# Electrical formula Equations, Formulas and forms for Electrical Engineering. Universitas Padjadjaran

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Electrical Formulas

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Sym bols &

Form ulae

Electrical Formulae Electrical Quantities

Quantity Symbol Unit Name Unit Symbol

Electromotive force E, e* Volt V

Potential difference V, v* Volt V

Current I, i* Ampere A

Magnetic fl ux Φ Weber Weber

Frequency f Hertz Hz

Resistance R Ohm Ω

Inductance L Henry H

Impedance Z Ohm Ω

Reactance X Ohm Ω

Power,dc,or active P Watt W

Power, reactive Q Volt-ampere

reactive VAr, var

Power, total or apparent

S Volt-ampere VA

Power factor angle ϕ - °, deg.

Angular velocity ω Radians per second

Rotational velocity n Revolutions per second

s-1 ,rev s-1

Revolutions per minute

min-1, rpm

Effi ciency η -

Number of pairs of poles

p -

* Capital and small letters designate rms and instantaneous value respectively.

AC Single-Phase All quantities r.m.s. values: V = I Z Total or apparent power in VA = Vl = I

2Z = V2 Z Active power in watts, W =Vl cos ϕ Reactive power in VAr = Vl sin ϕ

AC Three-Phase (Assuming Balanced Symmetrical Waveform) All quantities r.m.s values: Vl = Line-to-line voltage Vp = Phase voltage (line-to-neutral) Il = line current (wye) Ip = Phase current (delta) In a WYE connected circuit, Vp = Vl 3, Vl =3Vp, Il = Ip In a DELTA connected circuit: Ip = Il  3, Il =3 IpVl = Vp Total of apparent power in VA = 3 Vl Il Active power in watts,W = 3 Vl Il cos ϕ Reactive power in VAr = 3 Vl Il sin ϕ Power factor (pf) = cos ϕ

= Active power / Apparent power = W / VAr

Three-Phase Induction Motors All quantities rms values: kWmech = horsepower x 0.746 kWelec = 3 Vl Il cos ϕ at rated speed and load

where Vl = supply voltage Il = rated full load current cos ϕ = rated full load power factor

Effi ciency, η = (kWmech  kWelec) x 100 per cent Phase current Ip = Il for wye connection

Ip = Il  3 for delta connection

Loads (phase values) Resistance R, measured in Ohms (no energy storage) Inductive reactance, XL = ωL = 2π ƒL Ohms (stores en- ergy)

Where ƒ = frequency (Hz), L = Inductance (H) Capacitative reactance, XC = 1/ (ωC) = 1/ (2πƒC)

Where ƒ = frequency (Hz), C = Capacitance (F)

Impedance Impedance is the algebraic sum of the separate load values thus:

Z = (R2 + XL 2) or (R2 + XC

2)

If R, XL and XC are present in series in the same circuit then XL and XC may be summated, treating XC as nega- tive, thus

Z = (R2 + (XL - XC) 2)

CTi Automation - Phone: 800.894.0412 - Fax: 208.368.0415 - Web: www.ctiautomation.net - Email: [email protected]

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Sy m

bo ls

& F

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ul ae

Electrical Formulae

Ohms Law

Amperes = Volts or Ohms = Volts Ohms Amperes

or Volts = Amperes x Ohms

Power in DC Circuits

Horsepower = Volts x Amperes 746

Watts = Volts x Amperes

Kilowatts = Volts x Amperes 1,000

Kilowatts-Hours = Volts x Amperes x Hours 1,000

Power in AC Circuits

Kilovolt-Amperes (KVA):

kVA (1Ø) = Volts x Amperes 1,000

kVA (3Ø) = Volts x Amperes x 1.73 1,000

Kilowatts (Kw)

kW (1Ø) = Volts x Amperes x Power Factor 1,000

kW (3Ø) = Volts x Amperes x Power Factor x 1.73 1,000

Power Factor = Kilowatts Kilovolts x Amperes

Other Useful Formulae

Three-Phase (3Ø) Circuits

HP = E x I x 3 x Eff x PF 746

Motor Amps = HP x 746 E x 3 x Eff x PF

Motor Amps = kVA x 1000 3 x E

Motor Amps = kW x 1000 3 x E x PF

Power Factor = kW x 1000 E x I x 3

Kilowatt Hours = E x I x Hours x 3 x PF 1000

Power (Watts) = E x I x 3 x PF

Material Densities Materials lb/in3 gm/cm3

Aluminum 0.096 2.66 Brass 0.299 8.3 Bronze 0.295 8.17 Copper 0.322 8.91 Hard Wood 0.029 0.8 Soft Wood 0.018 0.48 Plastic 0.04 1.11 Glass 0.079-0.090 2.2-2.5 Titanium 0.163 4.51 Paper 0.025-0.043 0.7-1.2 Polyvinyl chloride 0.047-0.050 1.3-1.4 Rubber 0.033-0.036 0.92-0.99 Silicone Rubber, without fi ller

0.043 1.2

Cast Iron, gray 0.274 7.6 Steel 0.28 7.75

Friction Coeffi cients Ffr=µWL Materials µ Steel on Steel (greased) ~0.15 Plastic on Steel ~0.15-0.25 Copper on Steel ~0.30 Brass on Steel ~0.35 Aluminum on Steel ~0.45 Steel on Steel ~0.58 Mechanism µ Ball Bushings <0.001 Linear Bearings <0.001 Dove-tail Slides ~0.2++ Gibb Ways ~0.5++

Mechanism Effi ciencies Acme screw with brass nut ~0.35-0.65 Acme screw with plastic nut ~0.50-0.85 Ballscrew ~0.85-0.95 Chain and Sprocket ~0.95-0.98 Preloaded Ballscrew ~0.75-0.85 Spur or Bevel gears ~0.90 Timing Belts ~0.96-0.98 Worm Gears ~0.45-0.85 Helical Gear (1 reduction) ~0.92

Mechanical Variables

CTi Automation - Phone: 800.894.0412 - Fax: 208.368.0415 - Web: www.ctiautomation.net - Email: [email protected]