Lesson 4: Electricity and Magnetism

Electricity and magnetism were once separate mysteries — amber attracting straw, lodestones pointing north. Then Oersted, Faraday, and Maxwell revealed one force: electromagnetism, the theory behind every motor, generator, and the phone in your pocket. China’s contributions run deep: the magnetic compass (Lesson 19) guided world navigation, and today China leads in ultra-high-voltage transmission, high-speed rail electrification, and battery technology. This lesson covers circuits, electromagnetism, and the applications powering modern civilization.

Electric Charge and Current

Charge comes in positive and negative; like repels, opposite attracts (Coulomb’s law: F = kq₁q₂/r²). Current is charge flow: I = Q/t, measured in amperes. A 2 A current moves 2 coulombs per second — about 10¹⁹ electrons! Conventional current flows positive-to-negative (Franklin’s guess); electrons actually drift negative-to-positive, slowly — the signal travels near light speed.

Voltage (potential difference) is energy per charge: V = W/Q. A 12 V battery gives each coulomb 12 J. Resistance opposes flow: Ohm’s law V = IR. A 12 V battery across 4 Ω drives 3 A. These three — V, I, R — are circuits’ vocabulary.

Power in circuits: P = VI = I²R = V²/R. A 220 V, 1,000 W kettle draws ~4.5 A and has R ≈ 48 Ω. China’s 220 V mains (vs. America’s 110 V) deliver the same power at half the current — less copper needed. Standards encode physics.

Circuits — Series and Parallel

Series: one path — current same everywhere, voltages divide. Two 10 Ω resistors in series across 12 V: R_total = 20 Ω, I = 0.6 A, each drops 6 V. One bulb burns out: the circuit breaks (old Christmas lights!).

Parallel: multiple paths — voltage same across branches, currents divide. Two 10 Ω in parallel: R_total = 5 Ω (1/R = 1/10 + 1/10), I_total = 2.4 A. Homes wire in parallel: each appliance gets full 220 V, independent switching. Parallel lowers resistance; series raises it.

Kirchhoff’s laws: current in = current out at junctions; voltage drops sum to zero around loops. These solve any circuit — the systematic method behind every electronics design, from flashlights to supercomputers.

Magnetism and Electromagnetism

Moving charges create magnetic fields: a current-carrying wire’s field circles it (right-hand rule). Electromagnets — coils around iron cores — lift scrap metal, drive motors, and (in maglev trains) levitate vehicles. Shanghai’s maglev uses electromagnetic suspension to float at 430 km/h.

Faraday’s law: changing magnetic fields induce current — the generator principle. Spin a coil in a magnetic field: AC electricity. Every power plant (coal, hydro, wind, nuclear) is a Faraday machine: something spins a generator. The Three Gorges’ turbines spin generators via falling water — electromagnetism electrified.

Maxwell unified it all: changing electric fields create magnetic fields and vice versa — self-propagating electromagnetic waves at light speed c. Light IS an electromagnetic wave; radio, X-rays, and WiFi are its siblings. Maxwell’s equations are physics’ crowning classical achievement.

Motors, Transformers, and the Grid

Motors reverse generators: current in a magnetic field feels force (F = BIL) — spinning coils do work. EVs’ motors (~90% efficient) are overtaking combustion engines; China’s BYD and others lead the transition. Maglev propulsion: linear motors unrolled flat, pushing trains without contact.

Transformers change AC voltage via shared magnetic flux: V₁/V₂ = N₁/N₂ (turns ratio). Step up to 1,000 kV for transmission (low current ⟹ low I²R losses), step down for homes. China’s ultra-high-voltage (UHV) lines — 1,100 kV AC, ±800 kV DC — move western hydropower 3,000+ km to coastal cities with minimal loss. The world’s most advanced grid.

The grid balances supply and demand instantaneously: generators spin faster/slower to match load. Renewables complicate this (sun and wind vary) — hence batteries, pumped hydro, and smart grids. China’s grid investments (world’s largest) are the energy transition’s backbone.

Electronics and Semiconductors

Semiconductors (silicon) conduct controllably — doping with impurities tunes conductivity. The transistor (1947) — a switch/amplifier the size of... now nanometers — enabled all digital technology. A modern chip holds 100+ billion transistors; SMIC and Huawei’s advances are China’s bid for chip self-sufficiency.

