CDS Physics · Formula sheet

Electricity and Magnetism formulas

8 formulas, 6 reference tables and 32 common traps for CDS Physics Electricity and Magnetism, grouped by subtopic.

Charge and Current

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}}

$W$ work done (energy) in joules
$q$ charge in coulombs
$K$ kinetic energy gained from rest
$m$ mass of the particle

Current, cells and emf

Current and emf

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

$Q$ charge passing in time t
$ε$ emf of the cell, in volts
$P$ power the cell delivers

Static charge, conductors and insulators

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

Common traps

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.

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).

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.

Resistance and Circuits

Learn this subtopic in the notes

Ohm's law and the resistance of a wire

Ohm's law and resistance of a wire

V = IR \qquad R = \rho\dfrac{l}{A} \qquad A = \pi r^{2} = \dfrac{\pi d^{2}}{4}

$ρ$ resistivity of the material
$l$ length of the wire
$A$ area of cross-section
$r, d$ radius and diameter of the wire

Resistors in series and in parallel

Series and parallel

R_s = R_1 + R_2 + R_3 \qquad \dfrac{1}{R_p} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}

Rₛtotal resistance in series
Rₚtotal resistance in parallel

Resistivity: a property of the material

Material	Resistivity at 20 °C (Ω m)	Where it is used
Silver	1.60 × 10⁻⁸	The best conductor; too costly for wiring
Copper	1.62 × 10⁻⁸	House wiring
Aluminium	2.63 × 10⁻⁸	Overhead power lines (light and cheap)Q CDS 2017 (II) and 2018 (I): an aluminium wire of the same size as a copper wire has more resistance, so it gives out more heat for the same current.
Tungsten	5.20 × 10⁻⁸	Bulb filaments
Nichrome (alloy)	About 1.1 × 10⁻⁶	Heater coils
Glass	10¹⁰ to 10¹⁴	An insulatorQ CDS 2022 (I): silver, nichrome and glass in increasing order of resistivity.
Rubber	10¹³ to 10¹⁶	Covering on wires

Common traps

Thickness counts through the square of the diameter

Resistance depends on the area, and area goes as

d^{2}

. Doubling the diameter divides the resistance by 4, not by 2.

Stretching changes both length and area

Pull a wire to

n

times its length and it also gets thinner. Its resistance becomes

n^{2}

times, not

n

times.

Resistivity is not resistance

Changing the length or area of a wire changes its resistance, never its resistivity. Resistivity changes only with the material and the temperature.

The unit is ohm metre, not ohm per metre

From

\rho = RA/l

: ohm × m² ÷ m = ohm metre (or ohm centimetre). Ohm per metre and ohm per square metre are wrong.

Aluminium resists more than copper

Copper's resistivity is lower than aluminium's. So for wires of the same size, the aluminium one has the larger resistance and gives out more heat for the same current.

The parallel total is smaller than the smallest resistor

Adding a resistor in parallel always lowers the total, because it opens another path. If your parallel answer is bigger than the smallest resistor, the working has gone wrong.

Most heat from a battery comes from the smallest total resistance

Across a fixed voltage the heat per second is

V^{2}/R

. The smallest

R

, the all-parallel joining, gives the most heat. The rule

I^{2}R

(bigger

R

, more heat) holds only when the current is fixed.

Electric Power and Home Wiring

Learn this subtopic in the notes

Electric power and the heating effect

Electric power and Joule heating

P = VI = I^{2}R = \dfrac{V^{2}}{R} \qquad H = I^{2}Rt \qquad P' = P\left(\dfrac{V'}{V}\right)^{2}

$P$ power in watts
$H$ heat produced in time t, in joules
$P′, V′$ power at a voltage other than the rated one

Electrical energy and the unit on the bill

Electrical energy

E = Pt \qquad 1\ \text{kWh} = 1000\ \text{W} \times 3600\ \text{s} = 3.6 \times 10^{6}\ \text{J}

$E$ energy used
$P$ power (in kW for units)
$t$ time (in hours for units)

Fuses, short circuits and house wiring

Wire or part	Fact
Live and neutral	220 V r.m.s. between themQ CDS 2023 (I): the r.m.s. voltage between live and neutral in Indian homes is 220 V.
Live wire	Red insulation (the code in NCERT); the fuse and switch go in it
Neutral wire	Black insulation (the code in NCERT)
Earth wire	Green insulation; joined to the metal body of an applianceQ CDS 2022 (I): a green wire is the earth wire, not the live wire.
Fuse	Low melting point wire in the live line; melts when the current is too bigQ CDS 2018 (II): a 5 A fuse at 220 V allows 1100 W, so eleven 100 W bulbs.
Short circuit	Live meets neutral; the current rises sharply and the fuse blows

Bulbs and energy changes

Device	Energy change
Filament bulb	Electrical to light, and much more heat
LED	Electrical to light, very little heat
Laser	Electrical to a narrow beam of light of one colour
Television set	Electrical to light and sound
Electric heater or iron	Electrical to heat
Electric motor or fan	Electrical to mechanical
Candle	Chemical to heat and lightQ CDS 2018 (II): the candle is the one that does not turn electrical energy into light.

Common traps

The resistance stays fixed, not the power

A bulb's rating tells you its resistance. On a lower voltage, work out

V^{2}/R

again. At half the voltage the power is one quarter, not one half.

