Voltage, Current, Power — What Goes All the Way Around Undiminished

The Small Print on the Back of the Charger

If you flip over a phone charger, there is tiny print. It reads something like "Output 5V 2A". On the handle of a hair dryer, a number like "1,500W" is stamped. The three letters V, A, and W measure different things. And the three are tied together by a single multiplication, so if you know two of them, the remaining one comes out. The examples in this article are set with the outlets of South Korean homes, meaning outlets where 220V enters.

Before reading the three letters, let us put aside a common thought. It is the thought that when a light bulb turns on, electricity that rode the wires is used up in the bulb, and a little less remains in the returning wire. Because fuel, rice, and phone batteries all shrink when used, this is a natural guess. In fact, the thought that "it shrinks when used" has worked well in explaining numerous everyday things (DOI: 10.1080/0950069950170303). This article starts from separating what does not shrink and what shrinks even after passing through a light bulb.

A Road That Goes in a Circle — Circuits and Current

Let us think of a flashlight. A battery, a bulb, and two metal strips connecting the two are all there is. Turn on the switch and the light comes on; disconnect one strip and it goes off. A circuit is a closed path without any breaks where electricity comes out of a battery, passes through a device, and returns to the battery. The switch is a device that breaks and connects this path in one place. The very idea of a circuit is one of the concepts that children learning it for the first time find difficult (DOI: 10.1088/0031-9120/23/2/004).

Let us give a name to what moves along that path. Current is the flow of electricity flowing along a wire, and how much of it passes a point in one second is measured in a unit called the amp. The "2A" on a charger is precisely this scale. What then is it that flows? Charge is the amount of electricity held by very small particles like electrons, and when these particles move in one direction, it becomes current. The particles moving inside a metal wire are electrons. A widely accepted picture is that of electrons moving inside the wire in response to the difference between both ends of the wire (DOI: 10.1080/0950069960180203).

Let us transfer this picture to a ski resort chairlift. The skiers are the charges. The lift carries the skiers to the top, and the skiers ride down the slope and get back in line for the lift. The current is how many people pass a point like the lift boarding station in one second. Even if it runs all day, the number of skiers does not decrease. What decreases is the height gained at the top, and that height is all used up while coming down the slope.

It is the same in a circuit where the number does not decrease. Students with different ideas about current designed and ran experiments themselves to sort out those ideas. Among them was the idea that current is used up in the bulb and disappears. The result was that current is conserved, and the students did not welcome that result (DOI: 10.1080/0950069950170303). The current before passing the bulb and after passing it is the same. The bulb is a place that stands in the way of the flow, not something that eats up the charges. The same students created a two-part model that separates moving charges from what makes those charges move, and this model became a stepping stone for students trying to move away from the consumption model (DOI: 10.1080/0950069950170303).

What then is it that decreases in the bulb? Physics textbooks answer this question. What decreases is energy. The energy given to the circuit by the battery changes into light and heat while the charges pass through the bulb and goes out into the room. The charges do not decrease and make a round trip. The one line to take away is this. What gets used up in the bulb is energy, and the current remains the same even after making a full circle.

There is one gap in the chairlift picture. The lift carries skiers up one by one, but the charges inside the wire fill the entire circuit from the beginning. So when you close the switch, the charges all over the circuit begin to move almost all at once, and the light turns on without needing to wait for the charges that just set out from the battery to reach the bulb. Therefore, picturing that charges carry loads of energy like skiers carrying their own height down with them is wrong. Energy crosses the circuit without waiting for the charges to arrive.

The Difference That Makes It Flow — Voltage

A new battery in a drawer has 「1.5V」 written on it. Since it is connected to nothing, no current flows. Even so, that 1.5V remains just as it is. Voltage is the difference that makes electricity flow between two points, and is measured in units called volts. The 1.5V of a battery is the difference between its two ends, the bump side and the flat side. Voltage is always a value that asks 「between where and where」.

In a lift, voltage is the height difference between the top and the bottom. The greater the height difference, the larger the energy a single skier can release while coming down. Voltage is just the same, determining the magnitude of the energy that changes when the same amount of charge passes between two points. There is a reason this article uses the height difference analogy. In a study where 12 middle school students were interviewed in groups about how they understood four analogies featured in a Norwegian textbook, the students were able to reason about continuous circuits and current using all four analogies—the ski lift, water pipes, a waterfall, and a bowling ball—yet still found voltage difficult. The authors conclude that the analogies connecting voltage to energy transfer via height difference seemed useful, even though they require the more abstract concept of a space where gravity acts, namely a 「field」. It is not a study that measured and compared effects, and the subjects said to have found it useful are also the bundle of height difference analogies. The same study notes that weaknesses in how analogies are presented can severely impair understanding, and that such weaknesses were common in the textbooks examined (DOI: 10.5617/nordina.6882, small-scale interview study). Since the lift was also one of the analogies featured in that textbook, this article too operates under that warning.

