---
title: "Voltage and the Voltmeter"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 56
exercises: 12
source: https://one-course.com/books/physics/1/en/chapter/56-voltage-and-the-voltmeter
---

# Chapter 56 — Voltage and the Voltmeter

Since the first [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) lit the first [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb), one word has done heavy, vague duty in this book: the “push”. Batteries push weakly, the mains pushes murderously, two batteries nose-to-tail push together. The push now becomes a measured quantity with a famous [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) — and its instrument, unlike last chapter’s, refuses to stand in the road.

## 56.1 Voltage

**Definition 56.1 (Voltage).**

The *voltage* $U$ between two points of a circuit [measures](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) the electrical push available between them — how hard the current is driven from one point to the other, as a waterfall’s height [measures](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) how hard it drives the millwheel. Voltage is always a *between*: between the two [terminals](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) of a [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery), between the two sides of a lamp — never at a single point alone. 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 *volt* ($\mathrm{V}$), honoring the inventor of the first [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery).

**Example 56.2 (The volt family album).**

A single round cell: $1.5\,\mathrm{V}$. The flat pocket [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery): $4.5\,\mathrm{V}$ — three cells nose-to-tail inside one wrapper. The rectangular [nine-volt](#def-g8-voltage-voltmeter-voltage) with both [terminals](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) on top: $9\,\mathrm{V}$, six hidden cells. A car [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery): $12\,\mathrm{V}$. The wall socket: $230\,\mathrm{V}$ — more than a hundred and fifty little cells’ worth of push, which is the whole quantitative content of “the socket, never”. Lightning between cloud and ground: hundreds of millions of [volts](#def-g8-voltage-voltmeter-voltage), briefly.

**Proposition 56.3 (Voltage without current).**

[Voltage](#def-g8-voltage-voltmeter-voltage) and current are different quantities, and [voltage](#def-g8-voltage-voltmeter-voltage) comes first. A [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) alone in a drawer, wired to nothing, drives no current at all — yet between its [terminals](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) the full $1.5\,\mathrm{V}$ stands ready, measurable, like a waterfall’s height on a day the mill is closed. Push can exist without a march; the march never exists without a push.

**Definition 56.4 (Voltmeter).**

A *voltmeter* [measures](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) the [voltage](#def-g8-voltage-voltmeter-voltage) between two points — so it is connected *across* them: *[in parallel](https://one-course.com/books/physics/1/en/chapter/30-series-and-parallel-circuits#def-g5-series-parallel-circuits-parallel)* with the component of interest, one lead on each side, like a surveyor holding a level between two heights. Built opposite to the [ammeter](https://one-course.com/books/physics/1/en/chapter/55-current-intensity-and-the-ammeter#def-g8-intensity-ammeter-ammeter) in every way, it opposes current almost *completely*: connected across anything, it draws next to none — so clipping it on disturbs nothing, and no loop need ever be broken.

![The voltmeter takes the surveyor’s stance: across the lamp, one lead each side, measuring the push between — and never standing in the road.](https://one-course.com/images/onecourse/chapters/physics-1/g8-voltage-voltmeter/fig-6dae37cb0dd6.svg)

*The [voltmeter](#def-g8-voltage-voltmeter-voltmeter) takes the surveyor’s stance: across the lamp, one lead each side, measuring the push between — and never standing in the road.*

**Method 56.5 (Measuring a voltage).**

1. leave the circuit intact — nothing is broken for a [voltmeter](#def-g8-voltage-voltmeter-voltmeter) ;
2. clip one lead to each side of the component: the $\mathrm{V}$ lead where the conventional current enters, the common lead where it leaves;
3. largest range first, step down to comfort;
4. read, and write the [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) .

The two meters’ manners, side by side: [ammeter](https://one-course.com/books/physics/1/en/chapter/55-current-intensity-and-the-ammeter#def-g8-intensity-ammeter-ammeter) — break the road, stand in it, oppose nothing; [voltmeter](#def-g8-voltage-voltmeter-voltmeter) — break nothing, stand aside, oppose everything. Confusing the two manners is the workshop’s most expensive habit.

