Charge vs Current: What Is the Difference?

A quantity and its rate

Charge is a property that objects have and that you can count. Essential knowledge 10.1.A.1 calls it a fundamental property of all matter, described as positive or negative (10.1.A.1.i), and 10.1.A.1.ii names the elementary charge $e$ as the smallest indivisible amount. It is measured in coulombs, and a system has a definite amount of it at a definite moment.

Current is what charge does per second. The AP Physics 2 sheet defines it as a rate:

and 11.1.A.1 says in words that current is the rate at which charge passes through a cross-sectional area of a wire. One ampere is one coulomb per second. A current is not an amount of anything; it is an amount divided by a time.

That is the whole distinction, and the grammar gives it away. You can ask how much charge, and you can ask how much current, but the second question is really asking how fast. A wire with $2 \ \mathrm{A}$ in it does not contain two of anything. It has two coulombs crossing each cross-section every second, and it will keep doing so for as long as the circuit is closed.

The practical consequence runs through every circuit question you will meet. Charge can accumulate somewhere. Current cannot. Charge sits on a capacitor plate, on a rubbed rod, on an isolated conductor. Nothing anywhere stores a current, because a rate is not the sort of thing that can be kept in a box.

Side by side

The row that catches people out is the last one. Essential knowledge 11.1.A.1.ii says that if the current is zero in a section of wire, the net motion of charge carriers in the wire is also zero, although individual charge carriers will not have zero speed. Zero current is a statement about a net, not about stillness. The wire is full of charge either way, which is why zero current does not mean zero charge and full current does not mean more charge is present.

The case that separates them: charging a capacitor

One circuit makes the two quantities behave in visibly opposite ways at the same instant. Close a switch on a battery, a resistor and an uncharged capacitor in series, and watch the two numbers.

Read the two columns against each other. The current starts high and dies; the charge starts at zero and climbs. They are not two measurements of the same thing at different scales. One is the derivative of the other, which is why the current is largest exactly where the charge is rising fastest and zero exactly where the charge has stopped changing.

The CED supplies both ends of the table. 11.8.B.2.i says that immediately after being placed in a circuit an uncharged capacitor acts like a wire and charge can easily flow to or from the plates, which is why the current is at its maximum with nothing yet stored. 11.8.B.1.ii says that for a charging capacitor the time constant is the time required for the capacitor's charge to increase from zero to approximately 63 percent of its final asymptotic value, and 11.8.B.1.iii gives the discharging counterpart, a fall to approximately 37 percent of the initial value.

One detail is worth pausing on, because it looks like a contradiction. The current on both sides of the capacitor is the same at every instant, even while charge accumulates on the plates. Nothing crosses the gap. As charge arrives on one plate, an equal amount leaves the other, so the branch behaves like an unbroken series path for current while still storing charge. Charge accumulates on the plates; it does not accumulate in the wire.

Direction without being a vector

Charge is a signed scalar: a $-3 \ \mathrm{nC}$ charge is a number with a minus sign, not an arrow. Current is stranger, and the CED words it carefully.

Essential knowledge 11.1.A.2 in AP Physics 2 reads that although current is not a vector quantity, it does have a direction, and that direction is associated with what the motion of positive charge would be but not with any coordinate system in space. AP Physics C: Electricity and Magnetism words the same idea differently at 11.1.A.4, calling current a scalar quantity that has a direction, and adding that because its direction is relative to the current carrier and not to space, current does not obey the laws of vector addition and has no vector components. Either phrasing gives you the same rule: never resolve a current into $x$ and $y$ components.

The direction that current does have is a convention, chosen once and applied everywhere:

• 11.1.A.2.i The direction of conventional current is chosen to be the direction in which positive charge would move.
• 11.1.A.2.ii In common circuits, current is actually due to the movement of electrons, which are negative charge carriers.

So in a copper wire the electrons drift one way and the labelled current points the other, and both descriptions are correct at once. Negative charge moving left carries as much charge rightward past a cross-section as positive charge moving right would, so every measurable prediction agrees.

The exam settles it for you, twice. A boundary statement under Topic 11.2 says that unless otherwise specified, all circuit schematic diagrams will be drawn using conventional current. The exam conventions box on the AP Physics 2 equation sheet says the same in four words: current is conventional current. Use the conventional direction for loop-rule signs, for right-hand rules and for every arrow you draw, and mention electron drift only if a question asks about the carriers.

Counting the carriers

Because charge is quantized, a coulomb is a count. 10.1.A.1.ii calls $e$ the smallest indivisible amount of charge, and the sheet prints $e = 1.60 \times 10^{-19} \ \mathrm{C}$ in the constants box. 10.1.A.1.iii adds the assignments: an electron carries $-e$, a proton $+e$, and a neutron none.