The reason voltage is difficult is that it is easily confused with current. Many students treat voltage as a property that current possesses (DOI: 10.1119/5.0046298). When solving problems, it is also common to keep one's eyes only on current, and to project the properties of current onto other quantities like voltage (DOI: 10.1119/1.1614813). A battery in a drawer is a counterexample to that. Even when the current is 0, the voltage is 1.5V.

Another long-lasting idea is viewing a battery as a spring that sends out a constant current. In interviews with high school and college students, this idea was most frequently used to explain answers (DOI: 10.1119/1.1614813), and remained both before and after taking university classes (DOI: 10.1080/03043799108939504). A battery is closer to producing a constant voltage than a constant current (DOI: 10.1119/5.0046298). One must be careful here because the lift analogy breaks down. A real lift is a machine whose very design fixes the number of people carried up per minute, so the lift ultimately determines the number of people coming down the slope as well. This is precisely the picture that 「batteries produce a constant current」. Batteries are not like that. What a battery determines is the height, namely the voltage side, and for the same battery, how much passes per second depends on the device connected to it. Because real batteries drop in voltage slightly when a large amount is drawn at once or as they wear down, 「constant voltage」 is a close approximation.

The Degree of Blocking Flow — Resistance and Ohm's Law

Even when plugged into the same 220V outlet, a lot of current flows through an electric heater, while a little flows through a small desk lamp. Since the outlet is the same, what makes the difference is the device itself. Resistance is the degree to which a device or wire blocks the flow of electric current, measured in units called ohms. This is precisely the side the students in the earlier scenario were trying to cross. It is the path from viewing a lightbulb as a place that consumes electric charge to viewing it as a place that blocks the flow (DOI: 10.1080/0950069950170303).

There is a simple relationship among voltage, current, and resistance. Ohm's law is the relationship that voltage and current are proportional in objects like metal wires where the temperature is kept constant, meaning that dividing the voltage by a constant resistance yields the current (DOI: 10.1017/s0007087400015089). The name comes from Georg Ohm, who put forward this formula, and it originally refers to the formula connecting voltage, current, and resistance in metal conductors. Let us make up some numbers to make the calculation easy. If you attach a lightbulb with a resistance of 6 ohms to a 3V battery, dividing 3 by 6 yields a current of 0.5 amperes flowing. When the voltage is the same, if the resistance is twice as high, the current is halved.

Ohm's law does not hold for all components. Electrical engineering technology students in Quebec, Canada (aged 17–20) tended to view all circuits as linear and time-invariant, trying to replace even unfamiliar components with a single "equivalent resistance." They believed that voltage is always proportional to current, sometimes treating the two as nearly identical (DOI: 10.1080/0950069960180205). A close example is the lightbulb itself. The thin wire inside an incandescent bulb gets larger in resistance as it gets hotter, so in a turned-on bulb, voltage and current are not precisely proportional.

The lift illustration was not used in this section. While the lift shows the looping flow and height difference well, it is weak at capturing the degree of blocking flow. Because no single analogy supports every aspect of a simple circuit, proposals emerge to use multiple analogies and tools together (DOI: 10.1088/1361-6552/ac03fe).

Energy delivered in 1 second — electric power

Electric power is the amount of energy electricity transfers in 1 second, measured in the unit of watts. Here, "transfers" refers to the amount of energy moving from a battery or outlet to an appliance during 1 second. It does not mean that electric charges carry energy like luggage. The "1,500W" on a hair dryer is this reading.

Thinking about a ski lift shows where electric power comes from. The energy released by a single skier coming down is determined by the height difference, and the number of skiers coming down per second is determined by the current. Multiplying the energy released by one person by the number of people coming down per second gives the energy used on the slope for 1 second. In a circuit, this is written as: Electric power is the value obtained by multiplying voltage and current. Multiplying volts by amperes gives watts.

