---
title: "Electric Power and Energy"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 68
exercises: 12
source: https://one-course.com/books/physics/1/en/chapter/68-electric-power-and-energy
---

# Chapter 68 — Electric Power and Energy

The electricity bill does not charge for [volts](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage), nor for [amperes](https://one-course.com/books/physics/1/en/chapter/55-current-intensity-and-the-ammeter#def-g8-intensity-ammeter-intensity) — it charges for something your family’s appliances have been quietly multiplying together all month. This chapter weds the two electrical quantities into a third, gives fast and slow spending their proper names, and ends at the meter by the front door: physics you can audit against real money.

## 68.1 Power: the rate of delivery

**Definition 68.1 (Power and the watt).**

The *power* $P$ of a device is the rate at which it converts [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) — [joules](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) per second. Its [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) is the *watt* ($\mathrm{W}$): one [joule](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) each second, honoring the engineer of the steam age; the *kilowatt* ($1\,\mathrm{kW}$ $=$ $1000\,\mathrm{W}$) serves the kitchen’s heavyweights. Power is not an amount of [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) but a *pace* of spending — a tap’s flow, not a bucket’s content.

**Proposition 68.2 (Electric power).**

A device fed [voltage](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) $U$ and drawing current $I$ receives electric [power](#def-g9-electric-power-energy-power)

$$
P = U \times I ,
$$

[watts](#def-g9-electric-power-energy-power) from [volts](https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter#def-g8-voltage-voltmeter-voltage) times [amperes](https://one-course.com/books/physics/1/en/chapter/55-current-intensity-and-the-ammeter#def-g8-intensity-ammeter-intensity). The formula computes in all three directions, and its second recipe runs the [fuse](https://one-course.com/books/physics/1/en/chapter/48-short-circuits-and-electrical-safety#def-g7-short-circuits-safety-fuse) box: $I = P/U$ tells what current an appliance’s rated [power](#def-g9-electric-power-energy-power) will pull from the mains.

**Example 68.3 (The household ladder).**

Read the plates on the family’s machines: an indicator [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source), $1\,\mathrm{W}$; a modern lamp, $5\,\mathrm{W}$ (its glowing ancestor spent sixty for the same [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) — the difference was [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat)); a laptop, $50\,\mathrm{W}$; a television, $100\,\mathrm{W}$; a washing machine heating its water, $2000\,\mathrm{W}$; the kettle, $2300\,\mathrm{W}$; an instant water heater, up to $9000\,\mathrm{W}$. The pattern of the ladder: anything whose job is *heating* climbs to the kilowatts — warmth is the costliest form of [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) to supply.

**Example 68.4 (The fuse box arithmetic).**

The kettle on the $230\,\mathrm{V}$ mains: $I = 2300 \div 230 =
10\,\mathrm{A}$ — the [ten-ampere](https://one-course.com/books/physics/1/en/chapter/55-current-intensity-and-the-ammeter#def-g8-intensity-ammeter-intensity) appliance of the old chapters, now derived. The $9000\,\mathrm{W}$ water heater: nearly $40\,\mathrm{A}$, demanding its own stout [branch](https://one-course.com/books/physics/1/en/chapter/30-series-and-parallel-circuits#def-g5-series-parallel-circuits-parallel) and breaker. And the overloaded multi-socket of the fire investigation: kettle, heater and fryer summing their $P/U$ currents past the [branch](https://one-course.com/books/physics/1/en/chapter/30-series-and-parallel-circuits#def-g5-series-parallel-circuits-parallel)’s rating — three innocents, one arithmetic crime, exactly as charged.

## 68.2 Energy: the amount delivered

**Proposition 68.5 (Energy from power and time).**

A device of [power](#def-g9-electric-power-energy-power) $P$ running for a time $t$ converts the [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy)

$$
E = P \times t ,
$$

[joules](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) from [watts](#def-g9-electric-power-energy-power) times seconds. Fast tap or long trickle, the bucket fills by the product: a $2300\,\mathrm{W}$ kettle’s three minutes ($2300 \times 180 \approx 4.1 \times 10^{5}\,\mathrm{J}$) spends more than a $5\,\mathrm{W}$ lamp’s whole day ($5 \times
86400 = 4.3 \times 10^{5}\,\mathrm{J}$) — almost exactly a tie, in fact: one boiling matches one day of good [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source).

