# Electrical Formulas | Electrical Formulas Sheet

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)