Now you can read the back of a charger. If it says "5V 2A", multiplying 5 by 2 gives a maximum of 10 watts. It works in reverse too. Plugging a 1,500-watt hair dryer into a 220V outlet divides 1,500 by 220, meaning about 6.8 amperes flow. For the made-up flashlight from the previous section, multiplying 3V by 0.5 amperes gives 1.5 watts. Electricity from an outlet constantly changes the direction it flows, making the math one step more complex, but for an appliance that generates heat like a heater, multiplying using the outlet's 220V is still correct. Most hair dryers are also appliances that generate heat. Appliances with spinning motors or electronic devices may draw more current than this calculation even at the same wattage.

Electric power is a concept that people still get wrong even after learning about circuits in university. In one survey, misconceptions about interpreting power consumed in a circuit appeared among university students both before and after instruction (DOI: 10.1080/03043799108939504).

Electric power also gets mixed up with resistance. When given voltage and current values and asked to predict resistance, many middle and high school students answered that resistance increases when current is large, and resistance also increases when voltage is large. The researchers noted that these answers brought to mind the concept of power rather than resistance, and the effects of systematically teaching the electricity unit and Ohm's law were limited, showing both positive and negative aspects (DOI: 10.1080/09500690110066520). Resistance is a property inherent to the appliance, and what increases when voltage and current both increase is the energy delivered in 1 second—in other words, electric power. If a large current flows at the same voltage, the appliance's resistance is actually small.

A "watt" is the amount for 1 second. Whether you use a hair dryer for 1 minute or an hour is not included in this number, and the numbers on your electricity bill count the amount multiplied by that exact time. That story is picked up by the very next step in this series.

Two Ways of Connecting — Series and Parallel

Let us return to the fictional flashlight from before. We have a 3V battery, a single 6-ohm light bulb, and a current of 0.5 amperes. If we add one more identical light bulb here, there are two ways to connect them.

Series is a connection where devices are linked in a single line, so that the current must pass through one before going to the next. If we connect two light bulbs in a line, the resistance becomes 12 ohms, which is 6 ohms plus 6 ohms, and the current decreases to 0.25 amperes, calculated by dividing 3 by 12. This 0.25 amperes is the same in both the first light bulb and the second light bulb. The 3V is split evenly between the two light bulbs at 1.5V each, and the electric power received by each light bulb decreases, making both of them dimmer.

Parallel is a connection where separate paths are made for each device to both ends of the battery or outlet, allowing each to receive the same voltage. If we connect two light bulbs side by side, both light bulbs fully receive 3.5V—meaning 3V each. A current of 0.5 amperes flows through each light bulb, making them as bright as when they ran alone, and a total of 1.0 amperes flows at the point where the two branches meet at the battery.

Counting from the battery side, the current changed from 0.5 to 0.25 when connected in series, and to 1.0 when connected in parallel. This calculation was done assuming the battery has a constant voltage, and even if you measure it in an actual circuit, the side that changes significantly is the current (though the battery voltage also drops slightly the more you draw). A battery keeps its voltage nearly constant, and the current varies depending on what is connected and how. If you view a battery as a constant current source, you cannot explain this difference. However, these numbers were made up just to show the calculation, and in actual light bulbs, the temperature and resistance of the thin filament change depending on the brightness, so the ratios do not come out exactly like this.

Parallel connection is not easy even for students majoring in electricity. Resistors connected in parallel were on the list of misconceptions that persisted even after class for university students (DOI: 10.1080/03043799108939504), and in a diagnostic test for a mandatory electrical course given to incoming first-year students at a New Zealand university, current and voltage—as well as the more basic connections of series and parallel—confused a considerable number of students (DOI: 10.1109/te.2011.2114663).

Outlets and lights in a house are connected in parallel. Therefore, no matter what you plug into any outlet, that device fully receives 220V, and even if you turn off the living room light, the refrigerator keeps running.

Two Appliances in One Power Strip

Let us use what we have learned so far in a single scenario. We plug both an electric kettle and an electric heating pad into a single power strip. Let us say the label reads 2,000 watts for the kettle and 200 watts for the heating pad. This number is made up for this article, and we assume both use power exactly as labeled.

The sockets of a power strip are in parallel with each other. Therefore, both the kettle and the heating pad each receive 220V. Because both are heat-generating appliances, the multiplication from the previous section fits well. If we divide power by voltage, about 9.1 amperes flows through the kettle and about 0.9 amperes through the heating pad. The two paths meet inside the power strip and share a single power strip cord that leads to the wall outlet. Through that cord flows about 10.0 amperes, which is the sum of the two currents. If we check, dividing the combined power of the two appliances, 2,200 watts, by 220 also gives 10.0 amperes.

