Voltage, Current & Resistance
Meet the three quantities that describe every circuit ever built — and the equations, real numbers and safety limits behind each one.
Musk's Rocket Science · Part 1 — Electricity Basics · Chapter 2 · 15 min read
In Chapter 1 we established that electricity is electrons on the move. But “electrons moving” alone does not tell you whether you are looking at a phone charger or a lightning bolt. To actually describe a circuit — to predict what it will do, design it safely, or troubleshoot it — you need three numbers: how hard the electrons are being pushed, how many are flowing per second, and how much the material resists that flow.
These three quantities — voltage, current and resistance — are the entire vocabulary of electrical engineering. Master them, and Ohm’s Law in Chapter 3 will feel less like a new fact to memorise and more like an obvious consequence of definitions you already understand.
2.1 — Voltage: electric potential energy per charge
Recall from Chapter 1 that a battery uses chemistry to create a surplus of electrons at one terminal and a shortage at the other. That imbalance stores potential energy — energy that has not been spent yet, but is ready to be, the instant you give the electrons a path to travel.
Voltage is the work required to move a unit of charge between two points — or equivalently, the energy released when a unit of charge moves from the high-potential point to the low-potential point.
V = W / Q
V is voltage in Volts, W is work (energy) in Joules, and Q is charge in Coulombs. One Volt is exactly one Joule per Coulomb.
This is also why voltage is often called electric potential difference. It is always a comparison between two points, never a property of a single point in isolation.
Worked example 2.1 — Energy delivered by a BESS during a peak-shaving event
A utility-scale BESS string operates at V = 1,500V DC. During a one-hour discharge to cover an evening demand peak, it holds a steady discharge current of I = 1,000A.
Charge moved: Q = I × t = 1,000A × 3,600s = 3,600,000 Coulombs
Rearranging V = W/Q: W = V × Q = 1,500 × 3,600,000 = 5,400,000,000 J
In megawatt-hours: 5.4×10⁹ ÷ 3.6×10⁹ = 1.5 MWh
Exactly matching 1,500V × 1,000A × 1h — the standard way BESS discharge energy is calculated for grid dispatch and settlement. The same arithmetic gives the kWh figure on any battery spec sheet: a 51.2V, 100Ah e-rickshaw pack holds 51.2 × 100 = 5,120 Wh, or 5.12 kWh.
Technical framing
Because voltage is a potential difference, it only makes sense to talk about the voltage across two points: across a BESS string’s terminals, across a power conversion system, across a motor winding. Engineers sometimes speak loosely of “the voltage at a point,” but that always implicitly means the difference relative to an agreed reference, commonly labelled ground or 0V.
2.1.1 — Real-world voltage, revisited
Chapter 1 introduced the voltage comparison chart. The core intuition is worth restating: voltage by itself tells you nothing about danger or power. A static discharge in a dry gigafactory clean room can reach thousands of volts with essentially no risk to a person, because so little charge is involved, while a 230V connection at a BESS site’s auxiliary supply can kill because it can sustain meaningful current. Which brings us to current.
2.2 — Current: the rate of charge flow
We defined current in Chapter 1 as I = Q/t — the rate at which charge passes a point. Here we go deeper on the two things that trip nearly everyone up: which way current flows, and why current, not voltage, is what actually hurts you.
2.2.1 — Benjamin Franklin's 50/50 guess
When Franklin studied static electricity in the 1740s — decades before anyone knew electrons existed — he had to arbitrarily assign a direction to the flow he was observing. He guessed that “electrical fluid” flowed from what he labelled the positive terminal to the negative. He had a 50% chance of being right.
He was wrong. When electrons were discovered in 1897 it became clear that in a metal wire the particles that actually move travel from negative to positive. But by then Franklin’s convention was baked into a century of mathematics, textbooks and engineering practice. Rather than rewrite everything, the field kept his direction and named it conventional current — the assumed direction of positive charge flow, from + to −, which remains the standard in every circuit diagram to this day.
