Defining electric current
Imagine a small area held normal to the direction in which charges flow. Both positive and negative charges may cross it, moving forward and backward. Over a time interval $t$, let $q_+$ be the net forward flow of positive charge and $q_-$ the net forward flow of negative charge across the area. The net charge crossing in the forward direction is $q = q_+ - q_-$. For a steady current this is proportional to $t$, and the quotient defines the current:
$$ I = \frac{q}{t} $$If $I$ comes out negative, the net flow is simply in the backward direction.
The figure below isolates the essential picture: a cross-section of area $A$ with charge crossing it. Current is a count of charge per second through that section — it says nothing about the area on its own, only about the rate of throughput.
Steady vs instantaneous current
Currents are not always steady. Lightning, for instance, is a violently unsteady flow of charge, whereas a torch or a cell-driven clock carries a steady current like water flowing smoothly in a river. For the general case we let $\Delta Q$ be the net charge crossing a section during the interval $\Delta t$ (between times $t$ and $t + \Delta t$). The current at time $t$ is the limit of this ratio as the interval shrinks to zero:
$$ I(t) = \lim_{\Delta t \to 0} \frac{\Delta Q}{\Delta t} = \frac{dq}{dt} $$
When the flow is steady, $I = q/t$ and $I = dq/dt$ give the same number. When the charge varies with time — say $Q = at - bt^2$ — only the derivative is correct, and the instantaneous current itself changes from instant to instant. NEET exploits this exact case (see the 2016 PYQ below).
| Form | Expression | When it applies |
|---|---|---|
| Steady / average current | I = q/t | Charge flows uniformly; same q every equal interval |
| Instantaneous current | I = dq/dt | General case; charge may vary with time |
The ampere and scale of currents
In SI units the unit of current is the ampere (A). The ampere is itself defined through the magnetic effects of currents, which the next chapter develops; in terms of charge flow, one ampere corresponds to one coulomb of charge crossing a section each second:
$$ 1\ \text{ampere} = \frac{1\ \text{coulomb}}{1\ \text{second}} $$
Smaller subdivisions are the milliampere ($1\ \text{mA} = 10^{-3}\ \text{A}$) and the microampere ($1\ \mu\text{A} = 10^{-6}\ \text{A}$). An ampere is roughly the order of magnitude of currents in domestic appliances; an average lightning flash carries tens of thousands of amperes, while the currents in our nerves are only microamperes.
| Quantity | Symbol | SI unit | Defining relation |
|---|---|---|---|
| Charge | q | coulomb (C) | — |
| Time | t | second (s) | — |
| Electric current | I | ampere (A) | I = dq/dt |
| Current density | j | A/m² | j = I/A |
Conventional current direction
When a potential difference is applied across a conductor, an electric field is set up inside it and the free electrons move opposite to the field. By convention, the direction of current is taken as the direction in which a positive charge would move. Since the carriers in a metal are negative electrons drifting toward the positive terminal, the conventional current points the opposite way — a negative charge moving one way is equivalent to a positive charge moving the other.
Electrons go one way, current is drawn the other
A frequent slip is to draw the current arrow along the electron drift. In the external circuit the conventional current runs from the positive terminal to the negative terminal, while electrons drift from negative to positive — exactly opposite.
Conventional current = direction of positive-charge motion = opposite to electron drift.
Current is a scalar
Although we draw an arrow for current along a wire, current is a scalar quantity. Currents do not obey the law of vector addition — at a junction they combine by ordinary algebraic addition, which is why Kirchhoff's junction rule simply adds and subtracts numbers. The scalar nature follows from the definition itself: the current through a section is the scalar product of the current density vector $\mathbf{j}$ and the area vector $\Delta\mathbf{S}$,
$$ I = \mathbf{j} \cdot \Delta\mathbf{S} $$A scalar product of two vectors is a scalar, so $I$ is a scalar.
An arrow does not make it a vector
The direction marked on a circuit wire is a flow indicator, not a vector component. Resolving currents into x and y parts, or adding two currents at a junction by the parallelogram law, is wrong. Current density $\mathbf{j}$ is the vector here, not $I$.
Current $I$ — scalar (algebraic addition). Current density $\mathbf{j}$ — vector.
Once a steady field drives this current, the linear relation $V = IR$ follows. Continue with Ohm's Law.
Current in conductors
A charge experiences a force in an electric field, and if free to move it contributes to a current. In atoms and molecules the electrons and nuclei are bound and cannot move freely; but in bulk metals some electrons are practically free to move within the material. These materials — conductors — develop currents when a field is applied. In a solid conductor the current is carried entirely by the negatively charged electrons against a background of fixed positive ions.
With no field: no net current
With no field present, the free electrons still move because of thermal motion, colliding with the fixed ions. After each collision an electron emerges with the same speed but in a completely random direction. With no preferred direction, the number of electrons moving any way equals the number moving the opposite way, so there is no net electric current.
Why a battery is needed for a steady current
Place charge $+Q$ on one end of a metallic cylinder and $-Q$ on the other. The field they create, directed from $+Q$ toward $-Q$, accelerates the electrons so they move to neutralise the charges. While they move, they constitute a current — but only for a very short while, after which the charges are cancelled and the current stops.
To keep the current flowing, a mechanism must continuously supply fresh charge to the ends, making up for whatever the electrons neutralise. A cell or battery does exactly this, maintaining a steady electric field throughout the body of the conductor and so a continuous current rather than a momentary one. The free electrons then acquire a small average velocity in the field direction superimposed on their random thermal motion — the drift discussed in the next subtopic.
Current density J = I/A
The current alone does not say how the flow is distributed across the section. The current per unit area, taken normal to the flow, is the current density $j = I/A$, with SI unit ampere per square metre (A/m²). Unlike current, current density is a vector, directed along the local electric field. If $E$ is the magnitude of a uniform field in a conductor of length $l$, the potential difference across it is $V = El$, and the magnitudes satisfy $E = j\rho$, which in vector form becomes
$$ \mathbf{j} = \sigma \mathbf{E} $$where $\sigma = 1/\rho$ is the conductivity — the microscopic statement of Ohm's law.
In terms of carriers, the same current density can be written $j = n e v_d$, linking it to the number density $n$ of electrons and their drift velocity $v_d$ — the bridge to resistivity and drift, taken up next.
Electric current & current in conductors
- Steady current: $I = q/t$; general instantaneous current: $I = dq/dt$.
- SI unit is the ampere; $1\ \text{A} = 1\ \text{C/s}$, defined via magnetic effects.
- Conventional current is the direction of positive-charge motion — opposite to electron drift.
- Current is a scalar (algebraic addition at junctions); $I = \mathbf{j}\cdot\Delta\mathbf{S}$.
- No field gives random thermal motion and zero net current; a cell maintains a steady field and a continuous current.
- Current density $j = I/A$ (A/m²) is a vector, $\mathbf{j} = \sigma\mathbf{E} = n e v_d$.