## 56.2 Rated voltages

**Definition 56.6 (Nominal voltage).**

Every lamp, [motor](https://one-course.com/books/physics/1/en/chapter/41-electric-circuits-and-safety#ex-g6-circuits-and-safety-motor) and appliance carries a *nominal voltage* — the push it is built for, stamped on its base or plate: a flashlight [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) “3.5 V”, a car headlamp “12 V”, a kettle “230 V”. Fed its nominal [voltage](#def-g8-voltage-voltmeter-voltage), the device performs as designed; fed much less, it sulks — dim lamp, lazy [motor](https://one-course.com/books/physics/1/en/chapter/41-electric-circuits-and-safety#ex-g6-circuits-and-safety-motor); fed much more, it burns out — brilliantly, once.

**Example 56.7 (Matching lamp to battery).**

A “3.5 V” [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) on the $4.5\,\mathrm{V}$ flat [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery): slightly overdriven — bright, and short-lived. On a single $1.5\,\mathrm{V}$ cell: a sleepy orange glow. On the $9\,\mathrm{V}$ [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery): one dazzling instant, then the thin thread parts — the filament’s obituary. The label is a contract: honor it, and the lamp lives its advertised life.

**Remark 56.8 (Why 230 V kills).**

Now the old absolute rule gets its number. The body’s damp conducting road, offered $4.5\,\mathrm{V}$, passes a current too small to feel. The same road at $230\,\mathrm{V}$ — fifty times the push — passes fifty times the current, well past the few hundredths of an [ampere](https://one-course.com/books/physics/1/en/chapter/55-current-intensity-and-the-ammeter#def-g8-intensity-ammeter-intensity) that stop a heart. The socket is not “somewhat” stronger than your [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) bench: it is two orders of magnitude beyond it, and the rulebook’s severity is plain arithmetic.

## 56.3 First voltage readings

**Example 56.9 (Around a simple loop).**

One [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery), one lamp, meters in hand. Across the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery): $4.5\,\mathrm{V}$. Across the lamp: $4.5\,\mathrm{V}$ — the lamp receives what the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) offers. Across a stretch of connecting *wire*: $0\,\mathrm{V}$, or as near as the meter can say — a good wire is a level road, spending none of the push. The push lives across the *workers*, not along the roads: a reading worth remembering when next chapter’s laws make it official.

**Example 56.10 (The open switch’s confession).**

Lamp dark, [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) open — where did the push go? Measure: across the dark lamp, $0\,\mathrm{V}$; across the *open [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch)*, the full $4.5\,\mathrm{V}$. The [battery’s](https://one-course.com/books/physics/1/en/chapter/48-short-circuits-and-electrical-safety#def-g7-short-circuits-safety-battery) push stands entire across the gap, waiting — the one place in the loop where two points are truly “far apart” electrically. Close the [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) and the readings trade places. An open [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) is where the [voltage](#def-g8-voltage-voltmeter-voltage) waits.

## 56.4 Exercises

**Exercise 56.1 ★.**

What does [voltage](#def-g8-voltage-voltmeter-voltage) [measure](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring), and why is it always “between”? Give its [unit](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) and the waterfall [image](https://one-course.com/books/physics/1/en/chapter/32-mirrors-and-reflection#prop-g5-mirrors-reflection-image).

**Solution of Exercise 56.1.**

The electrical push available between two points — like a waterfall’s height between its top and bottom driving the millwheel. Being a difference, it needs two points; 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 [volt](#def-g8-voltage-voltmeter-voltage), $\mathrm{V}$.

**Exercise 56.2 ★.**

From memory: the [voltages](#def-g8-voltage-voltmeter-voltage) of a round cell, the flat [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery), the rectangular [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery), a car [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery), the mains.

**Solution of Exercise 56.2.**

$1.5\,\mathrm{V}$; $4.5\,\mathrm{V}$; $9\,\mathrm{V}$; $12\,\mathrm{V}$; $230\,\mathrm{V}$.

**Exercise 56.3 ★.**

A [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) lies wired to nothing. What current flows? What does a [voltmeter](#def-g8-voltage-voltmeter-voltmeter) across it read? Which proposition speaks?

**Solution of Exercise 56.3.**

No current at all — no loop. The [voltmeter](#def-g8-voltage-voltmeter-voltmeter) reads the full $1.5\,\mathrm{V}$: [voltage](#def-g8-voltage-voltmeter-voltage) without current — push can wait; the march cannot start without it.

