20.1 Current

Electric Current

Electric current describes the flow of electric charge through a conductor. It's the foundation for understanding circuits, power systems, and basically everything electrical you'll encounter in this course.

Definition of Electric Current

Current is the rate at which electric charge flows past a point in a conductor. The formula is straightforward:

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

where $\Delta Q$ is the amount of charge (in coulombs) and $\Delta t$ is the time interval (in seconds).

• The symbol for current is $I$, and the unit is the ampere (A), which equals one coulomb per second (C/s).
• The charge carriers in metal conductors are free electrons, though in other contexts (like electrolyte solutions) they can be positive or negative ions.
• The direction charge carriers actually move depends on their sign. In a wire, electrons flow from the negative terminal toward the positive terminal of a battery.

Conventional Current

Before anyone knew electrons existed, physicists defined current as flowing from positive to negative. That convention stuck, and it's what you'll use in virtually all circuit analysis.

• Conventional current points in the direction positive charges would move: from the positive terminal of a battery, through the circuit, to the negative terminal.
• This is opposite to the actual direction electrons travel in a wire.
• Don't let this confuse you in problem-solving. The math works out the same either way. Just be consistent and use conventional current unless a problem specifically asks about electron flow.

Drift Velocity

Even though electrical signals travel through a circuit almost instantly, the individual electrons move surprisingly slowly. Their net motion under an applied electric field is called drift velocity ($v_d$).

• Electrons are constantly bouncing around randomly at thermal speeds on the order of $10^6$ m/s. Drift velocity is the small net displacement on top of all that random motion.
• Typical drift velocities in copper wire are on the order of fractions of a millimeter per second.

Current can be expressed in terms of drift velocity:

$I = nqAv_d$

where:

• $n$ = number of charge carriers per unit volume (carrier density)
• $q$ = charge of each carrier (for electrons, $q = 1.6 \times 10^{-19}$ C)
• $A$ = cross-sectional area of the conductor
• $v_d$ = drift velocity

Rearranging to solve for drift velocity:

$v_d = \frac{I}{nqA}$

Notice that for a given current, a thicker wire (larger $A$) means a lower drift velocity. The same total charge flow is spread across more area, so each carrier doesn't need to move as fast.

Electrical Properties and Ohm's Law

A few key terms tie current to the rest of circuit analysis:

• Voltage ($V$) is the electric potential difference between two points. It's what "pushes" charge through a circuit.
• Resistance ($R$) is a measure of how much a material opposes current flow. Higher resistance means less current for the same voltage.
• Ohm's Law connects all three: $V = IR$. If you know any two of these quantities, you can find the third.

Two categories of materials come up constantly:

• Conductors (like copper and aluminum) allow charge to flow easily because they have many free charge carriers.
• Insulators (like rubber and glass) have very few free carriers and strongly resist current flow.

For current to flow continuously, you need a closed circuit, meaning an unbroken conducting path from one terminal of the voltage source back to the other.