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Electrical Formulas | Electrical Formulas Sheet

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A

Absolute Permittivity

${{\varepsilon }_{o}}=8.84*{{10}^{-12}}$

Active Power

$\text{P=VICos(}\theta \text{) Watt}$

Apparent Power

$\text{S=VI volt-amp}$

B

C

Capacitance

$\text{C=}\frac{\text{ }\varepsilon {{\text{ }}_{\text{o}}}\text{ }\varepsilon {{\text{ }}_{\text{r}}}\text{A}}{\text{d}}$

Where,

εo= Absolute Permittivity

εr= Relative Permittivity

A=Plates Area

d= distance between plates

Conductance

$\text{Conductance}=\frac{1}{\text{Resistance}}=\frac{1}{\text{R}}$

Capacitive Reactance

${{\text{X}}_{\text{C}}}\text{=}\frac{1}{2\pi fC}$

Capacitive Susceptance

${{\text{B}}_{\text{C}}}\text{=}\frac{1}{{{\text{X}}_{\text{C}}}}$

Current in Series Circuit

$\text{I=}\frac{E}{{{R}_{1}}+{{R}_{2}}+{{R}_{3}}+\cdots +{{R}_{n}}}$

D

E

Energy Stored in a Capacitor

$\text{W=}\frac{1}{2}C{{V}^{2}}\text{ Joules}$

Electric Field

\[E=\frac{V}{d}\]

Where

E = Electric Field (V/m)

V = Voltage (V)

d = distance (m)

Electric current

\[I=\frac{\Delta q}{\Delta t}\]

Electric Flux Density

$\text{D=}\frac{Q}{A}$

Where,

Q=charge

A=Area

Electric Field Strength

$\Im \text{=}\frac{E}{d}$

Where,

E=Potential Difference

d= distance between the plates

Energy Stored in an Inductor

$\text{W=}\frac{1}{2}L{{I}^{2}}$

Energy Consumed

$\begin{align}  & E\text{=Power*Time} \\ & \text{W=P*t} \\\end{align}$

F

Frequency

$\text{F=}\frac{1}{T}$

Where T represents time period of one complete cycle

Flux Density

$\text{B=}\frac{\Phi }{A}$

Where,

Φ=flux

A=Area

G

H

I

Instantaneous Voltage

                                        \[\text{e = }{{\text{E}}_{\text{m}}}\text{ sin(}\omega \text{t)}\]

Where

Em=peak voltage

ω=angular frequency

Instantaneous Current

                                          \[\text{i = }{{\text{I}}_{\text{m}}}\text{sin(}\omega \text{t)}\]

Where

Im=peak current

ω=angular frequency

Inductances in Series

$\text{Ls=}{{\text{L}}_{\text{1}}}\text{+}{{\text{L}}_{\text{2}}}\text{+}{{\text{L}}_{\text{3}}}\text{+}\cdots$

Inductances in Parallel

$\frac{1}{{{L}_{p}}}=\frac{1}{{{L}_{1}}}+\frac{1}{{{L}_{2}}}+\frac{1}{{{L}_{3}}}+\cdots$

Inductive Reactance

${{\text{X}}_{\text{L}}}\text{=2}\pi \text{fL}$

Inductance

$L=\frac{{{e}_{L}}}{^{\Delta \Phi }{{/}_{\Delta t}}}$

Where,

∆Φ=change in flux

eL=induced emf

Inductive Susceptance

${{\text{B}}_{\text{L}}}\text{=}\frac{1}{{{\text{X}}_{\text{L}}}}$

Induced EMF

${{\text{e}}_{\text{L}}}\text{=}\frac{\Delta \Phi }{\Delta t}$

Where

∆Φ=change in flux

∆t=change in time

J

K

Kinetic Energy

\[KE=\text{ }\frac{1}{2}m{{v}^{2}}\]