**Exercise 56.4 ★.**

Contrast the two meters’ manners: connection, road-breaking, opposition to current. Which mistake builds a [short circuit](https://one-course.com/books/physics/1/en/chapter/48-short-circuits-and-electrical-safety#def-g7-short-circuits-safety-device) with a dial?

**Solution of Exercise 56.4.**

[Ammeter](https://one-course.com/books/physics/1/en/chapter/55-current-intensity-and-the-ammeter#def-g8-intensity-ammeter-ammeter): [in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series), the road broken for it, opposing almost nothing. [Voltmeter](#def-g8-voltage-voltmeter-voltmeter): [in parallel](https://one-course.com/books/physics/1/en/chapter/30-series-and-parallel-circuits#def-g5-series-parallel-circuits-parallel), nothing broken, opposing almost everything. The expensive mistake: an [ammeter](https://one-course.com/books/physics/1/en/chapter/55-current-intensity-and-the-ammeter#def-g8-intensity-ammeter-ammeter) wired across — [in parallel](https://one-course.com/books/physics/1/en/chapter/30-series-and-parallel-circuits#def-g5-series-parallel-circuits-parallel) — becomes a [short circuit](https://one-course.com/books/physics/1/en/chapter/48-short-circuits-and-electrical-safety#def-g7-short-circuits-safety-device) with a dial.

**Exercise 56.5 ★.**

What is a [nominal voltage](#def-g8-voltage-voltmeter-nominal)? Predict a “6 V” lamp’s behavior on $1.5\,\mathrm{V}$; on $6\,\mathrm{V}$; on $12\,\mathrm{V}$.

**Solution of Exercise 56.5.**

The push a device is built for. On $1.5\,\mathrm{V}$: a sleepy glimmer. On $6\,\mathrm{V}$: designed brightness and lifespan. On $12\,\mathrm{V}$: one brilliant instant, then the filament parts.

**Exercise 56.6 ★.**

In the simple loop, what does the [voltmeter](#def-g8-voltage-voltmeter-voltmeter) read across the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery), the lamp, and a stretch of wire? Where does the push live?

**Solution of Exercise 56.6.**

[Battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery): $4.5\,\mathrm{V}$; lamp: $4.5\,\mathrm{V}$; wire: about $0\,\mathrm{V}$. The push lives across the workers — the wire is a level road.

**Exercise 56.7 ★.**

[Switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) open: what stands across the dark lamp, and across the open [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch)? What happens to both readings at the click?

**Solution of Exercise 56.7.**

Dark lamp: $0\,\mathrm{V}$; open [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch): the full $4.5\,\mathrm{V}$, waiting across the gap. At the click they trade places: the closed [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) drops to about zero, the lit lamp takes up the $4.5\,\mathrm{V}$.

**Exercise 56.8 ★.**

Why does clipping a [voltmeter](#def-g8-voltage-voltmeter-voltmeter) across a working lamp disturb the circuit almost not at all? What does the meter decline to do?

**Solution of Exercise 56.8.**

It declines to carry current: opposing almost completely, it sips next to none through itself, so the lamp’s march and glow continue as if unobserved.

**Exercise 56.9 ★★.**

The flat $4.5\,\mathrm{V}$ [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) hides three cells. Draw (or describe) their arrangement, and compute the [voltage](#def-g8-voltage-voltmeter-voltage) if one cell were accidentally reversed — the flashlight chapter of years ago now with numbers. (Opposed pushes subtract.)

**Solution of Exercise 56.9.**

Three cells nose-to-tail: $1.5 + 1.5 + 1.5 = 4.5\,\mathrm{V}$. One reversed opposes the other two: $1.5 + 1.5 - 1.5 = 1.5\,\mathrm{V}$ — the flashlight mystery of years ago, now in [volts](#def-g8-voltage-voltmeter-voltage).

**Exercise 56.10 ★★.**

A camper’s lamp is rated $12\,\mathrm{V}$; the van’s [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) reads $12.6\,\mathrm{V}$ fresh and $11.2\,\mathrm{V}$ after a long evening. Describe the lamp’s evening, and why nothing burned out.

**Solution of Exercise 56.10.**

Fresh [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery): a shade over nominal — full cheerful brightness. As the evening drains the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) toward $11.2\,\mathrm{V}$, the lamp dims gently below its designed glow. Nothing burned: the [voltage](#def-g8-voltage-voltmeter-voltage) only ever sagged *below* nominal; the contract punishes excess, not shortage.

