Electrical cheat sheet (equations) M J Rhoades Ohms law E = I R where: E = volts I = amperage in amps R = resistance in ohms P = power in watts
where: P = watts, R= , R= , I = I= , I= 2
Power
P = E I where:
R=
2
P = power in watts E = volts I = amperage in amps
P=RxI , P= volts E = R I , E = , E = where F = in newtons = Electrostatic force F = K 2
2
1 2
e
2
e
2
q1 = charge first object in coulombs q2 = charge of second object in coulombs r = distance between centers of objects in meters K = constant 8.99 x 10 Potential difference
V=
where: V = volts W = work in joules q = charge in coulombs
9
−
2
Electric field strength E =
where: E = field strength in newtons/coulomb Fe = electrostatic force in newtons q = charge in coulombs
Current I =
∆
where: I = amperes in amps
∆ = change in charge in coulombs/ sec t = time in seconds
Resistance R =
where: R = ohms meters ters = resistivity in Ω * me 0
L = meters A = meter
Conductance G =
1
Resistivities at 20 C
2
Material
Resistivity ( Ω * m ) 2.82 x 10
Copper
1.72 x 10
Gold
2.44 x 10
Nichrome
150 x 10
Tungsten
5.60 x 10
R = resistance in ohms
where: B = magnetic flux density in teslas Φ = magnetic flux in webers A = area in square meters
-8 -8
where G = is in mhos
Magnetic flux density B =
-8
Aluminum
-8 -8
Permeability µ r =
µ µ0
where: µ r = the relative permeability in henries per meter or newton per
ampere squared (
) 2
µ = the permeability of the material in newton per ampere squared -7
µ 0 = the permeability of a vacuum ( 4π x 10 µ=
) 2
where: µ = permeability in newtons per ampere squared B = magnetic flux density in teslas H = field intensity ampere turns per meter
Tesla T =
2
where: T = tesla V = volts m = meters
Magnetomotive Force F m = N I
where Fm = Magnetomotive force in ampere turns N = number of turns I = amperes
Field Intensity
H=
=
where: H = field intensity in ampere turns/meter Fm = Magnetomotive force N I = ampere turns L = length between poles
Reluctance (1) R =
where: R = reluctance in Fm / Φ mmf = Fm or N I Φ = flux in webers
(2) R =
where: R = ampere turns / weber
µ
L = length of coil in meters µ = permeability of of the material in A = cross sectional area of coil, m
Flux ( 1) Φ =
− 2
where: Φ = magnetic flux in webers (Wb) Fm = Magnetomotive force in ampere turns R = reluctance in ampere turns / weber
(2) Φ =
where N I = ampere turns Wb = webers
Induced voltage V ind = -N
ΔΔ
where: Vind = induced voltage in volts N = number of turns in the coil
Δ = rate at which the flux cuts across the Δ conductor, Temperature coefficient of resistance ( α)
Δ
Rt = Ro + Ro(α T)
where: α = the temperature coefficient no units Rt = resistance at new temperature in ohms 0
Ro = the resistance at 20 C in ohms
Temperature Coefficient for various materials Material
Temperature coefficient 0
in Ω per C Aluminum
0.004
Carbon
-0.0003
Constantan
0
Copper
0.004
Gold
0.004
Iron
0.006
Nichrome
0.0002
Nickel
0.005
Series Circuits
Parallel Circuits
I = I1 = I2 = I3...
I = I1+ I2 + I3 + ...
V = V1+ V2 + V3 + ...
V = V1 = V2 = V3 ... 1
1
1
1
REq = R1 + R2 + R3 + ...
=
1
+
2
+
...
