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**399
**

*www.emersonct.com
*

**800-893-2321
**

**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

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* = *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* =3*Vp*, *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* = ω*L* = 2π ƒ*L* Ohms (stores en-
ergy)

Where ƒ = frequency (Hz), *L* = Inductance (H)
Capacitative reactance, *XC* = 1/ (ω*C*) = 1/ (2πƒ*C*)

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

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

*Z* = (R2 + X*L
*2) or (R2 + X*C
*

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 + (X*L* - X*C*)
2)

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

**400
**

*www.emersonct.com
*

** 800-893-2321
**

**Sy
m
**

**bo
ls
**

** &
F
**

**or
m
**

**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]