**Definition 68.6 (The kilowatt-hour).**

Household energies make ungainly joule-counts, so the meter speaks *kilowatt-hours* ($\mathrm{kWh}$): the [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) of one kilowatt sustained for one hour,

$$
1\,\mathrm{kWh} = 1000 \times 3600 = 3.6 \times 10^{6}\,\mathrm{J}
$$

— three point six million [joules](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) per [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) on the bill. With $P$ in kilowatts and $t$ in [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock), $E = P \times t$ delivers [kilowatt-hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) directly: the formula the meter lives by.

**Method 68.7 (Auditing an appliance).**

For any machine and month:

1. read its [power](#def-g9-electric-power-energy-power) $P$ on the plate (or compute $U \times I$ );
2. honestly estimate its running time $t$ — per day, then per month;
3. $E = P \times t$ in [kilowatt-hours](#def-g9-electric-power-energy-kwh) ( $P$ in $\mathrm{kW}$ , $t$ in [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) );
4. multiply by the tariff (take about $0.25$ currency [units](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) per $\mathrm{kWh}$ ) for the month’s cost.

The kettle, six minutes daily: $2.3 \times 0.1 \times 30 =
6.9\,\mathrm{kWh}$ a month. The television, three [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) daily: $0.1 \times 3 \times 30 = 9\,\mathrm{kWh}$. Small [powers](#def-g9-electric-power-energy-power) with long [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) rival big [powers](#def-g9-electric-power-energy-power) with short ones — the audit’s recurring lesson.

![Energy as area: power times time. The kettle’s tall sliver and the television evening’s long strip can enclose comparable areas — comparable kilowatt-hours.](https://one-course.com/images/onecourse/chapters/physics-1/g9-electric-power-energy/fig-9fc94c373a29.svg)

*[Energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) as area: [power](#def-g9-electric-power-energy-power) times time. The kettle’s tall sliver and the television evening’s long strip can enclose comparable areas — comparable [kilowatt-hours](#def-g9-electric-power-energy-kwh).*

## 68.3 The meter and the bill

**Example 68.8 (Reading the bill).**

The meter by the front door counts every [kilowatt-hour](#def-g9-electric-power-energy-kwh) that enters the house; the bill is its month’s difference times the tariff. A typical family’s $250$ monthly [units](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) decompose by audit: water heating and radiators first (the kilowatt club), then the cold appliances — modest [watts](#def-g9-electric-power-energy-power), but running always — then cooking, washing, [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) and electronics. The audit’s [power](#def-g9-electric-power-energy-power): it finds the real [levers](https://one-course.com/books/physics/1/en/chapter/17-levers-and-balance-scales#def-g3-levers-and-scales-lever). Replacing ten old $60\,\mathrm{W}$ [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) with $5\,\mathrm{W}$ ones saves more than unplugging every charger in the house a thousand times over.

**Example 68.9 (The standby vampires).**

Small print, long [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock): a television’s standby [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) sips $0.5\,\mathrm{W}$ — but for all $720$ [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) of the month: $0.0005 \times 720 = 0.36\,\mathrm{kWh}$. One vampire is harmless; a house with twenty sippers at a [watt](#def-g9-electric-power-energy-power) each pays $0.02 \times 720 \approx 14\,\mathrm{kWh}$ monthly for nothing. [Power](#def-g9-electric-power-energy-power) times time forgives no term: the second factor bites when the first one hides.

**Remark 68.10 (Power in the wider world).**

The [watt](#def-g9-electric-power-energy-power), born electric here, [measures](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) every [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) pace. Your resting body idles near $100\,\mathrm{W}$ — a glowing [ancestor-bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) of warmth (recall the crowded classroom’s stuffiness: thirty pupils, three kilowatts of biology). A cyclist sustains $200\,\mathrm{W}$; a car’s engine unleashes tens of kilowatts; the town’s power station, hundreds of millions of [watts](#def-g9-electric-power-energy-power); the sunlight falling on the town, comfortably more — the ceiling under which all the other paces work. Next chapter follows the grid’s [watts](#def-g9-electric-power-energy-power) to their spinning source.

