---
title: "From Power Plant to Home: The Alternator"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 69
exercises: 12
source: https://one-course.com/books/physics/1/en/chapter/69-from-power-plant-to-home-the-alternator
---

# Chapter 69 — From Power Plant to Home: The Alternator

A year’s worth of [kilowatt-hours](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-kwh) has flowed through your audits — but from where? Follow the cable out of the house, under the street, across the pylons, and it ends at a machine spinning in a great hall: the [alternator](#def-g9-alternator-alternator). Its secret is the loveliest surprise in this book’s electricity: the current-makes-magnetism discovery of last year, run backward.

## 69.1 Induction: the effect reversed

**Proposition 69.1 (Electromagnetic induction).**

Move a [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) near a [closed circuit](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-circuit) — or move the circuit near the [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) — and while the motion lasts, a [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) appears and drives a current: electricity *induced* by changing magnetism. The rules, from the bench:

1. only *change* induces: [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) at rest beside the coil, nothing — however strong the [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) ;
2. faster motion, stronger [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) , more turns of coil: bigger induced [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) ;
3. reverse the motion, reverse the induced current — approach and retreat drive opposite marches.

Last year a current made magnetism; this year moving magnetism makes a current. The two effects are one coin, read from its two faces — and the second face [powers](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-power) civilization.

**Method 69.2 (Induction on the bench).**

A coil of many turns, a bar [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet), a sensitive zero-centered meter:

1. connect the meter across the coil; hold the [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) still inside it: the needle sleeps at zero — strength alone induces nothing;
2. thrust the [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) in: the needle kicks one way — and returns to zero the instant the motion stops;
3. withdraw it: an equal kick, the other way;
4. thrust faster: a bigger kick. Jiggle the [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) in and out rhythmically, and the needle swings left, right, left — you are hand-cranking an [alternating current](https://one-course.com/books/physics/1/en/chapter/67-alternating-current#def-g9-alternating-current-dcac) .

![Induction on the bench: only a moving magnet wakes the coil — and the needle’s kick reverses with the motion.](https://one-course.com/images/onecourse/chapters/physics-1/g9-alternator/fig-e812fef210ae.svg)

*Induction on the bench: only a *moving* [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) wakes the coil — and the needle’s kick reverses with the motion.*

## 69.2 The alternator

**Definition 69.3 (Alternator).**

An *alternator* is induction made tireless: a [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) spun steadily beside a fixed coil (or a coil spun in a magnetic field). Each half-turn brings a pole toward the coil, then carries it away — change, endlessly renewed — so the induced [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) swings positive, negative, positive: *alternating*, by construction, tracing exactly the smooth sinusoid of the [oscilloscope](https://one-course.com/books/physics/1/en/chapter/67-alternating-current#met-g9-alternating-current-scope) chapter. Spin at fifty turns a second and the output alternates at $50\,\mathrm{Hz}$: the grid’s [frequency](https://one-course.com/books/physics/1/en/chapter/62-sound-speed-pitch-loudness#def-g8-sound-pitch-loudness-frequency) *is* a rotation [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula), kept in lockstep by every station on the network.

**Example 69.4 (The dynamo on your wheel).**

The bicycle dynamo is a pocket [alternator](#def-g9-alternator-alternator): the wheel spins a little [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) inside a fixed coil, and the lamp [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) — brighter and at higher [frequency](https://one-course.com/books/physics/1/en/chapter/62-sound-speed-pitch-loudness#def-g8-sound-pitch-loudness-frequency) as you pedal harder, exactly as the bench rules promise (and flickering at a crawl, as the alternating chapter observed). Its price is honest too: the dynamo drags — lighting the lamp costs your legs real effort. Induction gives no [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy); it *converts* motion into electricity, [joule](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) for [joule](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule), minus friction’s tax.

