5.4.1. Electric Current

Table of Contents

Flow of Charge

Electric current describes how electric charge moves through a material or region of space. When charges drift in an organized way, we say there is a current. In most everyday circuits, the moving charges are electrons inside metal wires. In other situations, such as in liquids, gases, or semiconductors, other charged particles can also contribute.

The symbol for electric current is usually $I$. Its SI unit is the ampere, abbreviated $\text{A}$. One ampere means that one coulomb of charge passes through a cross section each second.

The basic definition of electric current is
$$
I = \frac{\Delta Q}{\Delta t}
$$
where $\Delta Q$ is the amount of charge passing through a surface in time $\Delta t$.

If the flow changes from moment to moment, we use the instantaneous form,

$$
I = \frac{dQ}{dt}
$$

This means current is the rate at which charge passes a chosen cross section.

What Current Means Physically

Imagine a wire cut by an imaginary surface. If charges move through that surface, then there is a current. The current tells us how fast charge is crossing, not how fast an individual particle moves. A large current can result from many charges moving slowly, or fewer charges moving quickly.

In a metal wire, electrons are already present everywhere in the conductor. When an electric influence is applied, these electrons begin to drift, producing current throughout the wire. The current is therefore a collective effect of many moving charges.

Rendering scientific sketch…

Charge passing through a wire cross section

Direction of Current

By convention, the direction of current is defined as the direction positive charge would move. This is called conventional current. In metallic wires, the actual moving particles are usually electrons, which are negatively charged, so they move in the opposite direction to the conventional current.

This can seem strange at first, but it is a standard convention used throughout physics and electrical engineering.

Conventional current points in the direction of positive charge flow, even when the actual mobile charges are electrons moving the other way.

Current as a Scalar Quantity

Current is treated as a scalar quantity in simple circuit analysis. We usually assign a positive or negative sign depending on the chosen direction through a branch of a circuit. Even though charges move through space, the current value itself tells us the amount of charge flow per unit time through a surface.

For example, if $5\,\text{C}$ of charge pass through a wire in $2\,\text{s}$, then

$$
I = \frac{\Delta Q}{\Delta t} = \frac{5}{2} = 2.5\,\text{A}
$$

Unit of Current

Since charge is measured in coulombs and time in seconds, the unit of current is

$$
1\,\text{A} = 1\,\frac{\text{C}}{\text{s}}
$$

This unit is large enough to be useful in many practical circuits. Small electronic devices may involve milliamperes, $\text{mA}$, or microamperes, $\mu\text{A}$.

Current unit	Value in amperes
$1\,\text{mA}$	$10^{-3}\,\text{A}$
$1\,\mu\text{A}$	$10^{-6}\,\text{A}$
$1\,\text{kA}$	$10^3\,\text{A}$

Steady and Changing Current

If the same amount of charge passes each second, the current is steady, or constant. In that case, $I$ does not change with time. If the charge flow rate changes, then the current is time dependent.

For a steady current,

$$
Q = It
$$

This relation is useful only when $I$ is constant over the time interval considered.

For constant current,
$$
Q = It
$$
Do not use this directly if the current changes with time. In that case, use
$$
I = \frac{dQ}{dt}
$$
instead.

Microscopic Picture

Current comes from the motion of many charged particles. Suppose each particle carries charge $q$, and $N$ particles pass through a cross section in time $\Delta t$. Then the total charge passing is

$$
\Delta Q = Nq
$$

so the current is

$$
I = \frac{Nq}{\Delta t}
$$

This expression helps connect current to the number of moving charge carriers. It is especially useful for understanding that current is not a mysterious substance, but simply moving charge.

Sign of Current and Interpretation

If charge flows in the chosen positive direction, the current is positive. If it flows in the opposite direction, the current is negative. A negative current does not mean something is wrong. It simply means the actual flow is opposite to the direction you assumed.

This idea is very important when analyzing circuits and checking answers.

Simple Examples

Suppose $12\,\text{C}$ of charge pass through a wire in $3\,\text{s}$. Then

$$
I = \frac{12\,\text{C}}{3\,\text{s}} = 4\,\text{A}
$$

Suppose instead that the current in a device is $0.50\,\text{A}$ for $10\,\text{s}$. The total charge that passes is

$$
Q = It = 0.50 \times 10 = 5.0\,\text{C}
$$

If $2.0 \times 10^{19}$ electrons pass through a cross section in $4.0\,\text{s}$, then using the electron charge magnitude $e = 1.60 \times 10^{-19}\,\text{C}$, the total charge magnitude is

$$
Q = Ne = \left(2.0 \times 10^{19}\right)\left(1.60 \times 10^{-19}\right) = 3.2\,\text{C}
$$

so the current magnitude is

$$
I = \frac{Q}{t} = \frac{3.2}{4.0} = 0.80\,\text{A}
$$

Common Misunderstandings

A common misunderstanding is to think that current is used up as it moves through a wire. Current is a rate of flow of charge. In a simple series path, the same amount of charge per second passes each point.

Another misunderstanding is to confuse current with voltage or resistance. These are different ideas. Here, the focus is only on current itself, the rate of charge flow.

Current is not the same as charge. Charge is the amount, measured in coulombs. Current is the rate of flow of charge, measured in coulombs per second.

Summary Relation

Electric current is one of the central quantities in electricity. It tells us how quickly charge moves through a cross section. It can be written in average form or instantaneous form, and its direction follows the convention of positive charge flow.

Key formulas for electric current:
$$
I = \frac{\Delta Q}{\Delta t}
$$
$$
I = \frac{dQ}{dt}
$$
For constant current only,
$$
Q = It
$$

Understanding current clearly is the foundation for later topics such as current density, drift velocity, resistance, and circuit behavior.

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