Speed of light in vacuum: c = 300, 000, 000 m/s (3 x 10

All colours can be made up from red, green &/or blue depending on combination

Speed of sound in air: 350 m/s; through ground: 5000 m/s

Human audible range: 20 - c. 18,000 Hz

*Electromagnetic spectrum in order of increasing wavelength & decreasing frequency:*

Gamma rays: 0.01 nm

X rays: 1 nm

Ultra-violet rays: 0.2µm

Visible light: 0.4 - 0.7µm (R, O, Y, G, B, V, I)

Infra-red rays: 0.01mm

Microwaves: 1cm

Radar: 10cm

Television broadcasts: 1m

Radio broadcast wavelengths: 1km

Angle of incidence - angle of refraction = angle of deviation of light through medium.

Refractive index = c

e.g. the refractive index for a fibre optic cable = 3 x 10

Echoes & sonar: Speed of sound in air = 2s / t m/s

In water: s = vt/ 2 m/s

As temperature increases, speed of sound increases. Some speeds at rtp - m/s:

CO_{2}(g) - 267

Air - 343

H_{2}O(l) - 1483

Sea water - 1522

Al - 5100

Mild steel - 5200

*Electricity:*

Resistance = Voltage across conductor / Current through conductor (R = V / I)

Current = Charge, Q / Time, t (I = Q / t)

Power used = Energy converted / time, or Current x p.d. (Watts = Amps x Volts)

P = IV = I^{2}R or V^{2} / R if resistance is known. If time is known then W = VIt, and using Ohm's Law: W = I^{2}Rt = V^{2}t / R.

Potential difference between 2 points = Electrical energy converted, W / Charge transferred (V = W / Q)

Transistor as amplifier: Current gain = Collector current / Base current (I_{C} / I_{B})

Output potential using a potential divider to vary potential of cell = (R_{2} / R_{1} + R_{2})

Resistance directly proportional to wire length, and inversely proportional to cross - sectional area

In series:

Total e.m.f. of cells, c = c_{1} + c_{2} + c _{3}... sum of e.m.f.'s

Total resistance of resistors = R_{1} + R_{2} + R_{3} ... sum of resistances

p.d. across each resistor = V_{1} = I_{1}R_{1}, V_{2} = I_{2}R_{2} etc. using Ohm's Law

Current in circuit = e.m.f. of cell / Resistance in resistors + internal resistance of cell, (e.m.f. / R + r)

Parallel networks:

Cells: Total e.m.f. = e.m.f. of 1 cell

Resistors: Total resistance = Less than smallest resistance in group (1/R = 1/R_{1} + 1/R_{2} + 1/R_{3}

(I = amperes; p.d. & e.m.f. = volts; Charge = Coulombs; Resistance = Ohms; Power = watts)*Transformers:*

Secondary voltage / Primary voltage = No. turns in secondary coil / No. turns in primary coil, and V Out / V In = I in / I out

Energy Loss:

The greater the current, the greater the energy loss in a cable of given length. Use W = I^{2}Rt where W is heat energy loss in kJ.

*Miscellanea:*

Frequency of wave = 1 / Period of wave, (f = 1/T)

e = 2.718281828459

maxima: e^pi = 23.14069263

minima: e^-pi = 0.043213918

Simple interest = PRT / 100

Compound interest = P(1 + R/100)^{t}

% of increase as profit: Profit / Cost X 100

Exponential growth: Population = constant [(p_{1}/p_{2} = R)/100]^{t}

Depreciation: A = P(1 - R/100)^{T}% decrease as loss: Loss / Cost x 100

Decay function: y = A x 2^{-t/th} where A is the no. atoms at t_{o}, th = halflife.

Networks: Response time converted to km distance = Max. allowable distance

Mass to energy equivalence: E = mc^{2}

General relativity: (ds)^{2} = (1 - a/r)(dt)^{2} - 1/c^{2} [(dr)^{2} / (1 - a/r) + r^{2}(dtheta)^{2} + r^{2}sin^{2}theta(dø)^{2}]

*Logarithms:*

If y = a^{x}, then x = log_{a}y

And if log A ^{n} = n log A, e.g. P = k(R)^{t}, then log (P/k) = t log R.

Log A x B = log A + log B

Log A / B = log A - log B