![A hydroelectric plant: lifted water rushes down, spins the turbines, and the alternators send the energy away along the wires.](https://one-course.com/images/onecourse/chapters/physics-1/g9-alternator/img-8443687dded2.jpg)

*A hydroelectric plant: lifted water rushes down, spins the turbines, and the [alternators](#def-g9-alternator-alternator) send the [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) away along the wires.*

## 69.3 Every power plant is one machine

**Proposition 69.5 (The common core).**

Nearly all the world’s electricity, whatever its advertisement, is made the same way: something spins a *turbine* — a sturdy windmill of blades — and the turbine spins an [alternator](#def-g9-alternator-alternator). [Power](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-power) plants differ only in *what pushes the blades*:

1. thermal plants boil water with burning coal or gas — steam jets drive the turbine;
2. nuclear plants boil the water instead with the [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) of splitting atoms — steam again;
3. hydroelectric dams let a mountain lake fall through the blades — the childhood dam-chain, completed;
4. [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind) turbines skip the middleman: the [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind) is the blades’ push, an [alternator](#def-g9-alternator-alternator) in every nacelle.

One exception proves the rule: solar panels make electricity with no spin at all — by a [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) effect belonging to the university years.

![Every plant, one chain: something spins the turbine, the turbine spins the alternator, and induction does the rest. Only the first box differs from plant to plant.](https://one-course.com/images/onecourse/chapters/physics-1/g9-alternator/fig-3e1c45a8bab8.svg)

*Every plant, one chain: something spins the turbine, the turbine spins the [alternator](#def-g9-alternator-alternator), and induction does the rest. Only the first box differs from plant to plant.*

**Example 69.6 (Chains, audited).**

Write each plant as a childhood [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) chain, now with professional vocabulary. The dam: stored height $\to$ motion of falling water $\to$ rotation $\to$ electricity — the Sun, remember, lifted that lake by evaporation: hydro [power](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-power) is rain-deferred sunshine. The coal plant: chemical store $\to$ [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) $\to$ steam’s motion $\to$ rotation $\to$ electricity — with warmth leaking at every arrow, as the cooling towers’ plumes confess. [Wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind): moving [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air) (stirred by the Sun) straight to rotation. Sources that nature refills — water, [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind), sunlight — are called *renewable*; the burned and split stores are spent forever on human timescales.

**Remark 69.7 (Why the pylons hum at 400000 volts).**

The last promise of the alternating chapter falls due. A town needs, say, a hundred million [watts](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-power). By $P = U I$, that [power](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-power) can travel as an enormous current at modest [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) — or a modest current at enormous [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage). But wires [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) with the *current* (the old [heating effect](https://one-course.com/books/physics/1/en/chapter/54-electric-current-and-its-effects#prop-g8-electric-current-effects-three)), and every degree of pylon-warming is paid-for [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) lost to the crows. So the grid transports at breathtaking [voltages](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) — hundreds of thousands of [volts](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage), tiny currents, minimal loss — and steps the [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) down, neighborhood by neighborhood, to the tame $230\,\mathrm{V}$ of your wall. The stepping machine, the *transformer*, is two coils and induction once more — and it works only on current that alternates: the whole grid speaks AC because the transformer does.

## 69.4 Exercises

**Exercise 69.1 ★.**

State the three bench rules of induction. What does a strong [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) *at rest* induce?

**Solution of Exercise 69.1.**

Only change induces; faster motion, stronger [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) and more turns give bigger [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage); reversed motion reverses the current. A [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) at rest, however strong, induces exactly nothing.

**Exercise 69.2 ★.**

Why does an [alternator](#def-g9-alternator-alternator)’s output alternate? Tie the sign changes to the rotation.

**Solution of Exercise 69.2.**

Each half-turn of the rotor brings a pole toward the coil (inducing one way), then carries it off (inducing the other): the [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) must swing sign with every half-rotation — alternation is built into the spinning.

**Exercise 69.3 ★.**

At what rotation [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) does an [alternator](#def-g9-alternator-alternator) feed a $50\,\mathrm{Hz}$ grid? What must every station on the network therefore agree on?