**Exercise 56.11 ★★.**

A [voltmeter](#def-g8-voltage-voltmeter-voltmeter) mistakenly wired *[in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series)* with the lamp (loop broken, meter in the gap): predict the lamp’s behavior and the meter’s reading — remember what a [voltmeter](#def-g8-voltage-voltmeter-voltmeter) opposes. (The lamp’s silence and the meter’s number are both instructive.)

**Solution of Exercise 56.11.**

The [voltmeter](#def-g8-voltage-voltmeter-voltmeter) in the road opposes almost everything: the march all but stops, and the lamp stands dark. The meter, carrying the loop’s only push across itself, reads nearly the [battery’s](https://one-course.com/books/physics/1/en/chapter/48-short-circuits-and-electrical-safety#def-g7-short-circuits-safety-battery) full [voltage](#def-g8-voltage-voltmeter-voltage) — a correct number for a wrongly built circuit: instructive, and no fire.

**Exercise 56.12 ★★★.**

Two identical lamps [in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series) on $4.5\,\mathrm{V}$: a [voltmeter](#def-g8-voltage-voltmeter-voltmeter) finds about $2.25\,\mathrm{V}$ across each. The same lamps [in parallel](https://one-course.com/books/physics/1/en/chapter/30-series-and-parallel-circuits#def-g5-series-parallel-circuits-parallel) on the same [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery): predict each lamp’s [voltage](#def-g8-voltage-voltmeter-voltage), and reconcile both findings with the brightness rules you have known for years (series pairs dim, parallel pairs shine full). Which chapter-to-come will make your predictions law?

**Solution of Exercise 56.12.**

[In parallel](https://one-course.com/books/physics/1/en/chapter/30-series-and-parallel-circuits#def-g5-series-parallel-circuits-parallel) each lamp spans the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) directly: $4.5\,\mathrm{V}$ each — full nominal push, full brightness, as the old parallel rule promised. [In series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series) the two lamps *share* the $4.5\,\mathrm{V}$ — about $2.25\,\mathrm{V}$ each, an underfed pair glowing dim, as the old series rule observed. The chapter after next makes the sharing a law of [voltages](#def-g8-voltage-voltmeter-voltage).

## 56.5 Problem: The Battery Drawer Audit

**Problem 56.1.**

Weekend problem — the great battery drawer audit; a voltmeter, a shoebox of cells, and the family’s gadget shelf

Every house has the drawer: loose cells, mystery batteries, gadgets that “need new ones”. Audit day — [voltmeter](#def-g8-voltage-voltmeter-voltmeter) in hand.

**Part I — Sorting the cells.**

1. Describe the correct [voltmeter](#def-g8-voltage-voltmeter-voltmeter) connection to check a loose $1.5\,\mathrm{V}$ cell — and why no circuit needs building first.
2. The audit’s readings, fresh from the drawer: $1.58\,\mathrm{V}$ , $1.32\,\mathrm{V}$ , $0.9\,\mathrm{V}$ , $0.1\,\mathrm{V}$ . Sort them: fresh, usable, tired, dead.
3. A [nine-volt](#def-g8-voltage-voltmeter-voltage) [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) reads $8.9\,\mathrm{V}$ . Roughly what does each of its six inner cells contribute?
4. Why does a nearly dead cell still show *some* [voltage](#def-g8-voltage-voltmeter-voltage) although it can no longer [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) anything? (Its push survives feebly; what has it lost the strength to drive?)

**Part II — The gadget shelf.**

5. The camera wants two cells nose-to-tail. What [voltage](#def-g8-voltage-voltmeter-voltage) does it expect, and what will the pair of $1.32\,\mathrm{V}$ survivors from question 2 deliver?
6. The old radio takes four cells nose-to-tail and sulks below $5\,\mathrm{V}$ . Which drawer cells, if any, can crew it?
7. Little brother crams three cells into the two-cell torch “for extra brightness”, wedging the third across the spring. The [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) is rated $3\,\mathrm{V}$ . Predict the show, in [nominal-voltage](#def-g8-voltage-voltmeter-voltage) language.
8. The doorbell transformer plate reads “ $8\,\mathrm{V}$ ”. Someone proposes wiring the doorbell straight to a [nine-volt](#def-g8-voltage-voltmeter-voltage) [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) “since eight is almost nine”. Assess: fair match or slow murder?

