CDS Physics · Electricity and Magnetism

Charge and Current

Static charge and what conducts it, the energy a charge gains across a potential difference, and how a cell drives a current that an ammeter measures.

All Electricity and Magnetism notes

Why this matters

Seven CDS questions from 2017 (II) to 2026 (I), five of them MODERATE. Two send an electron and a proton through the same voltage, two are about static charge on an aircraft and in a Van de Graaff generator, and three ask what conducts, what an ammeter measures and what emf means.

Concept 1 of 3: Static charge, conductors and insulators

Rub two different materials together and electrons move from one to the other, so one ends up negative and the other positive. In a conductor the charge can flow away; in an insulator it stays where it was put. That is why a rubbed plastic comb picks up bits of paper, and why a body that collects charge needs a conducting path to the earth to lose it.

Definition

What to know:

Conductors let charge flow: metals, the human body, tap water, the earth. Insulators hold it: plastic, rubber, glass, dry wood.
Distilled water conducts very poorly because it has almost no dissolved ions. Salts dissolved in tap water or sweat make it conduct.
Rubbing (friction) is what charges a body: a comb on hair, an aircraft against the air in flight.
Earthing gives charge a path to the ground. An aircraft's slightly conducting tyres let its charge flow away when it lands; a lightning conductor does the same for a building.
A Van de Graaff generator carries charge on a moving belt to a hollow metal dome and builds up a very high voltage (millions of volts) while giving only a tiny current.

Material or device	What to remember
Silver, copper, aluminium	Good conductors: free electrons carry the charge
Human body	A conductor: the body's fluids carry dissolved ionsQ CDS 2021 (I): the human body is the conductor among a plastic sheet, distilled water and a thin wooden sheet.
Distilled water	A very poor conductor: almost no ions
Plastic, rubber, glass, dry wood	Insulators
Aircraft tyres	Made slightly conducting, so charge picked up by rubbing against the air flows to earth on landingQ CDS 2024 (II): conducting tyres remove the charge gathered by friction with the air.
Van de Graaff generator	Builds a very high voltage with a very small current
Lightning conductor	A pointed metal rod joined to a plate in the earth; carries the charge of a strike safely to the ground

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2021 · CDS (I) 2021 — General Knowledge · Q105Easy

Example 1 · Electricity and Magnetism · Charge and Current

Which one of the following is an electric conductor ?

Pure water is a poor conductor

Distilled water has almost no ions, so it hardly conducts. Tap water, sea water and sweat conduct because of the dissolved salts. Do not pick distilled water as the conductor.

An aircraft's charge comes from rubbing against the air

A flying aircraft is charged by friction with the air and dust, just as a comb is charged by hair. Its slightly conducting tyres let that charge flow to the earth when it lands.

Drill 2 more on static charge, conductors and insulators

Concept 2 of 3: Potential difference and the energy a charge gains

Potential difference is the energy given to each coulomb of charge that moves between two points. So a charge q pushed through a voltage V gains energy qV. An electron and a proton carry the same size of charge, so the same voltage gives them the same energy. The electron is about 1836 times lighter, so it ends up far faster.

Definition

The rules:

Potential difference $V = \dfrac{W}{q}$ . Its unit, the volt, is one joule per coulomb.
A charge $q$ that starts from rest and moves through $V$ gains kinetic energy $K = qV$ .
Electron and proton: charge of the same size, $1.6 \times 10^{-19}$ C, so the same energy through the same voltage.
Speed from $K = \tfrac{1}{2}mv^{2}$ : $v = \sqrt{\dfrac{2qV}{m}}$ . The lighter particle is the faster one.
1 electron-volt (eV) is the energy one electron gains through 1 V: $1.6 \times 10^{-19}$ J.

Potential difference and energy gained

V = \dfrac{W}{q} \qquad K = qV \qquad v = \sqrt{\dfrac{2qV}{m}}

Wwork done (energy) in joules
qcharge in coulombs
Kkinetic energy gained from rest
mmass of the particle

Worked example

An alpha particle (charge 2e, mass about 4 times a proton's) and a proton (charge e) start from rest and are accelerated through the same 500 V. Compare their kinetic energies and their speeds.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2019 · CDS (I) 2019 — General Knowledge · Q61Moderate

Example 2 · Electricity and Magnetism · Charge and Current

An electron and a proton starting from rest get accelerated through potential difference of 100 kV. The final speeds of the electron and the proton are

V_e

and

V_p

respectively. Which one of the following relations is correct?

