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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 fl ux ΦWeber Weber
Frequency f Hertz Hz
Flux linkage λWeber-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 ωRadians 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 = V2앛 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 앛앀3, Vl =앀3Vp, Il = Ip
In a DELTA connected circuit: Ip = Il 앛 앀3, Il =앀3 Ip Vl =
Vp
Total of apparent power in VA = 앀3 Vl Il
Active power in watts,W = 앀3 Vl Il cos ϕ
Reactive power in VAr = 앀3 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 = 앀3 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 앛 kWelec) x 100 per cent
Phase current Ip = Il for wye connection
Ip = Il 앛 앀3 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 = 앀(R2 + XL
2) or 앀(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 nega-
tive, thus
Z = 앀(R2 + (XL - XC)2)
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