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Voltage is like air pressure

Voltage is analogous to air pressure. Air molecules repel each other. The reason why isn't important, but the fact is that if you squeeze a volume of air into a smaller space, the air molecules will exert a greater pressure on each other and the inner walls of the container. It's like filling a tire. If you force air into a tire, you will have some air pressure inside the tire. Force more air in, and you will get more pressure. Force enough air into the tire, and you will get enough pressure exerted on the tire walls to support the car. Once the tire is inflated, if you open the filler valve, the high-pressure air inside the tire will escape to the atmosphere where the pressure is lower.

There is an electronic component called a capacitor. We will discuss capacitors later. However, a capacitor acts much like a tire. We can put electricity into a capacitor and get electrical pressure. We call electrical pressure voltage. Put in more electricity, and we will get more voltage. We can store electricity under pressure (voltage) in a capacitor just like we can store air under pressure in a tire.

Another way to develop air pressure is to block airflow in a hose. For example, if we open the valve of the air hose used to fill our tire, the air will escape, and there will be little or no pressure in the hose. However, if we block that flow, we will get significant pressure in the hose (like putting your thumb over a garden hose). Likewise, if you block the flow of electricity in a wire, you will get voltage in the wire.

Voltage is always a differential

Whenever we measure pressure, we are always comparing one pressure to another. Voltage is no different. Let’s look at the tire again. Let’s say you are at the beach. The location is important because it puts you at sea level. Now let’s say you put a pressure gauge on the tire and see that it contains a pressure of 30 pounds per square inch (30 psi). The question is, what is the actual pressure inside the tire? Isn’t it 30 psi? Actually, no. It’s about 45 psi. How can that be? Why does the gauge say 30 psi if the actual pressure is 45 psi? The reason is that the air around you already has a pressure of about 15 psi (Actually about 14.7 psi, but let’s keep the math simple). The gauge is actually comparing the pressure inside the tire to the pressure outside the tire and telling you the difference. If you drive your car to an altitude of 6,000 feet above sea level, the ambient pressure is about 12 psi. Assuming nothing changed except the altitude, your gauge will now read about 33 psi. In Tibet, there are two roads that go higher than 18,000 feet above sea level. At this altitude, where the ambient air pressure is about 7.5 psi your gauge will read about 37.5 psi. Finally, if you could get your tire into outer space, where the ambient pressure is zero, you gauge will finally read the actual pressure in your tire, which is 45 psi.

Measuring voltage is like measuring air pressure

Voltage, being a measurement of pressure, works the same way. This is why a voltmeter has two probes. The red probe will normally go to the higher voltage and the black probe will normally go to the lower voltage. The meter will then tell the voltage difference between the two probes. One voltage is meaningless unless it is compared to another voltage.

A barometer tells us the difference between two air pressures

If pressure is always a differential, where do we get the 15 psi for the ambient air pressure? In 1643 Evangelista Torricelli wanted to find out why suction pumps could not pump water higher than about 34 feet. He made a glass tube with an inside diameter that equaled one square inch. The tube was about three feet long and sealed at one end. He filled the tube with mercury and upended it into a bowl of mercury. Mercury flowed out of the tube into the bowl as you would expect, but stopped when the column of mercury in the tube fell to about 30 inches tall.

The reason the mercury did not fall below 30 inches was that the air was pushing down on the surface of the mercury in the bowl. This pressure forced the mercury up the tube as there was no pressure at the top of the tube to resist it. No air had been introduced into the tube, so the space above the column of mercury contained a vacuum. Torricelli then weighed the mercury in the tube. It weighed about 14.7 pounds. Therefore, the pressure pushing the mercury up the tube was equal to about 14.7 pounds per square inch.

The height of the mercury in the tube is the same regardless of the size or shape of the tube. Putting a ruler next to the tube gives you the ambient air pressure measured in the convenient units of inches of mercury. This is not a joke. Air pressure may be stated in pounds per square inch, newtons per square meter (pascals) or bars, but in the U.S. is commonly stated in inches of mercury (inHg). Other countries may use millimeters of mercury (mmHg). At sea level, the standard ambient air pressure is 29.92 inHg. Torricelli’s barometer measures ambient air pressure by comparing it to a vacuum. We get one pressure compared to another pressure where that other pressure is absolute zero.

