002.【A Physical Worldview】⚡ Resistance and Current
nA, A, and kA Are Not the Same Current
⚡ Resistance × 🔌 Current
Why “Current Flows / Doesn’t Flow” So Often Misses the Point
Does current flow, or not?
Is resistance high, or low?
That’s how we were taught.
But that dichotomy is nothing more than humans rounding away orders of magnitude.
🔑 A Common Language First: Electricity Also Switches by Prefix
| Prefix | Symbol | Value |
|---|---|---|
| nano | n | $10^{-9}$ |
| micro | μ | $10^{-6}$ |
| milli | m | $10^{-3}$ |
| (base) | – | $10^{0}$ |
| kilo | k | $10^{3}$ |
| mega | M | $10^{6}$ |
| giga | G | $10^{9}$ |
n → μ → m → A → k → M → G
At each step, the meaning of electricity changes.
⚡ Resistance: Conductors and Insulators Are a Continuum
| Material | Resistivity |
|---|---|
| Copper | $10^{-8}\,\Omega\cdot\mathrm{m}$ |
| Aluminum | $10^{-8}\,\Omega\cdot\mathrm{m}$ |
| Silicon | $10^{2}\sim10^{5}\,\Omega\cdot\mathrm{m}$ |
| Oxide layer | $10^{16}\,\Omega\cdot\mathrm{m}$ |
| Air | $10^{14}\,\Omega\cdot\mathrm{m}$ |
The words conductor, semiconductor, and insulator
do not describe different kinds of matter.
They describe whether resistivity is
$10^{-8}$ or $10^{16}$.
That’s not a category difference.
It’s a 16-order-of-magnitude difference.
🔌 Current: Same “Ampere,” Different Worlds
| World | Current |
|---|---|
| Transistors | nA = $10^{-9}\,\mathrm{A}$ |
| Analog circuits | μA = $10^{-6}\,\mathrm{A}$ |
| Electronics | mA = $10^{-3}\,\mathrm{A}$ |
| Home appliances | A = $10^{0}\,\mathrm{A}$ |
| Motors | $10^{2}\,\mathrm{A}$ |
| Lightning | $10^{5}\,\mathrm{A}$ |
| Solar flares | $10^{11}\,\mathrm{A}$ |
In the nA world,
the question is “does it leak?”
In the A world,
the question is “does it move?”
Beyond kA,
the question becomes “does it break?”
🧠 Why Engineers Talk Past Each Other
- The nA person says: “No current flows.”
- The A person says: “Of course it flows.”
- The kA person says: “Stop—this is dangerous.”
They are all looking at the same physics.
The only difference is
which order of magnitude they are standing in.
⚠️ ON / OFF Is an Illusion
Current is almost never exactly zero.
We are just ignoring $10^{-12}$ A.
“Doesn’t flow” simply means:
At this order of magnitude, it doesn’t matter.
🧭 Take-Home Summary
- Resistance and current are continuous quantities
- Conductor/insulator, ON/OFF are human abstractions
- nA, A, and kA are not the same current
Physics is one.
What’s discontinuous is human scale intuition.