Quick Facts
Speed of light in vacuum: c = 300, 000, 000 m/s (3 x 108 m/s)
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
Formulae:
Angle of incidence - angle of refraction = angle of deviation of light through medium.
Refractive index = ca / cm (speed of light through medium)
e.g. the refractive index for a fibre optic cable = 3 x 10 8 / 2 x 10 8 = 1.5
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:
CO2(g) - 267
Air - 343
H2O(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 = I2R or V2 / R if resistance is known. If time is known then W = VIt, and using Ohm's Law: W = I2Rt = V2t / R.
Potential difference between 2 points = Electrical energy converted, W / Charge transferred (V = W / Q)
Transistor as amplifier: Current gain = Collector current / Base current (IC / IB)
Output potential using a potential divider to vary potential of cell = (R2 / R1 + R2)
Resistance directly proportional to wire length, and inversely proportional to cross - sectional area
In series:
Total e.m.f. of cells, c = c1 + c2 + c 3... sum of e.m.f.'s
Total resistance of resistors = R1 + R2 + R3 ... sum of resistances
p.d. across each resistor = V1 = I1R1, V2 = I2R2 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/R1 + 1/R2 + 1/R3
(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 = I2Rt 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 [(p1/p2 = 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 to, th = halflife.
Networks: Response time converted to km distance = Max. allowable distance
Mass to energy equivalence: E = mc2
General relativity: (ds)2 = (1 - a/r)(dt)2 - 1/c2 [(dr)2 / (1 - a/r) + r2(dtheta)2 + r2sin2theta(dø)2]
Logarithms:
If y = ax, then x = logay
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