Where

m=mass of a body

v=velocity with which body is moving

L

M

Magnetic force

\[F=qvBsin\theta \]

Where

q=charge                                                                                               

v=velocity

B=magnetic field density

Magnetic force on a current carrying conductor

\[\text{F}=\text{BI}\ell \]

Where

F = force (N)

B= Magnetic Field (T)

I = current (A)

l = length (m)

Mutual Inductance

$M=\frac{{{e}_{L}}}{{}^{\Delta i}/{}_{\Delta t}}$

Mechanical Force

$\text{F=BIL}$

Where

B=flux density

L=length of a conductor

Magnetomotive Force

$\text{F=NI}$

Where

N=number of turns

N

O

Ohm’s Law

$\begin{align}  & \text{V=IR} \\ & \text{I=}\frac{V}{R} \\ & R=\frac{V}{I} \\\end{align}$

P

Potential Energy

 \[PE\text{ }=mgh\]

Where

m=body mas

g= gravitational acceleration (9.8 m/s2)

h=height

Permeability

$\mu =\frac{B}{H}$

Where

B=flux density

H=flux intensity (field strength)

Power

  \[\begin{align}  & P=VI\text{ (Sometimes refer to as Apparent Power in Power Systems)} \\ & P={{I}^{2}}R\text{ (Somtimes refer to as losses)} \\ & \text{P=}\frac{{{V}^{2}}}{R}\text{ (Normally, use it in Parallel Electric Circuit)} \\\end{align}\]

Power Factor

$\text{cos(}\theta \text{)=}\frac{P}{S}$

Where

P=Active Power

S=Apparent Power

Q

R

Reactive Power

$\text{Q=VI Sin(}\theta \text{) VAR}$

RMS AC Current

${{\text{I}}_{\text{rms}}}\text{=}\frac{{{I}_{p}}}{\sqrt{2}}=0.637\text{ }{{\text{I}}_{\text{p}}}$

Where

Ip=peak current

RMS AC Voltage

${{\text{V}}_{\text{rms}}}{{\text{=}}^{{{V}_{p}}}}{{/}_{\sqrt{2}}}=0.637\text{ }{{\text{V}}_{\text{p}}}$

Where

Vp= peak voltage

Reluctance

$\Re =\frac{F}{\Phi }$

Where

Φ=flux lines

F=mechanical force

Resistance

$R=\rho \frac{L}{A}$

 

S

System Efficiency

$\eta =\frac{Output}{Input}*100$

Sometimes, we do write input in terms of output such as:

$\eta =\frac{Output}{Output+Losses}*100$

Self-Inductance

$L={{\mu }_{o}}{{\mu }_{r}}{{N}^{2}}\frac{A}{l}$

Where

μo=Absolute Permeability

μr=Relative Permeability

N=number of turns

l=length of a coil

A=Area of coil

T

Total Series Resistance

$\text{R=}{{\text{R}}_{\text{1}}}\text{+}{{\text{R}}_{\text{2}}}\text{+}{{\text{R}}_{\text{3}}}\text{+}\cdots \text{+}{{\text{R}}_{\text{n}}}$

Total Supply Current to Parallel Current

$\begin{align}  & \text{I=}{{\text{I}}_{\text{1}}}\text{+}{{\text{I}}_{\text{2}}}\text{+}{{\text{I}}_{\text{3}}}\text{+}\cdots \text{+}{{\text{I}}_{\text{n}}} \\ & I=E(\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{3}}}+\cdots +\frac{1}{{{R}_{n}}}) \\\end{align}$

Total Parallel Resistance

          \[{{R}_{P}}\text{=}\frac{1}{\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{3}}}+\cdots +\frac{1}{{{R}_{n}}}}\]