**Solution of Exercise 69.3.**

Fifty turns per second (for the simple two-pole machine). Every station must hold exactly the same rotation rhythm — the whole network spins in lockstep, sharing one [frequency](https://one-course.com/books/physics/1/en/chapter/62-sound-speed-pitch-loudness#def-g8-sound-pitch-loudness-frequency).

**Exercise 69.4 ★.**

Name the two universal boxes of every power plant, and the one box that changes between coal, atom, dam and [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind).

**Solution of Exercise 69.4.**

The turbine and the [alternator](#def-g9-alternator-alternator). Only the pusher of the blades changes: flame’s steam, atom’s steam, falling lake, or [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind).

**Exercise 69.5 ★.**

Write the hydroelectric chain from mountain lake to your lamp — and name the celestial machine that filled the lake.

**Solution of Exercise 69.5.**

Lake’s stored height $\to$ falling water’s motion $\to$ turbine’s rotation $\to$ [alternator](#def-g9-alternator-alternator)’s electricity $\to$ transformer and grid $\to$ lamp. The Sun filled the lake: evaporation lifted the sea, rain delivered it to the mountains.

**Exercise 69.6 ★.**

Why does pedaling grow harder the instant the dynamo’s lamp switches on? Which principle forbids it being otherwise?

**Solution of Exercise 69.6.**

The lamp’s [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) must come from somewhere, and the only store on a bicycle is the rider: the dynamo converts leg-work into [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source), so the lamp’s [joules](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) appear as extra drag. [Energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) is converted, never conjured — the oldest law of the course.

**Exercise 69.7 ★.**

Sort into [renewable](#ex-g9-alternator-chains) and not: [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind); coal; the dam’s lake; uranium; sunlight. What defines the sorting?

**Solution of Exercise 69.7.**

[Renewable](#ex-g9-alternator-chains): [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind), the lake (rain refills it), sunlight. Not: coal, uranium — spent forever on human timescales. The sorting asks: does nature refill the store as we drain it?

**Exercise 69.8 ★.**

Why does the grid ship its [power](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-power) at hundreds of thousands of [volts](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage)? Name the formula that offers the choice and the effect that decides it.

**Solution of Exercise 69.8.**

$P = U I$ lets one [power](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-power) travel as high [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) with small current; the [heating effect](https://one-course.com/books/physics/1/en/chapter/54-electric-current-and-its-effects#prop-g8-electric-current-effects-three) makes the wires’ loss grow with the current. Small current, cool wires, saved [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) — so the grid ships high and steps down at the doorstep.

**Exercise 69.9 ★★.**

A demonstration [alternator](#def-g9-alternator-alternator) hand-cranked slowly [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) its lamp faintly with visible flicker; cranked fast, brightly and steadily. Account for both changes with the bench rules and the [frequency](https://one-course.com/books/physics/1/en/chapter/62-sound-speed-pitch-loudness#def-g8-sound-pitch-loudness-frequency) chapter.

**Solution of Exercise 69.9.**

Slow cranking: small induced [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) (rule two) — faint lamp — at few cycles per second: visible flicker, below the eye’s fusion rate. Fast cranking: bigger [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) — bright — and a [frequency](https://one-course.com/books/physics/1/en/chapter/62-sound-speed-pitch-loudness#def-g8-sound-pitch-loudness-frequency) the eye [fuses](https://one-course.com/books/physics/1/en/chapter/48-short-circuits-and-electrical-safety#def-g7-short-circuits-safety-fuse) smooth. Two dials, one crank.

**Exercise 69.10 ★★.**

A plant delivers $1 \times 10^{8}\,\mathrm{W}$. Compare the currents needed at $230\,\mathrm{V}$ and at $400\,000\,\mathrm{V}$ (scientific notation). Which could real cables carry?