If there is no malfunction, equal currents of the same magnitude flow in opposite directions at every moment through the two strands where current travels inside the power strip cord. As much as went to one side, it returns through the other. The kettle and the heating pad did not consume electric charge. They merely converted the energy received as 2,200 watts of total power into boiling water and a warm floor. The maximum current written on the back of the power strip is precisely the limit of this combined current. Whenever you plug another appliance into the power strip, the current of all plugged-in appliances is added to the power strip cord. If it is a heat-generating appliance, that current can be counted as watts ÷ 220, but if it is not a heat-generating appliance (such as an appliance with a rotating motor or electronic devices), more current than that calculation may flow. If the sum of the plugged-in appliance currents exceeds that label, it has exceeded the amount the power strip was built to handle. The numbers in this scenario are examples to show multiplication and addition, and this article does not judge what is safe to plug in together.

Why It Remains So Confusing For So Long

As summarized later in a book about a survey using the identical questions across five European countries in 1988, students' everyday thoughts were nearly identical across countries, the proportion of answers acceptable in physics was uniformly low, and no teaching method changed those thoughts easily (DOI: 10.4324/9780203985472-12, book summary). In a nationwide Taiwan survey asking about physics concepts overall (totaling over 13,000 students from elementary to high school), understanding of current in circuits did not improve as age increased (DOI: 10.1080/09500690601073210). The same misconceptions repeat across institutions and countries even among university engineering freshmen (DOI: 10.1109/te.2011.2114663). These misconceptions ignore countries and grade levels, repeating even in students who have just entered engineering school.

Analogies have long been studied as tools to clear up these misconceptions. In a lesson dividing 32 fourth-grade elementary students into four groups and varying how analogies were used, there are reports that analogies helped students overcome misconceptions (DOI: 10.1002/tea.20062, small-scale experiment), and there is also a single study showing that lessons using water analogies alongside circuit models were better than traditional lessons (DOI: 10.1016/j.sbspro.2015.04.530). At the same time, whether an analogy works depends on how it is presented and how directly students compare the analogy and the circuit (DOI: 10.12973/ejmste/75175). The lift in this article is under the same conditions. It fits well with a one-lap flowing motion and height differences. It does not fit the blocking degree, the way everything starts moving at once, the point that energy does not travel with charges, and the point that the lift decides how many people board per minute. This last mismatch has the same shape as the misconception "batteries produce a constant current" that this article tries to break, making it the spot to be most careful about when picturing the lift.

The picture of electrons marching in a line inside a wire is also one useful picture among many. There is a survey showing that a significant number of experts picture current as an action spread across the entire space around the wire rather than as particles, and which picture is better for learners remains an open question (DOI: 10.1080/0950069960180203). The fact seen earlier that "energy does not wait for charges to arrive" looks more natural in this spread-action picture. Whichever picture you use, the math is the same. Charges do not decrease and make one complete lap, and what turns into light and heat at the bulb is the energy the battery gave to the circuit.

Where to look next

• The next first step in this series covers the gap between watts and the numbers on your electricity bill—in other words, the difference between power and energy. 「How long was it used」, which was postponed at the end of this article, continues from there.
• 「How much electricity does AI use — the real reason why numbers differ across sources」 is a story about when the watts in this article grow to the gigawatt scale. The multiplication from this article is used there as is.
• 「Air is no longer enough — where does the heat generated by computation go」 covers, on a building scale, the scenes we saw with the kettle and electric blanket: where energy that moved into a device leaves as heat.