**Part III — The audit’s laws.**

9. In the torch ( [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) and cells [in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series) , [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) open), the auditor [measures](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) : across the open [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) , $3.1\,\mathrm{V}$ ; across the [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) , $0\,\mathrm{V}$ . Explain both, and predict both after the click.
10. Across every stretch of the torch’s wiring the meter says $0\,\mathrm{V}$ , lit or dark. What does this declare about good wire, in push-language?
11. The mains socket is *not* audited, by standing family law. Restate the law with this chapter’s number, and the arithmetic sentence behind it.
12. File the audit report: three sentences — what a [voltmeter](#def-g8-voltage-voltmeter-voltmeter) is and is never; what a label’s [nominal voltage](#def-g8-voltage-voltmeter-nominal) promises and threatens; and where, in any idle circuit, the [voltage](#def-g8-voltage-voltmeter-voltage) waits.

**Solution of Problem 56.1.**

**1.** Clip the [voltmeter](#def-g8-voltage-voltmeter-voltmeter)’s two leads to the cell’s two [terminals](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) — across, [in parallel](https://one-course.com/books/physics/1/en/chapter/30-series-and-parallel-circuits#def-g5-series-parallel-circuits-parallel); a [voltmeter](#def-g8-voltage-voltmeter-voltmeter) breaks nothing and needs no circuit: it [measures](https://one-course.com/books/physics/1/en/chapter/37-measurement-in-science-units-and-instruments#def-g6-measurement-in-science-measuring) the waiting push. **2.** $1.58\,\mathrm{V}$: fresh. $1.32\,\mathrm{V}$: usable. $0.9\,\mathrm{V}$: tired. $0.1\,\mathrm{V}$: dead — drawer to bin. **3.** About $8.9 \div 6 \approx 1.48\,\mathrm{V}$ each — six healthy cells. **4.** Its chemistry still raises a feeble push, but can no longer drive a useful march: the [voltage](#def-g8-voltage-voltmeter-voltage) survives as a promise the cell lacks the strength to keep under load. **5.** Two nose-to-tail: it expects $2 \times 1.5 =
3\,\mathrm{V}$; the survivors deliver $2 \times 1.32 =
2.64\,\mathrm{V}$ — the camera may work, grumbling. **6.** Four cells must total $5\,\mathrm{V}$ or better: four fresh $1.58$s give $6.3\,\mathrm{V}$ — fine; mixing in the $1.32$s, any crew totaling at least $5\,\mathrm{V}$ serves (e.g. two fresh and two usable: $1.58 \times 2 + 1.32 \times 2 =
5.8\,\mathrm{V}$). The tired and dead need not apply. **7.** Three cells: $4.5\,\mathrm{V}$ onto a $3\,\mathrm{V}$ [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) — half again over nominal: one glorious over-bright evening at best, most likely a prompt burnout. The contract punishes excess. **8.** Slow murder, gentle but real: $9\,\mathrm{V}$ on an $8\,\mathrm{V}$ device is a steady over-push — it will run, warm, and age fast. Nominal means nominal; “almost” is how filaments die young. **9.** The [battery’s](https://one-course.com/books/physics/1/en/chapter/48-short-circuits-and-electrical-safety#def-g7-short-circuits-safety-battery) push waits, entire, across the only true gap — the open [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch); the idle [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb), carrying no current, shows none. After the click: [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) near $0\,\mathrm{V}$, [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) near $3.1\,\mathrm{V}$ — the push moves from the gap to the worker. **10.** That good wire is a level road: it delivers the march without spending push — all the [voltage](#def-g8-voltage-voltmeter-voltage) is saved for the workers. **11.** “The socket is $230\,\mathrm{V}$ — fifty times the strongest [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) in this drawer; fifty times the push drives fifty times the current through the same damp hands, and the heart stops at hundredths of an [ampere](https://one-course.com/books/physics/1/en/chapter/55-current-intensity-and-the-ammeter#def-g8-intensity-ammeter-intensity). Audits end at the drawer.” **12.** For example: “A [voltmeter](#def-g8-voltage-voltmeter-voltmeter) stands across, never in the road. A label’s [nominal voltage](#def-g8-voltage-voltmeter-nominal) promises designed performance and threatens burnout beyond it. And in any idle circuit, the [voltage](#def-g8-voltage-voltmeter-voltage) waits at the gap — across the open [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch), ready.”