3
where: I = amperes V = voltage REq = resistance equivalent R = circuit resistance
Two resisters in parallel
RT =
1 2
1+
where RT = total resistance in ohms
2
R1 = first resistance in ohms R2 = second resistance in ohms
Counter electromotive force (CEMF) CEMF = -L
∆ where: ∆
CEMF = induced voltage in volts L = inductance in henries
Inductance
L=
∆ = time rate of change of current in amps/sec ∆
where: L = inductance in heneries Φ = flux in webers I = current in amperes
Inductive reactance X L = 2π f L where: XL = inductive reactance in ohms f = frequency in hertz L = inductance in henries Inductors in series
LEq = L1 + L2 + L3 +... where LEq = the equivalent inductance in henries L123 = inductors in henries
Inductors in parallel
1
1
1
1
=
+
1
2
+
+... where LEq = the equivalent inductance in henries
3
L123 = inductors in henries
Capacitance
C=
where: C = capacitance in farads (F) (coulombs / volt) Q = amount of charge in coulombs V = the voltage in joules / coulomb
Capacitance of two plates
(8.85 x 10
C=K
-12
) where: C = capacitance in farads K = dielectric constant from tables, no units A = area of the plates in square meters
d = distance between the plates in meters 8.85 x 10 Capacitive reactance
Xc =
1
2
-12
= constant of proportionality in F meters
where: Xc = capacitive reactance in ohms f = frequency in hertz C = capacitance in farads
π = 3.1416 Work stored in a capacitor W stored
= 2
2
where: Wstored = energy stored in joules C = capacitance in farads V = voltage in volts
Capacitors in series
1
1
1
+
1
=
1
+
2
+... where: CEq = the equivalent capacitance in farads
3
C123 = component capacitance in farads Capacitors in parallel Capacitive time constant
C Eq = C1 + C2 + C3 +... T c = R C where: Tc = capacitive time constant in seconds R = resistance in ohms C = capacitance in farads
Internal resistance (Battery) V L = VB - IL RI where: VL = loaded voltage in volts VB = Unloaded battery volts in volts IL RI = internal voltage drop in volts
Generated voltage in a dc generator V G = K Φ N where: VG = generated voltage in volts K = fixed constant for the generator no units Φ = magnetic flux strength in webers N = speed in revolutions per minute
Resonance frequency (undamped) of a LC circuit (1) f =
1
2
where: f = frequency in hertz L = inductance in henries C = capacitance in farads
(2)
= 1
o
where:
= freq in radians / second o
L = inductance in henries C = capacitance in farads Power factor
Pf =
where: Pf = power factor expressed in decimals P = real power in watts S = apparent power in volt amp reactive ( VAR
Efficiency motor
M eff =
where: Meff = efficiency in percentage Pin = power in in watts or horse power Pout = power out in watts or horse power
AC / DC power /current formulas for motors V volts, I = amps, PF = power factor, Eff = efficiency HP = horse power W = watts DC amps =
746
AC amps 3phase =
,
AC amps(120 240) =
, 746
746
1.73
AC / DC motor cont. DC amps =
1000
AC amps(120,240) =
, AC amps 3phase = , AC amps3phase =
, AC amps(120, 240) =
1000
1000
1000
1.73
1000
1.73
, AC kw(120, 240) = , AC kw 3 phase = , AC kv-amps 3 phase = AC kv-amps (120,240) = , AC hp(120,240) = , DC hp = AC hp 3 phase = where:V = primary voltage in volts Transformer voltage and current V = DC kw =
1.73
1000
1000
1000
1.73
1000
1000
746
746
1.73
746
p
p
Vs = secondary voltage in volts Is = secondary current in amps Ip = primary current in amps Transformer voltage and turns in coil
V = p
where: Vp = voltage in primary coil in volts Vs = voltage in secondary coil in volts Ip = current in primary coil in amps Ts = turns in secondary coil
I = Is = Vs =
Transformer amperes and turns in coil
p
Resistor color codes by just looking at a resistor in a circuit you can tell certain things about it if it follows the standard code. The fourth is the tolerence The fifth is the max % the resistance will change over 1000 hours of operation
Indicates the Second number
The third is the multiplier
The first color gives the first value of the resistor Color code table
Numeral
multiplier
Black
0
1
Brown
1
10
Red
2
1000 (1k)
Orange
3
100
Yellow
4
10000(10k)
Green
5
100000 (100k)
Blue
6
10
Violet
7
10
Grey
8
10
white
9
10
4th band ,tolerance ,silver ± 10%, gold ± 5%, no band, 20%
5th band, brown ± 1%, red band, .1 %, no band, > ± 1 %
6 7 8
9
In our example, red, violet, green, we have 27 x 100k or 270 kΩ , ± 10 % tolerance, ± 1 % change. The way I remembered this code was with a mind trick. "Bad boys rape our young girls but violet gives willingly. It seems, when you say this once, you will never forget the code.