## 68.4 Exercises

**Exercise 68.1 ★.**

Define [power](#def-g9-electric-power-energy-power) and its [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) — tap or bucket? Write both formulas of the chapter.

**Solution of Exercise 68.1.**

[Power](#def-g9-electric-power-energy-power) is the pace of [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) conversion — [joules](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) per second, in [watts](#def-g9-electric-power-energy-power): the tap’s flow, not the bucket. $P = U \times I$ and $E = P \times t$.

**Exercise 68.2 ★.**

Compute [powers](#def-g9-electric-power-energy-power): a lamp at $230\,\mathrm{V}$ drawing $0.022\,\mathrm{A}$; a starter [motor](https://one-course.com/books/physics/1/en/chapter/41-electric-circuits-and-safety#ex-g6-circuits-and-safety-motor) at $12\,\mathrm{V}$ drawing $100\,\mathrm{A}$.

**Solution of Exercise 68.2.**

Lamp: $230 \times 0.022 \approx 5\,\mathrm{W}$. Starter: $12
\times 100 = 1200\,\mathrm{W}$.

**Exercise 68.3 ★.**

The fuse-box recipe: what currents do a $2300\,\mathrm{W}$ kettle and a $700\,\mathrm{W}$ microwave pull at $230\,\mathrm{V}$?

**Solution of Exercise 68.3.**

Kettle: $2300 \div 230 = 10\,\mathrm{A}$; microwave: $700 \div
230 \approx 3\,\mathrm{A}$.

**Exercise 68.4 ★.**

Why do heating appliances crowd the top of the household [power](#def-g9-electric-power-energy-power) ladder?

**Solution of Exercise 68.4.**

Because warmth is the costliest form of [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) to supply: raising water’s or a room’s [temperature](https://one-course.com/books/physics/1/en/chapter/15-temperature-and-thermometers#def-g3-temperature-thermometers-temperature) devours [joules](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) at a pace lamps and electronics never approach — so every heater’s plate reads in kilowatts.

**Exercise 68.5 ★.**

Convert: $1\,\mathrm{kWh}$ to [joules](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) (show the two factors). Why did the meter’s makers abandon the [joule](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule)?

**Solution of Exercise 68.5.**

$1\,\mathrm{kWh} = 1000 \, \text{W} \times 3600 \, \text{s} =
3.6 \times 10^{6}\,\mathrm{J}$. A month of [joules](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) runs to ten digits; the meter’s makers chose a [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) that keeps household months in comfortable hundreds.

**Exercise 68.6 ★.**

[Energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) check: which spends more, a $2\,\mathrm{kW}$ heater for half an hour or a $100\,\mathrm{W}$ television for a whole evening of five [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock)?

**Solution of Exercise 68.6.**

Heater: $2 \times 0.5 = 1\,\mathrm{kWh}$. Television: $0.1
\times 5 = 0.5\,\mathrm{kWh}$. The half-hour heater outspends the whole television evening, twofold.

**Exercise 68.7 ★.**

Audit one machine: a $50\,\mathrm{W}$ laptop used four [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) daily, for a thirty-day month, at $0.25$ per $\mathrm{kWh}$. [Energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) and cost?

**Solution of Exercise 68.7.**

$E = 0.05 \times 4 \times 30 = 6\,\mathrm{kWh}$; cost $6 \times
0.25 = 1.5$ currency [units](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) — a month of homework for the price of a pastry.

**Exercise 68.8 ★.**

What does the front-door meter count, and how does the bill turn its count into money?

**Solution of Exercise 68.8.**

Every [kilowatt-hour](#def-g9-electric-power-energy-kwh) entering the house. The bill subtracts last month’s reading from this month’s and multiplies the difference by the tariff.

