SPI Physics · Formula sheet

Electricity and Magnetism formulas

8 formulas, 3 reference tables and 22 common traps for SPI Physics Electricity and Magnetism, grouped by subtopic.

Ohm's Law and Resistance

Current, charge and potential difference

Current and potential difference

I = \frac{Q}{t} \qquad V = \frac{W}{Q}

$Q$ charge, in coulombs
$t$ time, in seconds
$W$ work done, in joules

Ohm's law: V = IR

Ohm's law

V = IR \qquad I = \frac{V}{R} \qquad R = \frac{V}{I}

What a wire's resistance depends on

Resistance of a wire

R = \rho \frac{L}{A}

$ρ$ resistivity of the material
$L$ length of the wire
$A$ area of cross-section

Common traps

Time in minutes

Current is coulombs per SECOND. 30 C in one minute is

\frac{30}{60} = 0.5

A, not 30 A.

Dividing the wrong way round

Resistance is

R = \frac{V}{I}

. For 6 V and 4 A that is 1.5

\Omega

;

\frac{I}{V} = \frac{4}{6}

is not a resistance at all.

Thinking V/I changes along a straight-line graph

A straight line through the origin means V/I is the SAME at every point. That is what Ohm's law says, so the conductor is ohmic.

Leaving out the temperature condition

Ohm's law holds for a metal only while its temperature stays constant. A hot filament's resistance rises, so its V against I graph curves.

Mixing resistance with resistivity

Cutting or stretching a wire changes its resistance, but its resistivity stays the same: resistivity belongs to the material, not the wire.

Thicker means more resistance

It is the other way round. Doubling the area of cross-section halves the resistance, because the current has more room.

Series and Parallel Circuits

Learn this subtopic in the notes

Adding resistors in series and in parallel

Series and parallel

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

Equal resistors and cutting a wire

n equal resistors

R_s = nR \qquad R_p = \frac{R}{n} \qquad \text{cut into } n \text{ and joined in parallel: } \frac{R}{n^2}

Common traps

Adding resistances that are in parallel

Plain adding is only for series. A 3

\Omega

and a 6

\Omega

resistor in parallel give 2

\Omega

, not 9

\Omega

: a parallel total is always smaller than the smallest resistor.

Swapping what is shared

In series the CURRENT is the same and the voltages differ; in parallel the VOLTAGE is the same and the currents differ.

Splitting the battery voltage between parallel branches

Two branches joined straight across a battery each have the full battery voltage. Share the voltage only between resistors that are in series inside one branch.

Forgetting that cutting changes each piece

Each half of a cut wire has half the resistance. Joining two halves of a 10

\Omega

wire in parallel gives

\frac{5}{2} = 2.5\,\Omega

, not

\frac{10}{2} = 5\,\Omega

Picking series for the minimum

Series always gives the largest total and parallel the smallest. 'Minimum resistance' from equal resistors means all of them in parallel.

Electric Power and House Wiring

Learn this subtopic in the notes

Electric power: P = VI

Electric power

P = VI = I^2R = \frac{V^2}{R}

Electrical energy and the kilowatt hour

Electrical energy

E = Pt \qquad E\,(\text{kWh}) = \frac{P\,(\text{W}) \times t\,(\text{h})}{1000} \qquad 1\text{ kWh} = 3.6 \times 10^6\text{ J}

House wiring and safety devices

Part	What it is or does
Live wire	Red insulation, at 220 V
Neutral wire	Black insulation, at zero potential
Earth wire	Green insulation, joined to the metal body of an appliance and to a plate buried in the ground
Fuse	A wire that melts and breaks the circuit when too much current flows
MCB (miniature circuit breaker)	A switch that trips by itself on too much current, and can be reset
Main switch	A double pole switch that cuts both the live and the neutral wire The earth wire is never switched off.
Short circuit	Live and neutral touch, so the resistance drops and a huge current flows
Overloading	Too many appliances on one socket draw more current than the wiring is meant for

Indian mains: 220 V AC at 50 Hz. Appliances are joined in parallel.

Common traps

Halving the voltage halves the power

For a fixed resistor

P = \frac{V^2}{R}

, so halving V gives one fourth of the power, not half.

Using milliamperes as amperes

Change mA to A before multiplying: 300 mA is 0.3 A, so at 220 V the power is 66 W, not 66000 W.

Leaving time in minutes

In joules the time must be in seconds. A 50 W lamp for 3 minutes uses

50 \times 180 = 9000

J, not 150 J.

Calling the kWh a unit of power

Kilowatt is power; kilowatt HOUR is energy. The bill counts kWh because it charges for energy used.

A thick fuse wire

A thick wire has low resistance and does not melt easily, so it fails to break the circuit. A fuse wire is thin.

Earthing as protection against overload

Earthing carries a leaking current away from a metal body to save the user. Overload and short circuit are the fuse's job.

Magnetic Effects of Current

Learn this subtopic in the notes

Force on a current in a magnetic field: the motor

Force on a wire and torque on a coil

F = BIL \qquad \tau = NIAB\sin\theta

$B$ magnetic field, in tesla
$I$ current, in amperes
$L$ length of wire in the field, in metres
$N$ number of turns of the coil
$A$ area of the coil, in square metres
$θ$ angle between the field and the normal to the coil

The magnetic field of a wire, a loop and a solenoid

Source	Shape of the field lines
Straight wire	Circles around the wire, centred on it; weaker farther away
Circular loop	Circles near the wire; nearly straight lines at the centre
Solenoid, inside	Parallel straight lines: the field is uniform Uniform inside a long solenoid, not circular.
Solenoid, outside	Like a bar magnet: from the N end round to the S end
Bar magnet	N to S outside, S to N inside, forming closed loops

Circular lines belong to a straight wire; straight parallel lines to the inside of a solenoid.

Electromagnetic induction and the generator

Fact	Value
Energy change in a generator	Mechanical energy to electrical energy
Rule for the induced current	Fleming's right hand rule
Current reverses	Once every half revolution of the coil Twice in each full turn, not once.
Rings in an AC generator	Slip rings (current keeps alternating)
Rings in a DC generator	Split ring commutator (current flows one way)
AC frequency in India	50 Hz, so the current changes direction 100 times a second

A motor and a generator are built alike: a coil, a magnet and rings. Only the energy change is reversed.

Common traps

Calling the field inside a solenoid circular

Circular field lines are around a straight wire. Inside a long solenoid the lines are straight and parallel, so the field is uniform.

Mixing up the clock rule

Seen from a face, clockwise current gives a south pole and anticlockwise gives a north pole.

Using the right hand for a motor

The LEFT hand rule gives the force on a current, as in a motor. The right hand rule is for the induced current in a generator.

Measuring the angle from the coil's plane

\tau = NIAB\sin\theta

\theta

is measured from the coil's normal. If the plane makes

30^\circ

with the field, the normal makes

60^\circ

, and

\sin 60^\circ = \cos 30^\circ

One reversal per turn

The current reverses every HALF revolution, so twice in each full turn. A 50 Hz supply changes direction 100 times a second.

Electricity and Magnetism formulas

Ohm's Law and Resistance

Current, charge and potential difference

Ohm's law: V = IR

What a wire's resistance depends on

Common traps

Series and Parallel Circuits

Adding resistors in series and in parallel

Equal resistors and cutting a wire

Common traps

Electric Power and House Wiring

Electric power: P = VI

Electrical energy and the kilowatt hour

House wiring and safety devices

Common traps

Magnetic Effects of Current

Force on a current in a magnetic field: the motor

The magnetic field of a wire, a loop and a solenoid

Electromagnetic induction and the generator

Common traps

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