In plain English
Every circuit diagram you will ever see draws current arrows from + to −. That is conventional current, and it is a 280-year-old historical accident, not a physical fact about which way electrons move. The electrons go the opposite way.
Both descriptions give the same correct answers for voltage, current and power. It is purely a labelling convention — but one worth knowing the origin of.
2.2.2 — How much current, really?
Table 2.1 — Typical current across the energy stack
| System | Typical current | Why |
|---|---|---|
| BMS cell balancing current | ~50 mA | Deliberately small — balancing bleeds or shuttles a tiny fraction of pack current between cells, over a long charge cycle |
| EV home AC charging (Level 2) | ~32A | Single-phase residential charging, current-limited by the wall circuit and the onboard charger |
| EV DC fast charger (350kW ultra-fast) | ~437A | High-voltage 800V-class DC fast charging pushes current far higher to hit target charge times |
| Offshore wind turbine generator output (6MW class) | ~5,000A | Large power at a relatively low generator voltage (690V) demands very high current before step-up transformation |
| Grid substation fault current | ~20,000A | A near-zero-impedance fault briefly draws enormous current until protective relays clear it |
| Lightning bolt | ~20,000–30,000A | Massive charge separation discharging through ionised air in a fraction of a second |
2.2.3 — The safety table that actually matters
This is the single most practically important chart in the chapter. Contrary to popular belief, voltage does not kill you — current does. A given voltage only becomes dangerous current if your body completes a low-enough-resistance path, which is what section 2.3 is about.
Table 2.2 — Current-based shock severity (illustrative thresholds)
| Current | Effect |
|---|---|
| 0.1–1 mA | Just perceptible — a faint tingle |
| 1–5 mA | Mild shock sensation, generally harmless |
| 5–10 mA | Painful shock; muscle control still retained |
| 10–20 mA | Involuntary muscle contraction — the “can’t let go” threshold |
| 20–50 mA | Breathing muscles affected, severe pain, possible unconsciousness |
| 50–100 mA | Risk of ventricular fibrillation begins |
| 100–200 mA | High risk of fibrillation — frequently fatal without immediate defibrillation |
Important
This is exactly why a many-thousand-volt static discharge in a dry gigafactory clean room (Chapter 1) is harmless — far too little charge and current actually flow — while a fault on a 400V EV charging cabinet or a BESS auxiliary supply can kill, because it can sustain tens to hundreds of milliamps through a person who completes the circuit. Chapter 3’s Ohm’s Law shows precisely how voltage, body resistance and the resulting current relate, which is what makes these thresholds predictable rather than mysterious.
These thresholds are illustrative figures from electrical safety literature, included to build intuition. They are not a substitute for professional electrical safety guidance, and individual susceptibility varies with current path, duration and health.
2.3 — Resistance: opposition to flow
Not all materials let electrons through equally. Resistance measures how much a material opposes current, in Ohms (Ω). But resistance is not purely a property of a material — it also depends on the object’s shape. A short, fat copper rod resists current far less than a long, thin copper wire, even though both are copper.
R = ρ · (L / A)
R is resistance in Ohms, ρ (“rho”) is the material’s resistivity in Ω·m, L is length in metres, and A is cross-sectional area in m².
Longer wires resist more; thicker wires resist less; and the material itself sets the baseline through ρ.