**Exercise 68.9 ★★.**

The [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) swap: ten $60\,\mathrm{W}$ ancestors versus ten $5\,\mathrm{W}$ moderns, four [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) nightly, thirty nights. Compute both monthly energies and the saving — in [kilowatt-hours](#def-g9-electric-power-energy-kwh) and at $0.25$ each.

**Solution of Exercise 68.9.**

Ancestors: $0.6 \times 4 \times 30 = 72\,\mathrm{kWh}$. Moderns: $0.05 \times 4 \times 30 = 6\,\mathrm{kWh}$. Saving: $66\,\mathrm{kWh}$ — $16.5$ currency [units](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) monthly, from one afternoon on a stepladder.

**Exercise 68.10 ★★.**

A hair dryer’s plate reads “230 V, 2000 W”. Its current? May it share a $16\,\mathrm{A}$ [branch](https://one-course.com/books/physics/1/en/chapter/30-series-and-parallel-circuits#def-g5-series-parallel-circuits-parallel) with the $2300\,\mathrm{W}$ kettle, both running? Show the sum.

**Solution of Exercise 68.10.**

Dryer: $2000 \div 230 \approx 8.7\,\mathrm{A}$. With the kettle’s $10\,\mathrm{A}$: $18.7$ — past the $16\,\mathrm{A}$ [branch](https://one-course.com/books/physics/1/en/chapter/30-series-and-parallel-circuits#def-g5-series-parallel-circuits-parallel)’s rating: the breaker will (rightly) end the experiment.

**Exercise 68.11 ★★.**

An electric car’s [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) stores $60\,\mathrm{kWh}$. How long could that run the $2.3\,\mathrm{kW}$ kettle? The $5\,\mathrm{W}$ lamp? And what does the pair of answers teach about the size of transport’s [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) appetite?

**Solution of Exercise 68.11.**

Kettle: $60 \div 2.3 \approx 26$ [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock). Lamp: $60 \div
0.005 = 12000$ [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) — a year and four months. Yet the same store drives the car only a few hundred kilometres: moving a tonne of machine devours [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) on a scale beside which household lighting is a rounding error.

**Exercise 68.12 ★★★.**

The kettle test, end to end: $1.5\,\mathrm{L}$ of water from $20\,{}^{\circ}\mathrm{C}$ to the boil needs about $5.0 \times 10^{5}\,\mathrm{J}$ of [heat](https://one-course.com/books/physics/1/en/chapter/34-heat-and-insulation#def-g5-heat-and-insulation-heat). Time the family kettle ($2300\,\mathrm{W}$): predict its boiling time from $E = P t$, then explain why the real kettle takes a little longer — where do the missing [joules](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) go, by the oldest law of the [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) chapters?

**Solution of Exercise 68.12.**

Prediction: $t = E/P = 5.0 \times 10^{5} \div 2300 \approx
217\,\mathrm{s}$ — about three and a half minutes. The real kettle runs longer: part of its [joules](https://one-course.com/books/physics/1/en/chapter/66-kinetic-energy-and-road-safety#def-g9-kinetic-energy-safety-joule) leak past the water — warming the kettle’s own body, the [air](https://one-course.com/books/physics/1/en/chapter/10-air-around-us#def-g2-air-around-us-air), escaping as early steam. [Energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) is never destroyed, but neither is it all delivered where intended: the chain’s leak, timed at last in your own kitchen.

## 68.5 Problem: The Home Energy Audit

**Problem 68.1.**

Weekend problem — the family energy audit; plates, meters and the month’s bill; finding the real levers

Armed with the two formulas and the tariff ($0.25$ per $\mathrm{kWh}$), the family audits a month (30 days). The inventory: kettle $2300\,\mathrm{W}$, $6$ minutes daily; television $100\,\mathrm{W}$, $4$ [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) daily; refrigerator — special case below; ten lamps $5\,\mathrm{W}$ each, $5$ [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) daily; washing machine $2\,\mathrm{kW}$, one $1$-hour hot cycle every other day; water heater $2.5\,\mathrm{kW}$, $2$ [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) daily; standby sippers totaling $10\,\mathrm{W}$, always on.

