Every river runs from high ground to low, and the drop is what moves it. Whoever understands the drop can build a waterfall of their own.
⟨ transmission ends ⟩Look at any battery and you will find a number on it. One says 9 V, and an AA cell says 1.5 V. In The Current you saw that the wires are already full of electricity, and that the battery pushes it round. The number on a battery says how hard it pushes. To see that push for yourself, you need a voltmeter.
The tool below is an analogue voltmeter. Its needle swings across a scale of numbers. A red cable plugs into its + post and a black cable into its − post. Each cable ends in a probe, a metal tip on a handle. You touch the tip to whatever you want to measure. A voltmeter measures only voltage. At a real bench most people use a multimeter, which measures current as well. We will learn how to use a multimeter in The Meter.
Start with the 9 V battery on its own. If only the red probe touches the + end, will the needle move?
This is an analogue voltmeter, the kind used in school labs, with a scale from 0 to 10 V. It lets only a tiny current through itself, too small to change what it measures. The battery here gives the 9 V printed on it. The voltmeter and the battery are not shown at their real sizes.
A voltmeter reads the difference between the two points its probes touch. With only one probe on the battery there is no second point, and nothing to compare. The + end and the − end differ by 9 V, and that difference is called the battery’s voltage.
What the voltmeter compares between the two points is energy. The voltage between two points is how much energy each bit of electricity gains or loses on its way from one to the other. It is measured in volts, written V, which is where the voltmeter gets its name.
Often we need a higher voltage than one cell gives. The usual way to get it is to join several cells, the + end of one to the − end of the next. On the bench below, four 1.5 V cells are joined like that. What do you think the voltmeter will read across all four?
The cells never run down on this bench. A real cell gives less and less as it is used up.
The voltmeter reads 6.0 V, four times what one cell gives. Joined + to −, each cell adds its 1.5 V on top of the one before it. I picture the row as a staircase. Every cell is one step up, and the voltmeter tells you how high one probe stands above the other.
Those steps only add up while every cell is joined + to −. Cells go into a holder by hand, and one can easily go in backwards. On the bench below you can flip one on purpose. How much of the 6.0 V do you expect to be left?
Nothing is joined to the row except the voltmeter. With two cells flipped the row gives 0 V. With three, the row pushes the other way and the needle goes below 0 as far as it can.
A flipped cell pushes against the others. It takes 1.5 V off the row instead of adding 1.5 V, so the row ends up 3.0 V lower. On the staircase it is a step down in the middle of the climb.
That is why every holder shows which way each cell should face. When something with fresh cells will not work, a cell put in backwards is the first thing I check.
What happens to the voltage once the battery lights something? On the bench below, a 9 V battery lights a red LED through a resistor. The current is the same all the way round a circuit. Is the voltage the same at every joint too?
The circuit is a 9 V battery, a 470 Ω resistor and a red LED, carrying 15 mA. While that current flows, the battery gives 8.97 V at its ends, because 0.03 V is lost inside it. The reading below the bench rounds that to 9.0. Along each 15 cm lead the voltage falls by less than a thousandth of a volt.
They do not. The joint between the red lead and the resistor reads 9.0 V, but the joint between the resistor and the LED reads only 1.9 V. So the voltage falls by most of the 9 V from one end of the resistor to the other. It falls by the last 1.9 V through the LED. Along the leads it hardly falls at all.
The current stays the same all round because no electricity is used up. The energy each bit carries is what gets used. A bit gains its energy in the battery. By the time it gets back to the − end, it has given all of it away. The resistor turns its share into heat, and the LED turns its share into light and heat.
On the staircase, the battery is the stairs up, and the resistor and the LED are the stairs down. The staircase is misleading about speed. A ball rolling down stairs speeds up, but the electricity comes out of each part no faster than it went in.
How big is the resistor’s share of the fall? You can measure it with a probe on each end. Before you do, work it out from the two readings on either side of the resistor.
Readings are rounded to one decimal place. With the probes swapped, the voltmeter is joined backwards, and the needle swings the wrong way, against the left end of its scale.
The voltmeter found 7.1 V between the resistor’s two ends. The voltage between a part’s two ends is called the voltage across that part. Across the LED it is 1.9 V.
That is true of every circuit, whatever is in it. Going once round a circuit, the voltage rises through the battery and falls through the parts. The rises and falls always add up to zero. Gustav Kirchhoff worked this out in the 1840s, and it is called Kirchhoff’s voltage law.
The Σ, the Greek letter sigma, means add them all up. With one battery, the law simply means that the battery’s voltage equals the voltages across the parts added together.
It is most often used to find the voltage across a part when we do not know it. If I know the battery’s voltage and the voltages across all the other parts, I can calculate the last one.
A battery or an adapter gives a fixed voltage, and it is printed on the case. The voltage across a resistor is printed nowhere, because it depends on the circuit it is in. To find it, put a probe on each end, or calculate it, which we will learn to do in The Three Numbers.
Four questions, if you want to check yourself.
Three AA cells sit in a holder, joined + to − in a row. What does the voltmeter read across the holder?
The same holder now has one cell put in backwards. What does the voltmeter read across it?
A circuit has a 9 V battery, a resistor and an LED. The LED has 2 V across it. What voltage is across the resistor?
The LED in a circuit is lit. One probe is on the battery’s + end and the other on the far end of the red lead. What does the voltmeter read?
Now we know what voltage is and how to measure it. The next question is what it does to the current. If we double the voltage, does the current double too? We find out in The Three Numbers.
Lesson 3 done.
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