The most common used electrical formulas - Ohms Law and combinations
Common electrical units used in formulas and equations are:
Sir, I have a farm for which I want to put 10 numbers of 25 watts CFL bulbs around the perimeter, the perimeter of the farm is around 1 KM. Can you please confirm what type of wire I need to use (gauge, insulation requirements, Copper vs Aluminum), Considering that I will be laying this underground through pipes (which might be exposed to water at timesI need wires that are resistant to. Perform electrical engineering calculations related to cables, motors, lighting/photometry etc.
- Volt - unit of electrical potential or motive force - potential is required to send one ampere of current through one ohm of resistance
- Ohm - unit of resistance - one ohm is the resistance offered to the passage of one ampere when impelled by one volt
- Ampere - units of current - one ampere is the current which one volt can send through a resistance of one ohm
- Watt - unit of electrical energy or power - one watt is the product of one ampere and one volt - one ampere of current flowing under the force of one volt gives one watt of energy
- Volt Ampere - product of volts and amperes as shown by a voltmeter and ammeter - in direct current systems the volt ampere is the same as watts or the energy delivered - in alternating current systems - the volts and amperes may or may not be 100% synchronous - when synchronous the volt amperes equals the watts on a wattmeter - when not synchronous volt amperes exceed watts - reactive power
- kiloVolt Ampere - one kilovolt ampere - kVA - is equal to 1000 volt amperes
- Power Factor - ratio of watts to volt amperes
Electrical Potential - Ohm's Law
Ohm's law can be expressed as:
U = R I (1a)
U = P / I (1b)
U = (P R)1/2 (1c)
Electric Current - Ohm's Law
I = U / R (2a)
I = P / U (2b)
I = (P / R)1/2 (2c)
Electric Resistance - Ohm's Law
R = U / I (3a)
R = U2/ P (3b)
R = P / I2 (3c)
Example - Ohm's law
A 12 volt battery supplies power to a resistance of 18 ohms.
I = (12 V) / (18 Ω)
= 0.67 (A)
Electric Power
P = U I (4a)
P = R I2 (4b)
P = U2/ R (4c)
where
P = power (watts, W, J/s)
U = voltage (volts, V)
I = current (amperes, A)
R = resistance (ohms, Ω)
Electric Energy
Electric energy is power multiplied with time:
W = P t (5)
where
W = energy (Ws, J)
t = time (s)
Alternative - power can be expressed
P = W / t (5b)
Power is consumption of energy by consumption of time.
Example - Energy lost in a Resistor
A 12 V battery is connected in series with a resistance of 50 ohm. The power consumed in the resistor can be calculated as
P = (12 V)2 / (50 ohm)
= 2.9 W
The energy dissipated in 60 seconds can be calculated
W = (2.9 W) (60 s)
= 174 Ws, J
= 0.174 kWs
= 4.8 10-5 kWh
Example - Electric Stove
An electric stove consumes 5 MJ of energy from a 230 V power supply when turned on in 60 minutes.
The power rating - energy per unit time - of the stove can be calculated as
P = (5 MJ) (106 J/MJ) / ((60 min) (60 s/min))
= 1389 W
= 1.39 kW
The current can be calculated
I = (1389 W) / (230 V)
= 6 ampere
Electrical Motors
Electronic Engineering Calculator
Electrical Motor Efficiency
μ = 746 Php / Pinput_w (6)
where
μ = efficiency
Php = output horsepower (hp)
Pinput_w = input electrical power (watts)
or alternatively
μ = 746 Php / (1.732 V I PF) (6b)
Electrical Motor - Power
P3-phase = (U I PF 1.732) / 1,000 (7)
where
P3-phase = electrical power 3-phase motor (kW)
PF = power factor electrical motor
Electrical Motor - Amps
I3-phase = (746 Php) / (1.732 VμPF) (8)
where
I3-phase = electrical current 3-phase motor (amps)
PF = power factor electrical motor
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Cable Length from Sag, Span
Formula:
L = S + ((8 * d2) / (3 * S))
Where,
L = Cable Length
S = Cable Span
d = Cable Sag
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Spring Resonant Frequency
Formula:
fres= (1/2)* √(k/M)Where,
fres = Spring Resonance
k = Spring Constant
M = Spring Mass
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Solenoid Coil Electromagnetic Force
Formula:
F = (n x i)2 x magnetic constant x a / (2 x g2)
Where,
F = Force,
i = Current,
g = Length of the gap between the solenoid and a piece of metal,
a = Area
n = Number of turns,
Magnetic constant = 4 x PI x 10-7.
