Electricity - Voltage, resistance, current and power.

Mechanical - Force, acceleration, velocity and power.

Metals and Materials - Metal properties and strength.

Optical - light reflection

Geometry - Angles and areas

Units conversion - SI (metric) and imperial conversion.

Electrical and electronic formula and data

Basic Electricity

V = I R P = V I E = P t
I = Q/(dt) E =1/2 C V^2

V = Voltage (V) I = Current (A) R = Resistance (ohm)
P = Power (W) E = Energy (J) t = time (s)
Q = Charge (C, A/h) dt = Difference in Time (s, h)

Resistors

Resistance in series: Rt = R1 + R2 + Rn

Resistance in parallel: 1/Rt = 1/R1 + 1/R2 + 1/Rn
Rt = total resistance R1, R2, Rn = resistance of each resistor (ohm)

Resistance in wire: p = R A /l 1/p = s
p (rho) = electrical resistivity (ohm*m) l = length R = resistance
s (sigma) = electrical conductivity (ohm^-1 * m^-1)

Capacitors

Charge: q = C V
q = charge (coulomb) C = capacitance, coulomb/volt, farad (F) V = voltage (V)

potential energy: U = 1/2 C V^2
U = potential energy, joules (J) C = capacitance, coulomb/volt, farad (F) V = voltage (V)

Resistance in oscillator: R = 2 pi f C
R = resistance (ohm) pi = pi, 3.14 f = frequency, (Hz) C = capacitance (F)

Capacitance in parallel: Ct = C1 + C2 + Cn

Capacitance in series: 1/Ct = 1/C1 + 1/C2 + 1/Cn

Inductors

Resistance in oscillator: R = 2 pi f L
R = resistance (ohm) pi = pi, 3.14 f = frequency, (Hz) L = inductance, Henry (H)

Inductance in series: Lt = L1 + L2 + Ln

Inductance in parallel: 1/Lt = 1/L1 + 1/L2 + 1/Ln

Time Constant

Charge: q=qo e^(-t/RC)
q = charge e = natural logarithmic (ln) t = time (s) RC = time constant R = resistance (ohm) C = capacitance (F)

Resonance Frequency
w = 1 / sqrt (LC)
w = omega, w = 2 pi f L = inductance (H) C capacitance (F)

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Mechanical formula and data:

Kinematics

d = v t d = 1/2 a t^2 v = (d2-d1)/(t2-t1)

a = (v2-v1)/(t2-t1) PE = m g h KE =1/2 m v^2

F = m a Fd = 1/2 Cd v^2 p = v m

v = w r W = F d P = F v

F = m g P = T w ac = v^2/r

F = u N

d = distance (m) v = velocity (m/s)
t = time (s) a = acceleration (m/s^2)
E = potential energy (J) KE = kinetic energy (J)
g = gravity (9.81 m/s^2) m = mass (kg)
F = force (N) w = angular velocity (rad/s) = 2 pi f
Fd = force due to drag Cd = coefficient of drag
P = power (W) T = torque (N*m)
ac = centripetal acceleration r = radius
u = coefficient of friction N = normal force (N)

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Metals and materials formula and data:

Stress and Strain

s = F/Ao s = E e t = G y p = m/V

s = stress (Pa) F = force (N)
E = modulus of elasticity, Young's Modulus (Pa)
e = strain (%) t = shear stress (Pa)
Ao = original cross-sectional area
y (gamma) = shear strain m = mass (kg)
V = volume (m^3) p (rho) = density (kg/m^3)
G = shear modulus (Pa)

Torsion

tmax = T c/J [shaft] J = 1/2 pi (c2^4 - c1^4) [shaft]

tmax = T/(c1 a b^2) [solid square]

tmax = T/(2t @) [thin walled square tube]

tmax = maximum shear stress (Pa)
T = torque (N*m)
c = distance to outer radius (m)
J = polar moment of inertia (m^4)
c2 = outer radius of shaft (m)
c1 = inner radius of shaft (m)
t = thickness of square tube (m)
@ = centerline area (m^2), (a-t)x(b-t)

a/b 1 1.2 1.5 2 2.5
c1 0.208 0.219 0.231 0.246 0.258

a/b 3 4 5 10 infinity
c1 0.267 0.282 0.291 0.312 0.333

Bending-Symmetrical Shapes

sm = M c/I

sm = maximun stress (Pa) M = moment (N*m)

c = distance from center (N.A) to edge (m)
I = moment of inertia (m^4)

Hallow or solid beam of length b (b2, b1) and height h (h2, h1):
I = 1/12 (b2h2^3 - b1h1^3)

Tube of r with/without r1:
I = 1/4 pi (r^4 - r1^4)

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Optical formula and data:

The Law of Refraction: n1 sin(theta1) = n2 sin(theta2)
n = index of refraction

Spherical mirror: 1/o + 1/i = 2/r
o = distance of object form mirror i = distance if image from mirror r = radius of curvature of mirror

Geometric formula and data:

Triangle

tan(theta)=y/x sin(theta)=y/R cos(theta)=x/R

sinA/a=sinB/b=sinC/c c^2=a^2 + b^2 -2ab cos(theta)

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Units and conversion formula and data:

SI Units

Prefix Symbols

Length and Area

1 inch = 25.4 mm
12 inches = 1 foot
3 feet = 1 yard
6 feet = 1 fathom
1 mil = 10^-3 in
1 mile = 1.609 km
1 nautical mile= 1852m

1 square mile = 640 acres
1 acre = 43 560 ft^2
1 hectare = 10^4 m^2 = 2.471 acre

Capacity (US) and Weight

1 ounce = 28.35 g
1 pound = 16 ounces
1 pound = 453.6 g
1 metric ton = 1000 kg
1 kg = 2.204 lb

1 gallon = 4 quart = 3.785 liters
1 quart = 2 pint
1 pint = 0.473 l

360 degrees = 1 revolution = 2 pi radians
pi = 3.141593

1 btu = 0.293 W
1 ft*lb/s = 1.356 W
1 hp = 550 ft*lb/s = 746 W
1 atmosphere = 1 atm = 76 cm Hg = 101.325 kPa = 14.7 psi
1 psi = 6.89x10^3 Pa
1 ksi = 6.89 MPa

(C)2007 Onstate Technologies.
Last update:May/07