**Solution of Exercise 69.10.**

At $230\,\mathrm{V}$: $I = 1 \times 10^{8} \div 230 \approx
4.3 \times 10^{5}\,\mathrm{A}$ — four hundred thousand [amperes](https://one-course.com/books/physics/1/en/chapter/55-current-intensity-and-the-ammeter#def-g8-intensity-ammeter-intensity): no cable on Earth. At $400\,000\,\mathrm{V}$: $I = 1 \times 10^{8} \div
4 \times 10^{5} = 250\,\mathrm{A}$ — ordinary transmission cable. The transformer’s case, closed.

**Exercise 69.11 ★★.**

Thermal and nuclear plants are, at heart, elaborate kettles. Defend this slogan with their chains — and locate the one link where the two differ.

**Solution of Exercise 69.11.**

Both chains read: store $\to$ [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) $\to$ boiling water $\to$ steam’s motion $\to$ rotation $\to$ electricity — elaborate kettles feeding turbines. The chains differ at exactly one link: what makes the [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat) — burning coal’s chemistry, or splitting uranium’s nuclei.

**Exercise 69.12 ★★★.**

The grand tour, run backward: tonight your lamp glows at $230\,\mathrm{V}$. Trace its [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) upstream through every box — transformer, pylons, [alternator](#def-g9-alternator-alternator), turbine, and one primary store of your choosing — naming the [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) form at each stage and the leaks along the way. Then answer the childhood question with a year-nine sentence: where does the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) in your room ultimately come from?

**Solution of Exercise 69.12.**

Upstream: the wall’s $230\,\mathrm{V}$ came through the neighborhood transformer ([voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) stepped down), along pylons at hundreds of kilovolts (transport form: [high-voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) AC, leaking a little warmth), from an [alternator](#def-g9-alternator-alternator) (rotation to electricity, by induction), spun by a turbine (steam or water’s motion), fed by a store — say the dam’s lifted lake, lifted by the Sun’s evaporation. So the year-nine sentence: the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) in your room is sunshine — stored, fallen, spun and shipped.

## 69.5 Problem: Night Shift at the Station

**Problem 69.1.**

Weekend problem — night shift at the hydroelectric station; induction, lockstep and the storm; the engineer’s log

You [shadow](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-shadow) the night engineer at the valley’s dam — lake above, town below, [alternators](#def-g9-alternator-alternator) humming between.

**Part I — The machine hall.**

1. The engineer opens a gate: water thunders through turbine three, and its [alternator](#def-g9-alternator-alternator) ’s meters wake. Write the [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) chain from lake to busbar.
2. Inside the [alternator](#def-g9-alternator-alternator) , what moves and what stands still — and why must something move at all?
3. The grid runs at $50\,\mathrm{Hz}$ . The engineer watches a dial keeping turbine three at exactly the matching rotation. What goes wrong at the wrong [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula) ? (What would its [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) ’s [frequency](https://one-course.com/books/physics/1/en/chapter/62-sound-speed-pitch-loudness#def-g8-sound-pitch-loudness-frequency) do?)
4. A trainee asks whether a stronger [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) in the rotor would give “free” extra [power](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-power) . Correct the dream with the dynamo’s honest price.

**Part II — The town’s demand.**

5. At 03:00 the town draws $2 \times 10^{7}\,\mathrm{W}$ . At the transport line’s $200\,000\,\mathrm{V}$ , what current leaves the station?
6. The same [power](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-power) at $230\,\mathrm{V}$ would need what current — and what does the comparison say about the transformer’s job?
7. At 07:00, kettles and heaters wake: demand doubles. What must the engineer feed the turbines more of, and what would happen to the grid’s [frequency](https://one-course.com/books/physics/1/en/chapter/62-sound-speed-pitch-loudness#def-g8-sound-pitch-loudness-frequency) if she fed too little? (The machines slow under load, like a cyclist on a hill.)
8. The station’s sister plant — a [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind) farm on the ridge — drops out as the [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind) dies. Which box of its chain failed, and which boxes stood entirely healthy?