Source Papers

• "A study of science-in-the-making as students generate an analogy for electricity" (1995) — DOI: 10.1080/0950069950170303 — Students' view of resistance as a charge consumer rather than a hindrance to flow; the consumption concept works well for everyday explanations. The results of a decisive experiment designed by students (conservation of electric current) are not well received; a two-part model separating the charge and what moves it using a carrier-load analogy serves as a transitional framework for students moving from the consumption model to the obstruction model. No mention of energy in the abstract.
• "Pupils' understanding of simple electrical circuits. Some implications for instruction" (1988) — DOI: 10.1088/0031-9120/23/2/004 — Difficulties children face with the concepts of circuits, current, and electrical energy, alongside instructional methods.
• "Images of electricity: how do novices and experts model electric current?" (1996) — DOI: 10.1080/0950069960180203 — The universally accepted model is electrons moving in response to potential difference, yet many experts use the concept of fields rather than particles. Implications for classroom application.
• "Ski lifts, bowling balls, pipe system or waterfall? Lower secondary students' understanding of analogies for electric circuits." (2020) — DOI: 10.5617/nordina.6882 — Group interviews examining how 12 middle school students understand four analogies found in Norwegian textbooks (not an effect measurement). All four analogies allow for the inference of continuity and electric current, voltage is difficult, and analogies connecting voltage to energy transfer via height differences are constructive even though they require the concept of fields. Weaknesses in the presentation method create major problems and are common in textbooks.
• "Putting Potential at the Core of Teaching Electric Circuits" (2022) — DOI: 10.1119/5.0046298 — Many students mistake voltage for a property of current, viewing the battery as a spring of constant current rather than constant voltage. Curricula and simulations placing potential difference at the core.
• "Students' understanding of direct current resistive electrical circuits" (2003) — DOI: 10.1119/1.1614813 — A 29-item diagnostic tool. Various misconceptions persist even after instruction; "the battery as a spring of constant current" is most frequently used in interviews, focusing on current and attributing the properties of current to voltage and resistance.
• "A Study of University Students' Understanding of Simple Electric Circuits Part 2: Batteries, Ohm's Law, Power Dissipated, Resistors in Parallel" (1991) — DOI: 10.1080/03043799108939504 — Misunderstandings present both before and after university instruction: the battery as a spring of constant current, misinterpretation of the functional relationship in Ohm's law, dissipated power, and parallel resistors.
• "The Ohm-Seebeck Dispute, Hermann von Helmholtz, and the Origins of Physiological Acoustics" (1977) — DOI: 10.1017/s0007087400015089 — "Ohm's law" traditionally refers to Ohm's formula connecting voltage, current, and resistance in metallic conductors (the main body of the paper deals with another Ohm's law in auditory physiology).
• "The persistence of students' unfounded beliefs about electrical circuits: the case of Ohm's law" (1996) — DOI: 10.1080/0950069960180205 — Electrical engineering technology students in Quebec, Canada (aged 17–20). They view all circuits as linear and static, replace all components with equivalent resistance, and treat voltage and current as similar due to the belief that voltage is always proportional to current.
• "High school students' understanding of resistance in simple series electric circuits" (2002) — DOI: 10.1080/09500690110066520 — Grades 8–12. Many judge resistance as an increasing function of both current and potential difference (closer to the concept of power). The effects of systematic instruction are limited and bidirectional.
• "An analogical simulation for teaching electric circuits: a rationale for use in lower secondary school" (2021) — DOI: 10.1088/1361-6552/ac03fe — No single analogy or model ideally supports all key aspects of simple direct current circuits. Development of a simulation used alongside bicycle chain and air pressure analogies.
• "An Investigation Into the Understanding and Skills of First-Year Electrical Engineering Students" (2011) — DOI: 10.1109/te.2011.2114663 — Diagnostic test for first-year students at the University of Auckland. Misconceptions are robust and widespread across institutions and countries, with a significant number of students confusing not only current and voltage but also series and parallel connections.
• "Teaching Electricity by Help of a Water Analogy (How to Cope with the Need for Conceptual Change)" (2005) — DOI: 10.4324/9780203985472-12 — A summary from a book chapter of a 1988 survey across 5 European countries (Shipstone et al., secondary citation) showing that students' everyday ideas were nearly identical across countries, the proportion of acceptable answers was equally low, and no teaching method changed them easily.
• "Investigating Primary and Secondary Students' Learning of Physics Concepts in Taiwan" (2007) — DOI: 10.1080/09500690601073210 — A nationwide sample of over 13,000 students using two-tier diagnostic questions. Understanding of certain concepts (such as current within a circuit) does not improve with age.
• "Promoting fourth graders' conceptual change of their understanding of electric current via multiple analogies" (2005) — DOI: 10.1002/tea.20062 — 32 fourth-grade students randomly divided into 4 groups. The use of analogies aids in deep understanding and overcoming misconceptions, with the source of difficulty being ontological presuppositions about the concept.
• "The Importance of Inquiry-Based Learning on Electric Circuit Models for Conceptual Understanding" (2015) — DOI: 10.1016/j.sbspro.2015.04.530 — The experimental group using mental models and water circuit analogies performed significantly better in understanding electrical concepts than the traditional instruction control group.
• "Analogies as Tools for Meaning Making in Elementary Science Education: How Do They Work in Classroom Settings?" (2011) — DOI: 10.12973/ejmste/75175 — The effectiveness of analogies is determined by the presentation method, context, and how much students participate in mapping correspondences. They serve as resources for understanding when their strengths and limitations are not ignored.