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Capacitor Energy (E) and RC Time Constant
Formula:
E = (V² x C) / 2T = R x C
Where,
E =Stored Energy (Joules),
T = Time Constant (S),
V = Volatge (V) ,
C = Capacitance (uF),
R = Load Resistance (Ohms).
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Physical Properties of Coil / Material
Formula Used:
T = bl / d
n = Turns/ T
cd = (2 x n x d) + bd
r = (n x d + bd) / 2
a = PI x r x r
L = (2 x PI x r x n) / 1000
rpm = .0333 *((0.812/2)*(0.812/2))/((d/2)*(d/2))
R = rpm x L
V = R x I
P = V x I
Where,
T = Turns per winding,
bl = Length of Bobbin,
d = Wire Diameter,
n = Number of windings,
cd = Outer diameter of coil,
bd = Diameter of Bobbin,
r = radius of middle of coil,
a = Cross sectional area,
L = Total Length,
rpm = Resistance/meter,
R = Resistance,
V = Voltage at Rated Current,
I = Current,
P = Power at Rated Current,
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Air Core Coil Inductance
Formula:
Inductance = ((d2) x (n2)) / (18d + 40l)
Where,
d = Coil Diameter,
l = Coil Length,
n = Number of turns.
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Parallel Resistor
Formula Used:
Rp = 1 / ((1/R1) + (1/R2))
Where,
Rp = Total Parallel Resistance
R1 & R2 = Resistors connected in parallel
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Straight Wire Inductance / Inductor
Formula:
L= 0.00508 x a x (log(2 x a/d)-0.75)
Where,
L = Inductance,
a,d = Length & Diameter of the wire,
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8051 PIC Microcontroller (UC) Time Delay
Formula Used:
TIC12 = 1 / (mhz / 12)TIC6 = 1 / (mhz / 6)
8-bit Timer Counter Maximum Run-Time for 12 clock = TIC12 * 256 / 1000
8-bit Timer Counter Maximum Run-Time for 6 clock = TIC6 * 256 / 1000
16-bit Timer Counter Maximum Run-Time for 12 clock = TIC12 * 65536 / 1000
16-bit Timer Counter Maximum Run-Time for 6 clock = TIC6 * 65536 / 1000
8-Bit DRT Reload Value for 12 clock = 256 -(DRT / TIC12 * 1000)
8-Bit DRT Reload Value for 6 clock = 256 -(DRT / TIC6 * 1000)
16-Bit DRT Reload Value for 12 clock = 65536 -(DRT / TIC12 * 1000)
16-Bit DRT Reload Value for 6 clock = 65536 -(DRT / TIC6 * 1000)
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Parallel Resistance of Electronic Circuit
Formula :
Where R1,R2,...Rn are the individual resistor values
Rtotal is the total resistance value in parallel
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Series Resistor / Resistance
Formula:
R=R1+R2+R3+.......
Where,
R = Total Resistors value
R1 = Individual Resistors value
R2 = Individual Resistors value
R3 = Individual Resistors value
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Microstrip Transmission Lines Impedance (Z0)
Formula:
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Electrical Admittance (Y)
Formula:
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Series Capacitor / Capacitance
Formula :
1/CTotal = 1/C0 + 1/C1 + 1/C2 + .... + 1/Cn
Where,C0,C1,..,Cn are the individual capacitors values
CTotal is the total capacitance value of an electrical circuit
1/CTotal = 1/C0 + 1/C1 + 1/C2 + .... + 1/Cn
Where,C0,C1,..,Cn are the individual capacitors values
CTotal is the total capacitance value of an electrical circuit
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Parallel Capacitor / Capacitance
Formula :
CTotal = C1 + C2 + C3 + .... + Cn
Where,C1,C2,..,Cn are the individual capacitors values
CTotal is the total capacitors value in parallel
Using this Online Electrical Calculator the
parallel Capacitors calculation in a circuit is made easier here.