Two numbers follow from that and both are worth carrying into the exam:

• One coulomb is an enormous amount of charge. It is about $6.25 \times 10^{18}$ elementary charges. This is why exam charges arrive in microcoulombs and nanocoulombs while exam currents arrive in whole amperes: a modest current moves a lot of coulombs, because it has a whole second to do it in.
• One ampere is a modest rate. A $1 \ \mathrm{A}$ current delivers exactly $1 \ \mathrm{C}$ per second, so a torch left on for a minute pushes $60 \ \mathrm{C}$ past every cross-section of its filament. Nothing in the torch had $60 \ \mathrm{C}$ stored in it.

That second point is the misconception the CED names directly. A battery does not store charge and current is not used up in a circuit. 11.1.A.1.i says electric charge moves in a circuit in response to an electric potential difference, sometimes referred to as electromotive force or emf. The charge was already in the conductor; the source supplies the potential difference that sets it moving.

Charge conservation is what makes all of this bookkeeping work. 10.2.A.2 states that any change to a system's net charge is due to a transfer of charge between the system and its surroundings, 10.2.A.2.i notes that charging typically involves the transfer of electrons to and from the system, and 10.2.A.2.ii says the net charge of a system will be constant unless there is a transfer of charge to or from it. Nothing on this page creates a coulomb.

When it costs a mark

"The current is used up by the bulb." The junction rule is a consequence of the conservation of electric charge (11.7.A.1), and charge has nowhere to go. The current leaving a bulb equals the current entering it. What the bulb consumes is the energy each coulomb carries, which is why the potential drops across it. Written on a free-response question, this error usually surfaces as a claim that the first of two identical series bulbs is brighter.

"The battery is running out of charge." A battery maintains a potential difference; it is not a charge reservoir that empties. Say that its emf falls, or that its stored chemical energy is depleted.

Substituting milliamps as amps. $250 \ \mathrm{mA}$ is $0.250 \ \mathrm{A}$, and $250 \ \mu\mathrm{C}$ is $2.50 \times 10^{-4} \ \mathrm{C}$. A factor of a thousand in either place still leaves an answer that looks like a plausible number of ohms or volts, which is what lets the slip survive a sanity check.

Forgetting to convert the time. $I = \Delta q/\Delta t$ takes seconds. Minutes and hours in the problem statement are there to be converted, and a charge that is 60 times too small is the usual result.

Resolving a current into components. Current has a direction and is still not a vector. Two wires meeting at $60^\circ$ do not combine their currents by the parallelogram rule; they combine by the junction rule, as plain sums.

Treating charge on capacitors in series as splitting. It does not. 11.8.A.2 states that as a result of conservation of charge, each of the capacitors in series must have the same magnitude of charge on each plate. Charge is the shared quantity there, and the potential difference is what divides.

When they track each other, and why that hides the difference

For a large slice of a circuits unit the two quantities are interchangeable in practice, which is exactly why the distinction stays invisible until a capacitor appears.

In a steady direct-current circuit, current is constant, so charge is just current times time. With $I$ fixed, $\Delta q = I \Delta t$ is a one-step conversion, and nothing ever forces you to notice which quantity a question is really about. Every steady-state resistor problem you solve is in this regime.

In a series loop, both are shared in a way that looks identical. The current is the same in every element (11.5.A.1.i), and the same charge passes through every element in any given interval. Two statements, one picture, and no reason yet to keep them apart.

They also agree numerically for one second. A current of $3 \ \mathrm{A}$ moves $3 \ \mathrm{C}$ in a second, and worked examples that happen to use $\Delta t = 1 \ \mathrm{s}$ make the two look like the same number under two names. It is a coincidence of the chosen interval.

The distinction turns on the moment something in the circuit can store charge, or the moment the current stops being steady. A charging capacitor breaks both conditions at once, which is why it is the standard test of whether a student has the two ideas apart. So does any question that asks how much charge flowed rather than how much current there was: the second is read off a meter, the first requires an interval, and if the current varied it requires an area under a graph rather than a product.

Where this sits on the AP exam

Charge is introduced in Unit 10, Electric Force, Field, and Potential, which carries 15 to 18 percent of the multiple-choice section over a suggested 14 to 21 class periods. Topic 10.1 establishes the property and its quantization, and Topic 10.2 is the conservation law and the charging processes.

Current opens Unit 11, Electric Circuits, also 15 to 18 percent of the multiple-choice section, over a suggested 12 to 20 class periods. Topic 11.1, Electric Current, holds the definition, the emf sentence, the zero-current clarification and the whole conventional-current convention. Its suggested skills are 1.A, 2.C, 3.B and 3.C.

AP Physics C: Electricity and Magnetism takes the same pair further. Its Topic 11.1 writes the definition as a derivative, $I = dq/dt$, adds current density as a genuine vector quantity (11.1.A.2.ii) with $\vec J = nq\vec v_d$, and relates the two by $I = \int \vec J \cdot d\vec A$. The scalar-with-a-direction point survives the upgrade: current density is the vector, current is not.

For the other pairing that trips people in this unit, the difference between something measured through an element and something measured across it, see voltage vs current. For the two conservation rules that govern each, see Kirchhoff's loop vs junction rule, and for what the source actually supplies, emf vs voltage.