**Part III — The storm.**

9. Lightning severs a transport line; breakers fire. The engineer reroutes [power](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-power) along neighboring lines. What property of the grid — one great parallel network — makes rerouting possible?
10. During the scramble, a warehouse’s [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) dim brown for a minute. Interpret: what sagged, and what were the warehouse’s [motors](https://one-course.com/books/physics/1/en/chapter/41-electric-circuits-and-safety#ex-g6-circuits-and-safety-motor) and lamps briefly underfed?
11. Dawn: the log must explain to the trainees why the whole night’s electricity was, at origin, sunshine. Draft the two-line explanation (lake, evaporation, rain).
12. Final line of the log, by tradition: the night’s physics in one sentence — motion, magnetism, and the town’s morning kettle in it.

**Solution of Problem 69.1.**

**1.** Lake’s height $\to$ water’s rushing motion $\to$ turbine’s rotation $\to$ [alternator](#def-g9-alternator-alternator)’s induced alternating [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) $\to$ the station’s busbar. **2.** The rotor [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) spins; the coils stand fixed. Without motion, no change of magnetism through the coils — and without change, induction gives nothing at all. **3.** The [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage)’s [frequency](https://one-course.com/books/physics/1/en/chapter/62-sound-speed-pitch-loudness#def-g8-sound-pitch-loudness-frequency) copies the rotation: wrong [speed](https://one-course.com/books/physics/1/en/chapter/52-motion-graphs-and-average-speed#def-g7-motion-average-speed-formula), wrong [frequency](https://one-course.com/books/physics/1/en/chapter/62-sound-speed-pitch-loudness#def-g8-sound-pitch-loudness-frequency) — and a machine out of step with the grid’s $50\,\mathrm{Hz}$ fights every other [alternator](#def-g9-alternator-alternator) on the network instead of helping them. **4.** A stronger rotor [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) does induce more — and the turbine immediately labors harder to keep it spinning against the stiffer magnetic drag: more electricity out demands more water through, [joule](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) for [joule](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule). The lake, not the [magnet](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet), pays. **5.** $I = 2 \times 10^{7} \div 2 \times 10^{5} = 100\,\mathrm{A}$. **6.** $I = 2 \times 10^{7} \div 230 \approx 8.7 \times 10^{4}\,\mathrm{A}$ — eighty-seven thousand [amperes](https://one-course.com/books/physics/1/en/chapter/55-current-intensity-and-the-ammeter#def-g8-intensity-ammeter-intensity): impossible cable. The transformer’s job is exactly this exchange — [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) up, current down, [power](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-power) unchanged. **7.** More water through the gates. Underfed, the loaded machines slow like a cyclist on a hill — and the grid’s [frequency](https://one-course.com/books/physics/1/en/chapter/62-sound-speed-pitch-loudness#def-g8-sound-pitch-loudness-frequency) sags below fifty: the network’s clocks and machines all feel a hungry grid. **8.** The first box only — the [wind](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-wind), the blades’ push. Turbine, [alternator](#def-g9-alternator-alternator) and transformer stood perfectly healthy, becalmed. **9.** The grid is one great parallel network: many roads join every station to every town, so a severed line’s share can flow by the surviving [branches](https://one-course.com/books/physics/1/en/chapter/30-series-and-parallel-circuits#def-g5-series-parallel-circuits-parallel) — parallel independence, at national scale. **10.** The rerouted, overloaded lines let the delivered [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) sag below nominal for a minute: the warehouse’s lamps dimmed and its [motors](https://one-course.com/books/physics/1/en/chapter/41-electric-circuits-and-safety#ex-g6-circuits-and-safety-motor) turned lazily — underfed, as any device below its [nominal voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-nominal) must be. **11.** “Tonight’s every [watt](https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy#def-g9-electric-power-energy-power) came from falling lake water; the Sun evaporated the sea and the rain carried it to our mountains. We spin sunshine here — stored in a lake, by way of the sky.” **12.** For example: “Motion past [magnets](https://one-course.com/books/physics/1/en/chapter/6-magnets#def-g1-magnets-magnet) made every [volt](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) of the night — and at seven, ten thousand kettles asked the lake to fall a little faster.”