Table 2.3 — Resistivity of common materials at room temperature
| Material | Resistivity ρ (Ω·m) | Category |
|---|---|---|
| Silver | 1.59 × 10⁻⁸ | Conductor (best common metal) |
| Copper | 1.68 × 10⁻⁸ | Conductor (industry standard) |
| Aluminium | 2.65 × 10⁻⁸ | Conductor (lightweight alternative) |
| Iron | 9.71 × 10⁻⁸ | Conductor (structural, higher resistance) |
| Nichrome | 1.10 × 10⁻⁶ | Resistive alloy — deliberately high resistance, used in heating elements |
| Human skin (wet) | ~1 × 10³ | Poor conductor — but current can still pass dangerously |
| Human skin (dry) | ~1 × 10⁵ | Much higher resistance — one reason dry hands are safer around electricity |
| Glass | ~1 × 10¹¹ | Insulator |
| Rubber | ~1 × 10¹³ | Insulator (wire sheathing, gloves, mats) |
| Teflon | ~1 × 10¹⁵ | Near-perfect insulator |
Worked example 2.2 — Sizing a BESS rack busbar
Consider a 2-metre copper busbar connecting a BESS rack’s string fuse to its power conversion system (PCS), with cross-sectional area A = 1.0 × 10⁻⁵ m² — 10mm², a realistic busbar sizing for high continuous current. Copper’s ρ = 1.68 × 10⁻⁸ Ω·m.
R = ρ · L / A = (1.68×10⁻⁸ × 2) / (1.0×10⁻⁵)
R = 3.36×10⁻⁸ / 1.0×10⁻⁵ ≈ 3.36 mΩ
A tiny resistance — but not zero. At 300A continuous rack current, this busbar alone would dissipate:
P = I²R ≈ 300² × 0.00336 ≈ 302 W as heat
A preview of why busbar cross-section, connector torque and thermal design matter so much in BESS engineering — a theme we return to when we cover power in Chapter 6 and internal resistance in Part 3.
Why this matters later
This resistivity equation is exactly why BESS and EV powertrain designers care so much about busbar cross-section, connector quality and cable gauge. A slightly undersized busbar, or a loose high-resistance connection, does not just waste energy as heat — under high continuous current that wasted power becomes a genuine thermal and fire risk.
This is the physics reason behind every torque-spec and cable-rating requirement in a BESS or EV integration manual, behind every “use adequately rated cable” warning in a battery datasheet, and behind the connector checks in our daily inspection routine.
2.3.1 — Conductance: resistance's mirror image
Occasionally it is more convenient to talk about how easily current flows rather than how much it is resisted. This is conductance, G, measured in Siemens (S).
G = 1 / R
A high-resistance material has low conductance, and vice versa. Conductance appears less often than resistance in everyday electronics, but frequently in materials science and in describing how leaky an imperfect insulator is.
2.4 — Bringing the three together
Quick reference — the three quantities
| Quantity | Symbol | Unit | Defining equation | What it answers |
|---|---|---|---|---|
| Voltage | V | Volt (V) | V = W/Q | How hard are electrons being pushed? |
| Current | I | Ampere (A) | I = Q/t | How much charge flows per second? |
| Resistance | R | Ohm (Ω) | R = ρL/A | How much does the material oppose that flow? |
Notice what is missing: we have not yet written down how voltage, current and resistance relate to each other in a working circuit. That relationship — arguably the single most useful equation in all of electrical engineering — is the entire subject of Chapter 3.
Chapter summary
- ✓Voltage (V) is electric potential energy per unit charge, V = W/Q, measured in Volts (Joules per Coulomb). It is always a difference between two points, like height in a gravitational analogy.
- ✓Current (I) is the rate of charge flow, I = Q/t, in Amps. Conventional current runs + to −, opposite to actual electron flow — a 280-year-old accident from Franklin’s incorrect 50/50 guess.
- ✓It is current, not voltage, that determines physiological danger — from a barely-perceptible 1mA tingle to a potentially fatal 100mA through the chest.
- ✓Resistance (R) depends on both material (resistivity ρ) and geometry (length and area), R = ρL/A, measured in Ohms.
- ✓Resistivity spans over 20 orders of magnitude, from silver and copper to Teflon.
- ✓Conductance (G = 1/R) is resistance’s mirror image, measuring how easily rather than how poorly current flows.
Test your understanding
- 1A battery moves 500 Coulombs of charge and does 6,000 Joules of work in the process. What is its voltage?
- 2Explain, in your own words, why conventional current and electron flow point in opposite directions — and why both descriptions still give correct circuit answers.