CTotal = C1 + C2 + C3 + .... + Cn
Where,C1,C2,..,Cn are the individual capacitors values
CTotal is the total capacitors value in parallel
Using this Online Electrical Calculator the
parallel Capacitors calculation in a circuit is made easier here.
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Horsepower (HP) and Watts Conversion
Formula:
Horsepower (HP) =W/HP
Where,
W = Power in wattsHP = Value of one HP
1 Electrical HP = 746 watts
1 Mechanical HP = 745.69987 watts
1 Metric HP = 735.49875 watts
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Power Factor for AC
Formula:
Power factor = kW/√ (kW)2 + (kVAr)2
Where,
kW = Real Power
kVAr = Reactive Power
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Three Phase Transformer Capacity
Formula:
V = (k x 1000) / (A x Ph)A = (k x 1000) / (V x Ph)
k = (Ph x V x A) / 1000
Where,
V = Volt
A = Amps
k = kVA
Ph = 3 phase (√3 = 1.732050808)
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Specific Work of Gas Turbine
Formula:
w = K / ((K - 1) * R * T1 * [1 - ((p2 / p1)((K-1)/K))])Where,
w = Specific Work Gas Turbine
K = Ratio Specific Heat Air
R = Individual Gas Constant
T1 = Absolute Temperature
p1 = Primary Pressure
p2 = Secondary Pressure
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3 Phase Power by Two Wattmeters Method
Formula:
P = ( V12 * I2 * cos ( 30 + θ ) ) + ( V13 * I3 * cos ( 30 - θ ) )
Where,
P = Three Phase Power
V12 , V13 = Voltage
I2, I3 = Current
θ = Displacement Angle
cos = Cosine
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Specific Work
Formula:
w = (p1 - p2) / ρt = (p2 - p1) / ρ
Where,
w = Specific Work of Pump
t = Specific Work of Turbine
p1 = Primary Pressure
p2 = Secondary Pressure
ρ = Density
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AVR Timer
Formula:
f = cf / po = ttt / tr2
rtt = t - (o * tr2)
rt = ttt / f
nf = f / ttt
Where,
f = Frequency
cf = System Clock Frequency
p = Prescaler Clock Value
o =Overflow Count
tr = Timer Resolution
ttt = Total Timer Ticks
rtt = Remainder Timer Ticks
rt = Real Time
nf = New Frequency
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Young's Modulus Spring Resonant Frequency
Formula:
fres = (d / (9* D2 * nf)) * √(G / ρ)Where,
fres = Spring Resonant Frequency
d = Wire Diameter
D = spring Diameter
nf = Total Number of Coils
G = Youngs Modulus of Material
ρ = Material Density
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Gearbox Ratio
Formula:
GF = (eRPM * h * 0.002975) / aMPH = GF / GR
Where,
GF = Gear Factor
GR = Gear Ratio
eRPM = Engine RPM (Revolution per Minute)
h = Tire Height
a = Axle Ratio
MPH = Miles per Hour
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Power Consumption mAh Calculator
Formula:
b = (c / h) * 0.70Where,
b = Average Current Consumption
c = Battery Capacity
h = Estimated Hours
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Electricity Cost
Formula:
Energy Consumed per Day = (p × h) / 1000Energy Consumed per Month = ((p × h) / 1000) × 30
Energy Consumed per Year = ((p × h) / 1000) × 365
Electricity Cost per Day = ((p × h) / 1000) × r
Electricity Cost per Month =(((p × h) / 1000) × 30) × r
Electricity Cost per Year = (((p × h) / 1000) × 365) × r
Where,
p = Power Consumption
h = Hours of Use per Day
r = Electricity Cost per Unit
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Wire Diameter
Formula:
D = 2 × √(A / π)Where,
D = Wire Diameter
A = Area
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Wire Gauge
Formula:
Wire Diameter in AWG = -10 - 20 × log(d)Where,
d = Wire Diameter
g = Diameter of Wire in Gauge