Same voltage gives the same energy, not the same speed

Equal charges through the same voltage gain equal energy

qV

. The speed then depends on the mass:

v = \sqrt{2qV/m}

, so the lighter particle is faster.

A volt is a joule per coulomb, not a joule

The volt measures energy per unit charge. The energy itself is

qV

, in joules (or in electron-volts for one electronic charge).

Drill 1 more on potential difference and the energy a charge gains

Concept 3 of 3: Current, cells and emf

Current is the amount of charge that flows past a point each second. A cell drives it: the emf of a cell is the energy it gives to each coulomb that passes through it. Some cells are used once and thrown away; others can be charged again. An ammeter sits in the path of the current to measure it; a voltmeter sits across a part to measure the voltage there.

Definition

The rules:

Current $I = \dfrac{Q}{t}$ . One ampere is one coulomb per second. Conventional current flows from the positive terminal to the negative outside the cell; electrons drift the other way.
emf $\varepsilon = \dfrac{W}{Q}$ , the energy given per coulomb. Since power $P = \varepsilon I$ , the emf is also the power per unit current. Its unit is the volt.
Primary cell: used once, cannot be recharged (dry cell, Leclanché cell).
Secondary cell: can be recharged (lead-acid car battery, lithium-ion phone battery).
Ammeter: measures current, joined in series, very low resistance. Voltmeter: measures potential difference, joined in parallel, very high resistance. A galvanometer detects a small current.

Current and emf

I = \dfrac{Q}{t} \qquad \varepsilon = \dfrac{W}{Q} = \dfrac{P}{I}

Qcharge passing in time t
εemf of the cell, in volts
Ppower the cell delivers

Worked example

A charge of 900 C passes through a lamp in 5 minutes. The lamp is run by a 12 V battery. Find the current and the power the battery delivers.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2026 · CDS (I) 2026 — General Knowledge · Q18Moderate

Example 3 · Electricity and Magnetism · Charge and Current

Which one among the following statements related to electric cells is correct ?

Ammeter in series, voltmeter in parallel

The ammeter must carry the same current as the circuit, so it goes in series and has very low resistance. The voltmeter goes in parallel across the part whose voltage you want, and has very high resistance.

Primary cells cannot be recharged

A primary cell is used once (a torch cell). A secondary cell is the rechargeable one (a car or phone battery). The names do not mean first and second in quality.

Drill 1 more on current, cells and emf

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Potential difference and the energy a charge gains
Potential difference and energy gained
$V = \dfrac{W}{q} \qquad K = qV \qquad v = \sqrt{\dfrac{2qV}{m}}$
Current, cells and emf
Current and emf
$I = \dfrac{Q}{t} \qquad \varepsilon = \dfrac{W}{Q} = \dfrac{P}{I}$

Reference tables (1)

Static charge, conductors and insulators7 rows

Material or device	What to remember
Silver, copper, aluminium	Good conductors: free electrons carry the charge
Human body	A conductor: the body's fluids carry dissolved ionsQ CDS 2021 (I): the human body is the conductor among a plastic sheet, distilled water and a thin wooden sheet.
Distilled water	A very poor conductor: almost no ions
Plastic, rubber, glass, dry wood	Insulators
Aircraft tyres	Made slightly conducting, so charge picked up by rubbing against the air flows to earth on landingQ CDS 2024 (II): conducting tyres remove the charge gathered by friction with the air.
Van de Graaff generator	Builds a very high voltage with a very small current
Lightning conductor	A pointed metal rod joined to a plate in the earth; carries the charge of a strike safely to the ground

Watch out for (6)

Pure water is a poor conductor
→ Static charge, conductors and insulators
An aircraft's charge comes from rubbing against the air
→ Static charge, conductors and insulators
Same voltage gives the same energy, not the same speed
→ Potential difference and the energy a charge gains
A volt is a joule per coulomb, not a joule
→ Potential difference and the energy a charge gains
Ammeter in series, voltmeter in parallel
→ Current, cells and emf
Primary cells cannot be recharged
→ Current, cells and emf

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