- 3Why can a many-thousand-volt static discharge in a dry gigafactory environment be harmless while a 400V EV charging cabinet fault can be lethal? Use the idea of current, not just voltage, in your answer.
- 4Using R = ρL/A, if you double a wire’s length and also double its cross-sectional area, what happens to its resistance?
- 5Why does dry skin protect you somewhat better than wet or sweaty skin, in resistivity terms?
- 6Challenge: a 500-metre aluminium overhead transmission conductor (ρ = 2.65 × 10⁻⁸ Ω·m, a realistic material choice for long-distance lines given its low weight-to-conductivity ratio) has a cross-sectional area of 3.0 × 10⁻⁴ m². Calculate its resistance. If 400A flows through it, roughly how much power (P = I²R) is dissipated as heat per span?
Frequently asked questions
What is voltage, in simple terms?+
Voltage is the work needed to move a unit of charge between two points, V = W/Q, measured in Volts — one Volt being exactly one Joule per Coulomb. It is always a difference between two points, never a property of a single point, which is why it is also called electric potential difference. The gravitational analogy is height: a charge at the positive terminal sits at the top of a hill.
Why does conventional current flow the opposite way to electrons?+
Benjamin Franklin arbitrarily guessed in the 1740s that charge flowed from positive to negative, decades before electrons were known. He had a 50% chance and was wrong — in a metal wire the electrons move from negative to positive. By the time electrons were discovered in 1897 his convention was embedded in a century of mathematics, so the field kept it and named it conventional current. Both give identical correct answers.
Is it voltage or current that kills you?+
Current. Voltage only becomes dangerous if your body completes a low-enough-resistance path to let meaningful current flow. Roughly 1mA is just perceptible, 10–20mA causes the “can’t let go” muscle contraction, and 100mA through the chest carries a high risk of fibrillation. This is why a many-thousand-volt static discharge in a dry gigafactory clean room is harmless — too little charge flows — while a fault on a 400V EV charging cabinet or a BESS auxiliary supply can be lethal, because it can sustain that current. These thresholds are illustrative and not a substitute for professional safety guidance.
What is resistivity and how is it different from resistance?+
Resistivity (ρ) is an intrinsic property of a material, measured in Ohm-metres. Resistance (R) is a property of a particular object, and depends on shape as well as material: R = ρL/A. A long thin wire and a short fat one of the same metal have the same resistivity but very different resistances.
Why does busbar and cable cross-section matter in a battery system?+
Because R = ρL/A means a thinner cable has higher resistance, and power dissipated as heat is P = I²R. A 10-metre copper cable of 2mm² area has only about 0.084Ω, but at 100A that still dissipates roughly 840W as heat. Under high current an undersized cable or a loose, high-resistance connection is a genuine fire risk, not just an efficiency loss.
How is the energy delivered by a battery or BESS calculated?+
Rearranging the definition of voltage, V = W/Q, gives W = V × Q, and since Q = I × t the energy is simply voltage × current × time. A 1,500V BESS string discharging 1,000A for one hour moves 3,600,000 Coulombs and delivers 5.4 × 10⁹ Joules, or 1.5 MWh. The same arithmetic gives the kWh figure on any battery spec sheet: a 51.2V 100Ah pack holds 5.12 kWh.
How much resistance does a busbar actually have, and does it matter?+
Very little, but not zero — and it matters a great deal at high current. A 2-metre copper busbar of 10mm² cross-section has R = ρL/A ≈ 3.36 mΩ. At 300A continuous that dissipates I²R ≈ 302W as heat. This is the physics reason behind every torque specification and cable rating in a BESS or EV integration manual: an undersized busbar or a loose, high-resistance joint becomes a thermal and fire risk, not just an efficiency loss.
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Musk's Rocket Science is an original educational series explaining the physics and chemistry behind everyday electricity and battery technology. Figures and worked examples use standard physical constants and representative real-world values for illustration.