**Part I — Machine by machine.**

1. The kettle’s month, in $\mathrm{kWh}$ .
2. The television’s and the ten lamps’ months.
3. The washing machine’s ( $15$ cycles) and the water heater’s months.
4. The standby sippers’ month — the second factor at work.

**Part II — The refrigerator and the sum.** The refrigerator’s compressor runs at $120\,\mathrm{W}$, but only a third of the time, cycling day and night.

5. Its effective average [power](#def-g9-electric-power-energy-power) , and its month in $\mathrm{kWh}$ .
6. Total the audit’s seven lines. Which three lines dominate?
7. The month’s bill at the tariff — and the water heater’s share of it in currency.
8. The meter read $2150$ [units](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) at the month’s start. Predict its end-of-month reading.

**Part III — The [levers](https://one-course.com/books/physics/1/en/chapter/17-levers-and-balance-scales#def-g3-levers-and-scales-lever).**

9. Proposal one: shorter showers — the heater drops to $1.5\,\mathrm{h}$ daily. Monthly saving, [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) and money?
10. Proposal two: a public campaign urges unplugging phone chargers ( $0.2\,\mathrm{W}$ each when idle). Audit one charger’s idle month and compare with proposal one; what does the contrast teach about audits versus slogans?
11. Proposal three: grandmother suggests the old habit of filling the kettle only as needed — half the water, half the [energy](https://one-course.com/books/physics/1/en/chapter/29-energy-in-everyday-life#def-g5-everyday-energy-energy) . New kettle line, and the month’s saving?
12. Write the audit’s conclusions: three sentences — where the [kilowatt-hours](#def-g9-electric-power-energy-kwh) truly live, which formula factor the standby case teaches, and which single household change pays best.

**Solution of Problem 68.1.**

**1.** $2.3 \times 0.1 \times 30 = 6.9\,\mathrm{kWh}$. **2.** Television: $0.1 \times 4 \times 30 =
12\,\mathrm{kWh}$; lamps: $0.05 \times 5 \times 30 =
7.5\,\mathrm{kWh}$. **3.** Washer: $2 \times 1 \times 15 = 30\,\mathrm{kWh}$; heater: $2.5 \times 2 \times 30 = 150\,\mathrm{kWh}$. **4.** $0.010 \times 720 = 7.2\,\mathrm{kWh}$ — ten hidden [watts](#def-g9-electric-power-energy-power), a kettle’s whole month. **5.** Average $120 \div 3 = 40\,\mathrm{W}$; month: $0.04 \times 720 = 28.8\,\mathrm{kWh}$. **6.** Total $\approx 242\,\mathrm{kWh}$. Dominant: the water heater ($150\,$), the washer ($30\,$), the refrigerator ($28.8\,\mathrm{kWh}$) — heating and always-on. **7.** $242 \times 0.25 \approx 60.6$ [units](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring); the heater’s share: $150 \times 0.25 = 37.5$ — well over half the bill. **8.** $2150 + 242 = 2392$ [units](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring). **9.** New heater line: $2.5 \times 1.5 \times 30 =
112.5\,\mathrm{kWh}$: saving $37.5\,\mathrm{kWh}$, about $9.4$ [units](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) of currency monthly. **10.** One idle charger: $0.0002 \times 720 =
0.14\,\mathrm{kWh}$ — about four hundredths of a currency [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring): proposal one outsaves it two-hundredfold per charger. Audits find [levers](https://one-course.com/books/physics/1/en/chapter/17-levers-and-balance-scales#def-g3-levers-and-scales-lever); slogans find chargers. **11.** Kettle line halves to $3.45\,\mathrm{kWh}$: saving $3.45\,\mathrm{kWh}$, under one currency [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) — grandmother’s habit is right, and modest. **12.** For example: “The [kilowatt-hours](#def-g9-electric-power-energy-kwh) live where water gets hot and where machines never sleep. The standby line teaches the time factor: tiny [powers](#def-g9-electric-power-energy-power) grow bills when $t$ is always. And the best-paying change is the shorter shower — the heater owns the bill, so its [hours](https://one-course.com/books/physics/1/en/chapter/8-measuring-time#ex-g2-measuring-time-clock) own the savings.”