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)