Diodes (one-way current), LEDs (light from current — China makes most of the world’s), solar cells (light to current — also China-led). P-n junctions’ physics underlies all three. The semiconductor is applied quantum mechanics (Lesson: extension).

Digital logic: transistors form gates (AND, OR, NOT); gates form circuits; circuits compute. From sand (silicon dioxide) to smartphones: the most transformative material story in history. Understanding semiconductors is understanding the information age’s physical basis.

Safety and Everyday Electricity

Household safety: fuses and breakers interrupt overcurrent (preventing I²R fires); grounding provides fault paths; insulation prevents shocks. China’s 220 V can kill — respect it. Never touch downed power lines; call professionals.

Static electricity: charge separation by friction — lightning is its giant form (a single bolt: ~10⁹ J). Lightning rods (Franklin) protect buildings; China’s tall towers bristle with them. Humidity reduces static; dry winter air invites shocks.

Energy literacy: read your electricity bill (kWh = energy!); a 1 kW heater running 3 hours uses 3 kWh. Phantom loads (standby power) waste ~5-10% of home electricity. Understanding watts, kilowatt-hours, and tariffs makes you an informed consumer — and citizen judging energy policy.

Deep Dive — From Tubes to Chips: The Electronics Revolution

Vacuum tubes (1904–1947): controlling electron beams in glass bulbs — the first electronics, powering radio, radar, and ENIAC (18,000 tubes, room-sized, 150 kW!). Tubes were hot, fragile, and power-hungry. China’s early computers (1958’s 103 model) used tubes — the starting line.

The transistor (1947, Bardeen-Brattain-Shockley): a solid-state switch — smaller, cooler, reliable. Then the integrated circuit (1958–59, Kilby and Noyce): many transistors on one silicon chip. Then Moore’s law: transistor counts doubling ~2 years — from 2,300 (Intel 4004, 1971) to 100+ billion today. Exponential progress for 50 years — civilization’s most sustained technological miracle.

How chips are made: ultrapure silicon ingots sliced into wafers; photolithography prints patterns with extreme-ultraviolet light (13.5 nm wavelength!); doping, etching, layering — hundreds of steps in dust-free fabs costing $20B each. ASML (Dutch) makes the only EUV machines; TSMC (Taiwan) makes the most advanced chips; China’s SMIC races to catch up — the "chip war’s" industrial core.

China’s chip drive: massive state investment (the "Big Fund"), SMIC’s advances (7 nm-class despite sanctions), Huawei’s Kirin comeback chips, and RISC-V (open-source chip architecture) as a hedge. The goal: semiconductor self-sufficiency — the 21st century’s most strategic technology. Physics (quantum mechanics), chemistry (materials), and engineering (lithography) converge in every chip.

Beyond silicon: gallium nitride (fast chargers, 5G), silicon carbide (EV power electronics — BYD’s advantage!), photonics (light instead of electrons), and quantum chips (Lesson 16’s frontier). Materials science drives each leap — Lesson 6’s bonding theory made practical.

The arc: from lodestone compasses (Lesson 19) to quantum chips — China’s electromagnetic journey spans 2,000 years. Every device you own contains billions of switches exploiting quantum physics discovered a century ago. Electronics is applied quantum mechanics — and the revolution isn’t over.

Quantum computing deeper: superconducting qubits (Google, IBM, China’s USTC) operate near absolute zero; trapped ions (exquisite control, slower); photonic (Jiuzhang’s approach — room temperature!). The DiVincenzo criteria list what a quantum computer needs: scalable qubits, initialization, long coherence, universal gates, measurement. Every platform trades these off differently.

Photonics — computing with light: photons don’t interact (no crosstalk, no heat!), making them ideal for communication and certain computations. Silicon photonics integrates optical components onto chips — data centers already use it. China’s photonic quantum advantage (Jiuzhang) hints at light-based computing’s future.

The end of Moore’s law? Transistor shrinks face quantum tunneling and economic walls ($20B fabs!). Responses: chiplets (many small dies packaged together — AMD’s strategy, China’s workaround for sanctions), 3D stacking, new materials (2D semiconductors like MoS₂), and new paradigms (neuromorphic, quantum). Progress continues — just not via shrinking alone.

