lasts six times as long, you are counting on six times nine thousand coulombs and you end up with more than a hundred thousand joules.
2:35That is confusing voltage with quantity, and that is the mix-up this whole video is about.
Combining sources
2:42One more thing about voltage sources: you can combine them, in two ways. Put two batteries in series, plus to minus, and the voltages add up. Two of one and a half make three volts. Put them the wrong way round, so plus against plus, and they work against each other and you are left with zero.
3:00Put them in parallel, plus to plus and minus to minus, and the voltage stays one and a half. What you gain is charge: it lasts twice as long.
Three things to remember
3:12Three things. Voltage is energy per charge: U is delta E divided by Q, and a volt is a joule per coulomb. Volts say how hard it pushes, capacity says how much charge is inside. Two batteries with the same number can be enormously different in how long they last.
3:32And in series voltages add up, in parallel they don't; in parallel you gain running time.
Two questions
3:38Two questions. One. A source gives twelve joules to three coulombs. How many volts is that? Two. You put four batteries of one and a half volts in series in a torch. What is the voltage, and what happens if you put one in the wrong way round?
The answers
3:57The first: U is delta E divided by Q, so twelve divided by three is four volts. Joules divided by coulombs is volts, so the unit checks out. The second: four times one and a half is six volts. Turn one round, and you don't subtract it down to four and a half, but down to three volts: that one doesn't count and also works against the rest.
4:19Four and a half is exactly the answer you get if you simply leave it out instead of letting it work against the rest.
Volts, capacity and combining sources
4:27Now you know what a volt actually tells you. On the channel there is a separate video about how you measure that voltage and that current in a circuit, without blowing up your meter.
Frequently asked questions
Why does a big battery last longer than a small one with the same voltage?
Because voltage and capacity are two different things. Voltage says how much energy each coulomb takes along, capacity says how many coulombs can come out in total. A big AA delivers about nine thousand coulombs, a small one about three thousand six hundred. At the same one and a half volts that is 1.4 times ten to the fourth joules against 5.4 times ten to the third, so two and a half times as much energy.
Does a 9 volt battery last six times as long as a 1.5 volt one?
No, quite the opposite. A nine-volt battery delivers about two thousand coulombs, against nine thousand for a big AA. So there is less charge in it, not more. In energy they are close together: nine times two thousand is 1.8 times ten to the fourth joules. Anyone who counts with six times nine thousand ends up with more than a hundred thousand joules and confuses voltage with quantity.
What happens when you put batteries in series or in parallel?
In series, plus to minus, the voltages add up: two batteries of one and a half volts give three volts. Put them the wrong way round, plus against plus, and they work against each other and you are left with zero. In parallel, plus to plus and minus to minus, the voltage stays one and a half volts and you gain running time: twice as much charge can come out.
Before this came electric current: what moves in a wire and how fast it goes. Next: how to measure voltage and current in a circuit without blowing up your meter.
This video gets audio tracks and subtitles in more languages. Choose your language in the player under the gear icon, at Audio track and at Subtitles.
Physics with Thomas: physics explained with visuals where they add something, and without visuals where they distract.
In this series
Electric currentthe electrons crawl, your lamp is on at once6:12
Voltage and capacitytwo batteries, the same number4:43
Connecting ammeter and voltmeterswapping them wrecks your meter4:10
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.