Electrical formulas
- 1. 399 www.emersonct.com 800-893-2321 Symbols&Formulae 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 flux 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 Efficiency 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 = I2 Z = V2 ȋ 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 ȋǰ3, Vl =ǰ3Vp, Il = Ip In a DELTA connected circuit: Ip = Il ȋ ǰ3, Il =ǰ3 Ip Vl = Vp Total of apparent power in VA = ǰ3 Vl Il Active power in watts,W = ǰ3 Vl Il cos ϕ Reactive power in VAr = ǰ3 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 = ǰ3 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 Efficiency, η = (kWmech ȋ kWelec) x 100 per cent Phase current Ip = Il for wye connection Ip = Il ȋ ǰ3 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 = ǰ(R2 + XL 2 ) or ǰ(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 = ǰ(R2 + (XL - XC)2 ) CTi Automation - Phone: 800.894.0412 - Fax: 208.368.0415 - Web: www.ctiautomation.net - Email: info@ctiautomation.net
- 2. 400 www.emersonct.com 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 filler 0.043 1.2 Cast Iron, gray 0.274 7.6 Steel 0.28 7.75 Friction Coefficients 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 Efficiencies 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: info@ctiautomation.net