Charge and current

YOU WILL BE ABLE TO

Define electric charge and state its SI unit, the coulomb.
Define current as the rate of flow of charge, i = dq/dt.
Compute current from a charge function, and total charge from a current function.
Distinguish conventional current direction from electron flow.

Everything in this course moves one thing around: electric charge. Charge is a fundamental property of matter, like mass. It comes in two signs — positive and negative — and in nature it arrives in fixed packets: every electron carries exactly −1.602 × 10⁻¹⁹ coulombs, every proton exactly +1.602 × 10⁻¹⁹ coulombs. The coulomb (C) is the SI unit of charge, and it is enormous: one coulomb is the combined charge of about 6.24 × 10¹⁸ electrons.

e = 1.602 \times 10^{-19}\ \text{C}

elementary charge

Charge that stays put is the subject of electrostatics. Circuits are about charge in motion. Current is defined as the rate at which charge crosses a boundary — imagine slicing a wire and counting the coulombs that pass through the cut each second.

i = \frac{dq}{dt}

current, amperes

One ampere (A) is one coulomb per second. Since charge is a function of time, current is its derivative — this is why Calculus I is the prerequisite. Going the other way, the total charge delivered between two times is the integral of the current.

q = \int i \, dt

charge from current

A current whose direction never changes is direct current (DC) — what a battery or a USB port supplies, and what every board you design in PCB Studio runs on. A current that reverses periodically is alternating current (AC) — Ontario's grid alternates 60 times per second (60 Hz). This course works in DC until CA-6, where AC gets the full treatment.

WORKED EXAMPLE

Current from a charge function

The charge passing a point in a wire is q(t) = 3t² − 2t mC, with t in seconds.
Differentiate: i(t) = dq/dt = (6t − 2) mA.
Evaluate at t = 2 s: i(2) = 6(2) − 2 = 10 mA.

i(2) = 10 mA

WORKED EXAMPLE

Charge from electron count

2.0 × 10¹⁹ electrons cross a boundary in 4.0 s, all in the same direction.
Total charge magnitude: q = (2.0 × 10¹⁹)(1.602 × 10⁻¹⁹ C) = 3.204 C.
Current magnitude: i = q/t = 3.204 C / 4.0 s ≈ 0.80 A.
The conventional current direction is opposite to the electron motion.

i ≈ 0.80 A, directed opposite to the electron flow

PRACTICE

A charge of 0.5 C passes through an LED every 25 s, at a steady rate. What is the current in milliamperes?

The charge entering a component is q(t) = 5t³ µC (t in seconds). Find the current at t = 1 s.

A steady current of 2 A flows for one minute. How much charge passes, and how many electrons is that?

A current i(t) = 6t mA flows into a capacitor from t = 0 to t = 2 s. What total charge is delivered?