Block 01 — Physical Quantities, Units, Charge & Current

Learning objectives

• Convert and compare values using SI base units and prefixes from atto (a) to exa (E).
• Explain electric charge as multiples of the elementary charge and compute total charge from particle count.
• Define electric current as time rate of charge flow, relate conventional current to electron flow, and use correct reference arrows.
• Apply unit analysis to check formulas and results.

90-minute plan

1. Warm-up (10 min): SI prefixes speed-drill; unit sanity checks (▶ quick quiz).
2. Core concepts & derivations (60 min): SI system & prefixes → charge and the elementary charge → current as charge per time; conventional vs electron flow; reference arrows in circuits.
3. Practice (15 min): ✎ Conversions & short calculations (prefixes; Q–I–t triangle); direction questions with mixed charge carriers.
4. Wrap-up (5 min): Recap key formulas and common mistakes; preview: voltage & potential (next block).

Conceptual overview

What’s the game? In circuits we count how much charge moves (Q, coulombs) and how fast it moves (I, amperes). SI units and prefixes let us express tiny sensor signals and huge lightning currents on one common scale. Current direction is a convention (positive-charge movement) and must not be confused with the motion of electrons, which are negatively charged and usually move the other way.

Core definitions & formulas

SI base & derived (used today)

• Charge $Q$ in coulomb (C); time $t$ in second (s); current $I$ in ampere (A).

Prefixes (selected)

• $1~\mathrm{mA}=10^{-3}~\mathrm{A}$, $1~\mathrm{\mu A}=10^{-6}~\mathrm{A}$, $1~\mathrm{nA}=10^{-9}~\mathrm{A}$, $1~\mathrm{kA}=10^{3}~\mathrm{A}$.
• Tip: move powers of ten, not the decimal point “by feeling”.

Charge (discrete and continuous)

• $Q = n \cdot e$ with $e=1.602\times 10^{-19}~\mathrm{C}$ (elementary charge).
• Typical values: single ion $e$; small capacitor on a sensor: $Q \sim \mathrm{pC}$–$\mathrm{nC}$.

Current (definition)

• $I = \dfrac{\mathrm{d}Q}{\mathrm{d}t}$ (or $I \approx \Delta Q / \Delta t$ for averages).
• Unit check: $[I]=\mathrm{C/s}=\mathrm{A}$.
• Typical values: biopotentials $\sim \mathrm{\mu A}$; GPIO pin $\sim \mathrm{mA}$; motor windings $\sim \mathrm{A}$.

Conventional vs electron flow

• Conventional current points in the direction positive charges would move.
• Electron flow is opposite in direction to conventional current in metals.
• Reference arrows for later circuit work: choose arbitrarily before calculation, then interpret sign after.

Worked example(s)

Example 1 — Prefix fluency & charge moved

A sensor draws $3.6~\mathrm{mA}$ continuously. a) Express this in $\mathrm{A}$ and in $\mathrm{\mu A}$. b) How much charge passes in $250~\mathrm{ms}$?

Solution. a) $3.6~\mathrm{mA}=3.6\times 10^{-3}~\mathrm{A}=3600~\mathrm{\mu A}$. b) $Q = I \cdot t = 3.6\times 10^{-3}~\mathrm{A}\cdot 0.250~\mathrm{s}=9.0\times 10^{-4}~\mathrm{C}=0.90~\mathrm{mC}$.

Example 2 — From particles to current

A current in a thin gold wire is due to electrons. In $20~\mathrm{ms}$, $n=7.5\times 10^{15}$ electrons pass a cross-section. What average current flows?

Solution. Total charge $Q = n e = 7.5\times 10^{15}\cdot 1.602\times 10^{-19}~\mathrm{C}\approx 1.20\times 10^{-3}~\mathrm{C}$. $I \approx Q/t = (1.20\times 10^{-3})/0.020 \approx 0.060~\mathrm{A}=60~\mathrm{mA}$. Direction: electron motion right→left implies conventional current left→right.

Example 3 — Mixed carriers & current direction

In an electrolyte between faces $A_1$ and $A_2$, during $\Delta t=1~\mathrm{s}$, $\Delta Q_p=+40~\mathrm{\mu C}$ moves from $A_1$ to $A_2$ and $\Delta Q_n=-25~\mathrm{\mu C}$ (negative) moves from $A_2$ to $A_1$. What is the algebraic current from $A_1$ to $A_2$?

Solution. Total charge transfer $\Delta Q=\Delta Q_p-\Delta Q_n = 40~\mathrm{\mu C}-(-25~\mathrm{\mu C})=65~\mathrm{\mu C}$. $I=\Delta Q/\Delta t=65~\mathrm{\mu A}$ from $A_1$ to $A_2$ (positive).

Quick checks

• What is the SI unit of charge? ++ Answer Coulomb (C). * Convert $47~\mathrm{k\Omega}$ to $\mathrm{\Omega}$. ++++ Answer $47~\mathrm{k\Omega}=47\,000~\mathrm{\Omega}$. * State the definition of $1~\mathrm{A}$ using charge and time. ++++ Answer $1~\mathrm{A}$ flows if $1~\mathrm{C}$ passes a cross-section in $1~\mathrm{s}$. * If electrons drift to the right, which way is conventional current? ++++ Answer To the left (opposite electron motion). * Compute the number of electrons in $1.0~\mathrm{nC}$. ++++ Answer $n=Q/e \approx (1.0\times10^{-9})/(1.602\times10^{-19})\approx 6.24\times10^{9}$ electrons. ++

Embedded resources

• 
• 

Common pitfalls & misconceptions

• Mixing up quantity vs unit (e.g., writing “mA” when you mean “m” as a prefix on amperes) or stacking prefixes (No: “$\mu k$A”).
• Confusing charge (C) with current (A) or voltage (V). Use unit analysis to catch errors early.
• Forgetting that conventional current follows positive charge flow; electrons go the opposite way in metals.
• Dropping sign information when interpreting reference arrows; always place arrows before calculation and read signs after.

Mini-assignment / homework (optional)

• Build a two-column “prefix ladder” from $10^{-18}$ to $10^{18}$ and place five real-world examples across it (e.g., biocurrent, USB device current, motor phase current). Bring it next time.
• Compute: A wearable draws $220~\mathrm{\mu A}$ in standby for $18~\mathrm{h}$. How much charge (in mAh and in C) is used?

References & links

• Later: voltage & potential and ideal sources → Block 02 — Voltage & Power.
• Later: resistance, conductance, and temperature dependence → Block 03 — Resistance & Practical Resistors.
• Lab safety and measurement rules → Laboratory regulations.

⚠ Safety: When measuring current, never put a multimeter in voltage mode across a source; use the current input and series connection to avoid a short circuit.