Three Phase Reactive Power

$\text{Q=}\sqrt{3}{{V}_{L}}{{I}_{L}}Sin(\theta )$

Where

VL=line voltage

IL=line current

Three Phase Active or True Power

$\text{P=}\sqrt{3}{{V}_{L}}{{I}_{L}}Cos(\theta )$

Where

VL=line voltage

IL=line current

Two Resistors in Parallel

$\text{R=}\frac{{{R}_{1}}*{{R}_{2}}}{{{R}_{1}}+{{R}_{2}}}$

Total Parallel Conductance

$\text{G=}{{\text{G}}_{\text{1}}}\text{+}{{\text{G}}_{\text{2}}}\text{+}{{\text{G}}_{\text{3}}}\text{+}\cdots \text{+}{{\text{G}}_{\text{n}}}$

Total Capacitance in Parallel

$\text{Cp=}{{\text{C}}_{\text{1}}}\text{+}{{\text{C}}_{\text{2}}}\text{+}{{\text{C}}_{\text{3}}}\text{+}\cdots$

Total Capacitance in Series

$\frac{1}{{{C}_{s}}}=\frac{1}{{{C}_{1}}}+\frac{1}{{{C}_{2}}}+\frac{1}{{{C}_{3}}}+\cdots$

Three Phase Apparent Power

$\text{S=}\sqrt{3}\text{ }{{\text{V}}_{\text{L}}}{{\text{I}}_{\text{L}}}\text{ volt-amp}$

Transformer Voltage/Turn Ratio

$\frac{{{E}_{s}}}{{{E}_{p}}}=\frac{{{N}_{s}}}{{{N}_{p}}}$

Transformer Current Ratio

$\frac{{{I}_{s}}}{{{I}_{p}}}=\frac{{{N}_{p}}}{{{N}_{s}}}$

 

Transformer EMF Equation

$E=4.44\Phi fN$

Where

Φ=magnetic flux lines

f=frequency

N=number of turns

Transformer Voltage Regulation

$Voltage\text{ Regulation=}\frac{{{V}_{NL}}-{{V}_{FL}}}{{{V}_{FL}}}*100$

Where

VNL=Secondary side voltage at No Load

VFL=Secondary side voltage at Full Load

Transformer Open Circuit Test Parameters

   \[\begin{align}  & {{\text{R}}_{\text{o}}}\text{=}\frac{\text{E}_{\text{p}}^{\text{2}}}{\text{P}} \\ & {{\text{X}}_{\text{o}}}\text{=}\frac{\text{E}_{\text{p}}^{\text{2}}}{\text{Q}} \\\end{align}\]

Where

Ep=Primary side voltage

 Transformer Short Circuit Test Parameters

 \[\begin{align}  & {{\text{R}}_{s}}\text{=}\frac{\text{P}}{\text{I}_{\text{p}}^{\text{2}}} \\ & {{\text{X}}_{s}}\text{=}\frac{\text{Q}}{\text{I}_{\text{p}}^{\text{2}}} \\\end{align}\]

Ip=Primary side current

Temperature Effect on Resistance

${{\text{R}}_{\text{2}}}\text{=}{{\text{R}}_{\text{1}}}\text{(1+}\alpha \Delta \text{T)}$

Where,

R1=resistance at 20 oC

Α=temperature coefficient of the material

∆T=temperature change from 20 oC

U

V

Voltage Divider

\[{{\text{V}}_{\text{n}}}\text{=E*}\frac{{{R}_{n}}}{{{R}_{1}}+{{R}_{2}}+{{R}_{3}}+\cdots }\]

Where,

Rn=resistance across which one wishes to measure the potential difference

E=voltage source

W

Wavelength

$\lambda \text{=}\frac{c}{f}$

Where,

c=speed of light (3*108 m/s)

f=frequency (Hz)

 

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About Ahmad Faizan

Mr. Ahmed Faizan Sheikh, M.Sc. (USA), Research Fellow (USA), a member of IEEE & CIGRE, is a Fulbright Alumnus and earned his Master’s Degree in Electrical and Power Engineering from Kansas State University, USA.

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