Conclusion — Why This Matters

Electricity and magnetism unified into electromagnetism — the theory behind every generator, motor, and the device you’re reading this on. China’s ultra-high-voltage grid, its high-speed rail’s electric traction, and its lead in batteries and 5G all rest on Maxwell’s equations. The compass needle that guided Zheng He’s fleets (Lesson 19) was magnetism’s first gift; the electromagnetic age is its fulfillment.

Going deeper — your home circuit, analysed like an engineer

A family in Guangzhou switches on, all at once: an electric kettle (1,500 W), an air conditioner (1,200 W), lights and electronics (300 W). The supply is 220 V.

• Total power: 1,500 + 1,200 + 300 = 3,000 W.
• Total current: I = P/V = 3,000/220 ≈ 13.6 A. The apartment's breaker is rated 16 A — everything just holds.
• Now add a 2,000 W space heater: P = 5,000 W, I = 5,000/220 ≈ 22.7 A — above 16 A, so the breaker trips. That trip is Lesson 4's safety physics working as designed: it cuts the current before I²R heating in the walls can start a fire.
• Cost: running the original 3.0 kW load for 4 hours uses E = Pt = 3.0 × 4 = 12 kWh. At ¥0.60 per kWh, that evening costs ¥7.20.

The parallel wiring of homes is what makes this analysis simple: every appliance sees the full 220 V and draws its own current, and the currents add at the meter. Engineers size cables and breakers from exactly this calculation — total current first, safety margin second.

Practical focus — finding resistance from a V–I graph

Data. A resistor is connected to a variable supply. Readings: 2.0 V → 0.20 A; 4.0 V → 0.41 A; 6.0 V → 0.59 A.

Analysis. Plot V against I; the points lie close to a straight line through the origin — the resistor obeys Ohm's law. Resistance = gradient = ΔV/ΔI = (6.0 − 2.0)/(0.59 − 0.20) = 4.0/0.39 ≈ 10 Ω. Averaging the three ratios V/I (10, 9.8, 10.2) gives the same answer; the gradient method is better because it uses all the data at once and exposes any bad point.

Evaluation. Had this been a filament lamp, the graph would curve: as current grows the filament heats, its resistance rises, and the gradient steepens. A curve is not failed data — it is the physics of temperature-dependent resistance, visible. Improvements for precision: take readings quickly (before self-heating), and repeat with the current reversed to cancel meter zero errors.

Common mistakes

• Adding parallel resistances directly. Parallel total is always *less* than the smallest branch: 1/R = 1/R₁ + 1/R₂.
• Believing transformers work on DC. They need *changing* flux — steady DC gives no induction after switch-on.
• Mixing up current directions: conventional current flows + to − outside the supply; electrons drift the other way.

Exam Experience

Question 1 (choice, 3 marks). Two identical lamps are available. They glow brightest (each at full brightness) when connected:

• A. In series across the supply
• B. In parallel across the supply
• C. One in series, one in parallel
• D. It makes no difference

Answer: B. In parallel each lamp receives the full supply voltage and draws its rated current. In series they share the voltage and glow dimly — and one failing lamp kills both.

Question 2 (choice, 3 marks). A transformer has 100 primary turns and 2,000 secondary turns. The primary is connected to 220 V AC. The secondary voltage is:

• A. 11 V
• B. 220 V
• C. 4,400 V
• D. 44,000 V

Answer: C. V₂/V₁ = N₂/N₁ = 20, so V₂ = 220 × 20 = 4,400 V — step-up, as used at power stations before transmission.

Question 3 (structured, 6 marks). A line with total resistance 8.0 Ω must deliver 5.0 × 10³ MW. Compare transmission at 500 kV and at 1,000 kV: (1) the current in each case; (2) the power lost as heat in each case; (3) one practical disadvantage of very high voltage.

Marking scheme. (1) I = P/V: at 500 kV, I = 5.0 × 10⁹/5.0 × 10⁵ = 1.0 × 10⁴ A [1]; at 1,000 kV, I = 5.0 × 10³ A [1]. (2) Loss = I²R: (10⁴)² × 8.0 = 8.0 × 10⁸ W = 800 MW [1]; (5.0 × 10³)² × 8.0 = 2.0 × 10⁸ W = 200 MW [1] — doubling the voltage quarters the loss, the entire logic of China's UHV grid. (3) Any one: costlier insulation and taller towers, corona discharge losses, safety clearance distances [1]. Conclusion sentence linking result to UHV policy [1].