• Author / Uploaded
• M J Rhoades

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• Inductancia
• Condensador
• Voltio
• Inductor
• Serie y circuitos paralelos

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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 R=

I= Power

𝐸 𝐼

𝑃 𝐸

,

R=

, I=

𝐸2 𝑃

𝐸 𝑅

where: P = watts, R =

𝐼2

𝑃

,I=

P = E I where:

𝑃

𝑅

P = power in watts E = volts I = amperage in amps

P = R x I2, P = volts

E=RI,E=

Electrostatic force

𝑃 𝐼

𝐸2 𝑅

,E= 𝑃𝑥𝑅

Fe = K

𝑞1 𝑞2 𝑟2

where Fe = in newtons =

𝑘𝑔 𝑥 𝑚 𝑠𝑒𝑐 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 9 Potential difference V =

𝑊 𝑞

where: V = volts W = work in joules q = charge in coulombs

𝑐𝑜𝑢𝑙𝑜𝑚𝑏 𝑁−𝑚𝑒𝑡𝑒𝑟𝑠 2

Electric field strength E =

𝐹𝑒 𝑞

where: E = field strength in newtons/coulomb Fe = electrostatic force in newtons q = charge in coulombs

Current I =

∆𝑞 𝑡

where: I = amperes in amps ∆𝑞 = change in charge in coulombs/ sec t = time in seconds

Resistance R =

𝜌𝐿 𝐴

where: R = ohms 𝜌 = resistivity in Ω * meters Resistivities at 200 C

L = meters A = meter2

Conductance G =

1 𝑅

Material

Resistivity ( Ω * m )

Aluminum

2.82 x 10-8

Copper

1.72 x 10-8

Gold

2.44 x 10-8

Nichrome

150 x 10-8

Tungsten

5.60 x 10-8

where G = is in mhos R = resistance in ohms

Magnetic flux density B =

𝛷 𝐴

where: B = magnetic flux density in teslas Φ = magnetic flux in webers A = area in square meters

Permeability µr =

µ

where: µr = the relative permeability in henries per meter or newton per

µ0

ampere squared (

𝑁 𝐼2

)

µ = the permeability of the material in newton per ampere squared µ0 = the permeability of a vacuum ( 4π x 10-7 µ=

𝐵 𝐻

𝑁 𝐼2

)

where: µ = permeability in newtons per ampere squared B = magnetic flux density in teslas H = field intensity ampere turns per meter

Tesla T =

𝑉 𝑥 𝑠𝑒𝑐 𝑚2

where: T = tesla V = volts m = meters

Magnetomotive Force Fm = N I where Fm = Magnetomotive force in ampere turns N = number of turns I = amperes

Field Intensity

H=

𝐹𝑚 𝐿

=

𝑁𝐼 𝐿

where: H = field intensity in ampere turns/meter Fm = Magnetomotive force N I = ampere turns L = length between poles

Reluctance (1) R =

𝑚𝑚𝑓 𝛷

where: R = reluctance in Fm / Φ mmf = Fm or N I Φ = flux in webers

(2) R =

𝐿

where: R = ampere turns / weber

µ𝐴

L = length of coil in meters µ = permeability of the material in

𝑇−𝑚 𝑁𝐼

A = cross sectional area of coil, m2

Flux ( 1) Φ =

𝐹𝑚 𝑅

where: Φ = magnetic flux in webers (Wb) Fm = Magnetomotive force in ampere turns R = reluctance in ampere turns / weber

(2) Φ =

𝑁𝐼 𝑁𝐼 𝑊𝑏

where N I = ampere turns Wb = webers

Induced voltage Vind = -N

Δ𝛷 Δ𝑡

where: Vind = induced voltage in volts N = number of turns in the coil Δ𝛷 Δ𝑡

= rate at which the flux cuts across the conductor,

Temperature coefficient of resistance (α)

𝑤𝑒𝑏𝑒𝑟𝑠 𝑠𝑒𝑐

Rt = Ro + Ro(α ΔT)

where: α = the temperature coefficient no units Rt = resistance at new temperature in ohms Ro = the resistance at 200 C in ohms

Temperature Coefficient for various materials Material

Temperature coefficient in Ω per 0C

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

REq = R1 + R2 + R3 + ...