A voltmeter tells us the difference between two voltages

Voltage, being electrical pressure, is measured much like air pressure. A voltmeter has two electrical probes. When you use a voltmeter, it is telling you the difference in voltage between those probes. It tells you how much higher or lower the voltage at the red probe is compared to the voltage at the black probe.

If a voltmeter reads 8.2 volts, it is telling you that the voltage at the red probe is 8.2 volts higher than the voltage at the black probe. If a voltmeter reads -12.6 volts, it is telling you that the voltage at the red probe is 12.6 volts lower than the voltage at the black probe. This, of course, assumes the standard conventional-current model (discussed later) where positive is greater than negative.

How do you find zero volts?

What is the actual voltage at the black probe? There is no way of knowing. All a voltmeter can tell you is the difference between two voltages. That’s it. There is no “actual” voltage at the black probe to measure. All you can do is tell that some voltage is higher or lower than the voltage at the black probe. An absolute zero voltage has never been defined so there is no electrical equivalent of a Torricelli’s barometer. No device can give you an absolute voltage reading. We will learn what zero volts means in electronics later when we discuss how to measure voltage.

Göethe's barometer acts more like a voltmeter than Torricelli’s barometer

The renowned German writer and amateur scientist, Johann Wolfgang Von Göethe,^[1] developed a water-based barometer that tells what the ambient air pressure is compared to an arbitrary air pressure (rather than an absolute pressure like Torricelli's barometer).

Voltage vs. electromotive force

Voltage is often called electromotive force (EMF), and it is often said that they are the same thing. There is actually a subtle difference.^[2] This sometimes confuses the novice and the expert alike, particularly where electricity and magnetic fields interract. EMF is so closely related to voltage that the difference is almost not worth discussing in electronics technology. However, some popular websites and videos—some created by people with advanced degrees in physics—that claim some fundamental laws of electricity are flawed. Their claims are partly based on misunderstanding the nature of EMF and how it differs from voltage. Their arguments are convincing if you don't know the nature of EMF and how to properly apply the laws. Complicating that is their cadre of followers who will loudly question your intelligence if you question their assertions. This undermines the trust of novice students. For example, if a student makes a mistake applying any law to a circuit, how can he or she know if they made a mistake or encountered an area where the law doesn't apply?

EMF is a force that tends to make electricity move. This force exists in batteries, generators, etc., and cannot be measured with a voltmeter. EMF can be thought of like the heating and rotation of the earth that cause wind. The heating and rotation spawn forces that make air move, but these forces cannot be measured with an air pressure gauge. However, if an obstacle blocks the wind, a pressure differential will develop between the windward and leeward sides. This pressure differential can be measured with a sensitive pressure gauge such as a liquid column manometer.

The EMF in a battery or generator is similar to the forces that cause wind in that it can't be measured with a voltmeter. However, at the terminals of a battery or generator, the flow of electricity is blocked. As explained above, blocking the flow of electricity causes voltage to develop (much like wind encountering an obstacle). Therefore, the EMF, which cannot be measured with a voltmeter, pushes electricity. When the electricity encounters a blockage, such as the open terminals of a battery or generator, or a circuit between the terminals, voltage develops, which can be measured with a voltmeter (the only time a voltage won't develop is if there is a direct short across the terminals).

The sources of EMF tend to be spread over some distance (such as the length of a coil in a generator). Therefore, EMF is sometimes measured in volts per unit of distance, such as volts per centimeter. The voltage at the terminals of a battery or generator equals the total EMF in the device. For example, if a generator coil is 10 mm long and produces one volt per mm of EMF, the total EMF is 10 volts. The voltage at the terminals of said generator will also be 10 volts. Perhaps the reason many conflate voltage and EMF is that EMF can be measured by blocking the flow of electricity to produce voltage, then measuring that voltage with a voltmeter. 10 volts of EMF will cause a 10-volt differential between the terminals.

¹	Göethe is a fun name that sounds nothing like how it is spelled to us non-Germans. The ''öe'' is pronounced much like the ''oo'' in ''wood'' with a hint of ''ea'' as in earth. The ''the'' is pronounced like a ''T'' with a hint of ''eh'' at the end. Native English speakers usually pronounce it something like ''Girta''with a hard ''G''.
²	Feynman Lectures No. 22 — AC Circuits

What is Voltage