More watts means less resistance

On the same voltage,

R = V^{2}/P

. So a 100 W bulb has a smaller resistance than a 25 W bulb. Students often guess the opposite.

Kilowatts times hours, not watts times hours

A unit is a kilowatt-hour. Divide the watts by 1000 before you multiply by the hours, or the answer comes out 1000 times too big.

A unit is energy, not power

The kWh measures energy (power × time). The kW measures power. A bill charges for energy, so it counts kWh.

Green is the earth wire

In the colour code NCERT uses, red is live, black is neutral and green is earth. Never take the green wire for the live one.

The fuse goes in the live wire

A fuse in the neutral wire would blow but leave the appliance still joined to the live supply, which is dangerous. The fuse and the switch always go in the live wire.

220 V is the r.m.s. value

The 220 V of the mains is its r.m.s. value. The voltage swings up to a peak of about 311 V (

220\sqrt{2}

The gas in a bulb is for a longer life

Argon is inert. It keeps the hot tungsten from oxidising and slows its evaporation, so the bulb lasts longer. It does not cut the power used or colour the light.

Magnetism and Induction

Learn this subtopic in the notes

Force on a moving charge and on a current

Magnetic force

F = qvB\sin\theta \qquad F = BIl\sin\theta \qquad \vec{F} = q\,\vec{v} \times \vec{B}

$q, v$ charge and its speed
$B$ magnetic field, in tesla
$θ$ angle between the velocity (or current) and the field
$I, l$ current and length of wire in the field

Electromagnetic induction and the transformer

Induction and the transformer

\varepsilon = -N\dfrac{\Delta\Phi}{\Delta t} \qquad \dfrac{V_s}{V_p} = \dfrac{N_s}{N_p} = \dfrac{I_p}{I_s}

$N$ number of turns in the coil
$ΔΦ/Δt$ rate of change of magnetic flux
$p, s$ primary and secondary coils

Magnets, magnetic materials and field lines

Type	Behaviour near a magnet	Examples
Diamagnetic	Weakly pushed away	Bismuth, copper, silver, water
Paramagnetic	Weakly pulled in	Aluminium, sodium, oxygen
Ferromagnetic	Strongly pulled in; can become a magnet	Iron, cobalt, nickelQ CDS 2016 (II): liquids and gases never show ferromagnetism.

Magnetic field of a current and the hand rules

Rule	What it gives	How to hold the hand
Right-hand thumb rule	Direction of the field round a current	Thumb along the current; curled fingers show the fieldQ CDS 2025 (I): the right-hand thumb rule gives the field round a straight conductor.
Fleming's left-hand rule	Direction of the force on a current in a field (motor rule)	Forefinger field, middle finger current, thumb force
Fleming's right-hand rule	Direction of the induced current (generator rule)	Forefinger field, thumb motion, middle finger induced current
Hund's rule	Not a magnetism rule: it fills electrons into orbitals	Not a hand rule (chemistry)

Common traps

Ferromagnetism needs a solid

Its domains need atoms held in a fixed crystal. The atoms of a liquid or gas move about freely, so fluids can be diamagnetic or paramagnetic but never ferromagnetic.

Field lines never cross, and need not be parallel

Field lines never cross, inside a magnet or outside it. They curve from pole to pole, so they are parallel only where the field is uniform (for example inside a long solenoid).

Declination alone does not give the direction

Declination gives the field's angle across the ground; dip gives its tilt below the horizontal. You need both to fix the direction of the Earth's field.

Thumb rule for the field, Fleming's rules for force and induced current

The right-hand thumb rule gives the field round a current. Fleming's left-hand rule gives the force (motors); Fleming's right-hand rule gives the induced current (generators). Hund's rule is chemistry.

Between opposite currents the fields add

Midway between two close wires with opposite currents, both fields point the same way, so the field is strong there, not zero. It is far away that the two nearly cancel.

Inside a long solenoid the lines are straight

The field inside a long solenoid is uniform: parallel straight lines along its axis. They are not circles, ellipses or curves.

No force along the field

If the charge moves parallel or anti-parallel to the field,

\sin\theta = 0

and there is no magnetic force. The force is biggest at right angles.

Turn the answer round for an electron

Fleming's left-hand rule and

q\,\vec{v} \times \vec{B}

give the force on a positive charge. An electron moving the same way feels the force in the opposite direction.

Step-up voltage means step-down current

A transformer cannot make energy. If it raises the voltage 10 times, the current on that side is about one tenth. Power in = power out (ideal).

A magnet at rest induces nothing

Induction needs a change of flux. A magnet held still inside a coil gives no current; moving it in or out gives one, and moving it faster gives a bigger one.

A transformer heats up from its own losses

The heat comes from the current in the windings (

I^{2}R

) and from hysteresis and eddy currents in the core. The cooling oil gets hot because of that heat; it is not the cause.

Electricity and Magnetism formulas

Charge and Current

Potential difference and the energy a charge gains

Current, cells and emf

Static charge, conductors and insulators

Common traps

Resistance and Circuits

Ohm's law and the resistance of a wire

Resistors in series and in parallel

Resistivity: a property of the material

Common traps

Electric Power and Home Wiring

Electric power and the heating effect

Electrical energy and the unit on the bill

Fuses, short circuits and house wiring

Bulbs and energy changes

Common traps

Magnetism and Induction

Force on a moving charge and on a current

Electromagnetic induction and the transformer

Magnets, magnetic materials and field lines

Magnetic field of a current and the hand rules

Common traps

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