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Electric Potential Energy
Formula:
Where,
V = Electric Potential
qN = Charge
ε0 = Permittivity(8.8541878176e-12 F/m)
rN = Point Distant
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Transformer Current
Formula:
I = P / VWhere,
I = Current
P = Power Rating
V = Voltage
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Transformer Primary Conductor Size
Formula:
δ = I / AWhere,
δ = Conductor Size
I= Current
A = Current density
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Number of Turns in a Transformer Coil
Formula:
Te = (1/(4.44 × F × M × A))T = Te × V
Where,
Te = Turns per Volts
T = Total Number of Turns
M = Magnetic flux
A = Area of Core
F = Operating Frequency
V = Voltage
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Transformer Wire Length
Formula:
Total Wire Length = Number of Turns × Perimeter of BobbinRelated Calculator:
Volume of Conductor
Formula:
Volume of Conductor = Area × LengthRelated Calculator:
Weight of Transformer Windings
Formula:
Weight of Windings(kg) = Density × Volume(m3)Related Calculator:
NE555 Timer Astable Circuit
Formula:
f = 1.44 / ((R1 + 2(R2)) × C)
THigh = 0.693 × (R1 + R2) × C
Tlow = 0.693 × R2 × C
d = ( THigh / ( THigh + l )) × 100
Where,
R1 = Resistor 1
R2 = Resistor 2
C = Capacitor
d = Duty Cycle
f = Frequency
THigh = Time High
Tlow = Time Low
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Electrostatic
Formula:
p = ε0 × e2 / 2Where,
p = Electrostatic Pressure
e = Electric Field
ε0 = Electric Constant(8.854×10-12)
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Real and Reactive Power
Electrical Engineering Calculators
Formula:
For Single Phaset = v × i × cos(p)
r = v × i × sin(p)
For Three Phase
t = √3 × v × i × cos(p)
r = √3 × v × i × sin(p)
Where,
t = Real power
r = Reactive power
v = Voltage
i = Current
p = Phase Angle
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DC Power
Formula:
P = V × IV = P / I
I = P / V
Where,
P = Power
V = Voltage
I = Current
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AC Power
Formula:
For Single PhaseP = V × I × cos(θ)
V = P / (I × cos(θ)
I = P / (V × cos(θ)
For Three Phase
P = √3 × V × I × cos(θ)
V = P / (3 × I × cos(θ)
I = P / (3 × V × cos(θ)
Where,
P = Power
θ = Power Factor Angle
V = Voltage
I = Current
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Power Consumption South Africa
Electrical Engineering Calculator Download
Formula:
p = (e × t) / 1000Where,
p = Power Consumption
e = Electricity Usage
t = Total Usage Time
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Copper Loss
Formula:
l = (a2 × b) + (c2 × d)Where,
l = Copper Loss
a = Primary Winding Current
b = Primary Winding Ohmic Resistance
c = Secondary Winding Current
d = Secondary Winding Ohmic Resistance
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Total Luminous Flux
Formula:
Ω = 2π(1-Cosθ)F = ΩIv
Where,
Iv = Maximum Luminous Intensity
θ = Cone Full Angle
Ω = Equivalent Solid Angle
F = Total Luminous Flux
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Coaxial Cable Impedance
Best Calculator For Electronics
Formula:
Z = (138 × log10 (d1 / (d2)) / √(R)F = 11.8 / (√(R) × π × ((d1 + d2) / 2))
T =( (7.354 × R) / (log10(d1 / d2)))/0.3048
D = (140.4 × log10(d1 / d2))/0.3048
V = (1 / √ (R)) × 100
Where,
Z = Impedance
d1 = Dielectric Outer Diameter
d2 = Inner Conductor Diameter
R = Dielectric Constant
F = Cutoff Frequency
T = Capacitance
D = Inductance
V = Velocity of Propagation
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