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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

Flux linkage λ Weber-turns -

Resistance R Ohm Ω

Inductance L Henry H

Capacitance C Farad F

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

rads-1

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 = I2Z = 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 Ip Vl =

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 energy)

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 + XC2)

If R, XL and XC are present in series in the same circuit

then XL and XC may be summated, treating XC as negative,

thus

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

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

400

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800-893-2321

Symbols & Formulae

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]