𝑅𝐸𝑞

=

1 𝑅1

+

1 𝑅2

+

1 𝑅3

...

where: I = amperes V = voltage REq = resistance equivalent R = circuit resistance

Two resisters in parallel

RT =

𝑅1 𝑅2 𝑅1 + 𝑅2

where RT = total resistance in ohms R1 = first resistance in ohms R2 = second resistance in ohms

Counter electromotive force (CEMF) CEMF = -L

∆𝐼 ∆𝑡

where:

CEMF = induced voltage in volts L = inductance in henries ∆𝐼

= time rate of change of current in amps/sec

∆𝑡

Inductance

L=

𝑁𝛷

where: L = inductance in heneries

𝐼

Φ = flux in webers I = current in amperes Inductive reactance XL = 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 𝐿𝐸𝑞

=

1 𝐿1

+

1 𝐿2

+

1 𝐿3

+... where LEq = the equivalent inductance in henries L123 = inductors in henries

Capacitance C =

𝑄 𝑉

where: C = capacitance in farads (F) (coulombs / volt) Q = amount of charge in coulombs V = the voltage in joules / coulomb

Capacitance of two plates

C=K

𝐴 𝑑

(8.85 x 10-12) 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 10-12 = constant of proportionality in F meters Capacitive reactance Xc =

1 2𝜋𝑓 𝐶

where: Xc = capacitive reactance in ohms f = frequency in hertz C = capacitance in farads

π = 3.1416 Work stored in a capacitor Wstored =

𝐶 𝑉2 2

where: Wstored = energy stored in joules C = capacitance in farads V = voltage in volts

Capacitors in series

1 𝐶𝐸𝑞

=

1 𝐶1

+

1 𝐶2

+

1 𝐶3

+... where: CEq = the equivalent capacitance in farads C123 = component capacitance in farads

Capacitors in parallel Capacitive time constant

CEq = C1 + C2 + C3 +... Tc = R C where: Tc = capacitive time constant in seconds R = resistance in ohms C = capacitance in farads

Internal resistance (Battery) VL = 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 VG = 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 2𝜋 𝐿 𝐶

where: f = frequency in hertz L = inductance in henries C = capacitance in farads

(2) 𝜔o =

1 𝐿𝐶

where: 𝜔o = freq in radians / second L = inductance in henries C = capacitance in farads Power factor

Pf =

𝑃

where: Pf = power factor expressed in decimals

𝑺

P = real power in watts S = apparent power in volt amp reactive ( VAR Efficiency motor

Meff =

𝑃𝑖𝑛 𝑃𝑜𝑢𝑡

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 =

𝐻𝑃 𝑥 746 𝑉 𝑋 𝐸𝑓𝑓

AC amps 3phase =

,

AC amps(120 240) =

𝐻𝑃 𝑥 746 𝑉 𝑥 𝐸𝑓𝑓 𝑥 𝑃𝐹

,

𝐻𝑃 𝑥 746 1.73 𝑥 𝑉 𝑥 𝐸𝑓𝑓 𝑥 𝑃𝐹

AC / DC motor cont. DC amps =

𝑘𝑤 𝑥 1000 𝑉

AC amps(120,240) =

, AC amps(120, 240) =

𝑘𝑉𝐴 𝑥 1000 𝑉

𝑘𝑤 𝑥 1000 𝑉 𝑥 𝑃𝐹

, AC amps3phase =

,

AC amps 3phase =

𝑘𝑉𝐴 𝑥 1000 1.73 𝑥 𝑉

𝐾𝑊 𝑥 1000 1.73 𝑥 𝑉 𝑥 𝑃𝐹

DC kw =

𝐼𝑥𝑉 1000

, AC kw(120, 240) =

AC kv-amps (120,240) = DC hp =

𝐼 𝑥 𝑉 𝑥 𝐸𝑓𝑓 746

AC hp 3 phase =

𝐼𝑥𝑉 1000

𝐼 𝑥 𝑉 𝑥 𝑃𝐹 1000

, AC kw 3 phase =

, AC kv-amps 3 phase =

, AC hp(120,240) =

1000

𝐼 𝑥 𝑉 𝑥 1.73 1000

𝐼 𝑥 𝑉 𝑋 𝐸𝑓𝑓 𝑥 𝑃𝐹 746

𝐼 𝑥 𝑉 𝑥 1.73 𝑥 𝑃𝐹

,

𝐼 𝑥 𝑉 𝑥 𝐸𝑓𝑓 𝑥 1.73 𝑥 𝑃𝐹 746

Transformer voltage and current Vp =

𝑉𝑠 𝑥 𝐼𝑠 𝐼𝑝

where:Vp = primary voltage in volts Vs = secondary voltage in volts Is = secondary current in amps Ip = primary current in amps

Transformer voltage and turns in coil Vp =

𝑉𝑠 𝑥 𝐼𝑝 𝑇𝑠

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

Vs =

Transformer amperes and turns in coil Ip = Is =

𝑉𝑝 𝑥 𝑇𝑠 𝑇𝑝 𝐼𝑠 𝑥 𝑇𝑠 𝑇𝑝 𝐼𝑝 𝑥 𝑇𝑝 𝑇𝑠

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

106

Violet

7

107

Grey

8

108

white

9

109

4th band ,tolerance ,silver ± 10%, gold ± 5%, no band, 20%

5th band, brown ± 1%, red band, .1 %, no band, > ± 1 %

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.