## Reactive load

**
Resistance
and Series Reactance
The impedance Z of a reactive load comprising resistance R and series
reactance X is:
Z = R + jX = |Z|Ðf
Converting to the equivalent admittance Y:
Y = 1 / Z = 1 / (R + jX) = (R - jX) / (R**

^{2}+ X

^{2}) = R / |Z|

^{2}- jX / |Z|

^{2}

**
When a voltage V (taken as reference)
is applied across the reactive load Z, the current I is:
I = VY = V(R / |Z| ^{2} - jX / |Z|^{2}) = VR / |Z|^{2}
- jVX / |Z|^{2} = I_{P} - jI_{Q}
The active current I_{P} and the reactive current I_{Q} are:
I_{P} = VR / |Z|^{2} = |I|cosf
I_{Q} = VX / |Z|^{2} = |I|sinf
**

The apparent
power S, active power P and reactive power Q are:

S = V|I| = V^{2} / |Z| = |I|^{2}|Z|

P = VI_{P} = I_{P}^{2}|Z|^{2} / R = V^{2}R
/ |Z|^{2} = |I|^{2}R

Q = VI_{Q} = I_{Q}^{2}|Z|^{2} / X = V^{2}X
/ |Z|^{2} = |I|^{2}X

**
The power factor cosf
and reactive factor sinf
are:
cosf = I _{P} / |I| = P / S
= R / |Z|
sinf = I_{Q} / |I| = Q / S
= X / |Z| **

Resistance and Shunt Reactance

The impedance Z of a reactive load comprising resistance R and shunt
reactance X is found from:

1 / Z = 1 / R + 1 / jX

Converting to the equivalent admittance Y comprising conductance G and shunt
susceptance B:

Y = 1 / Z = 1 / R - j / X = G - jB = |Y|Ð-f

**
When a voltage V (taken as reference)
is applied across the reactive load Y, the current I is:
I = VY = V(G - jB) = VG - jVB = I _{P} - jI_{Q}
The active current I_{P} and the reactive current I_{Q} are:
I_{P} = VG = V / R = |I|cosf
I_{Q} = VB = V / X = |I|sinf
**

The apparent
power S, active power P and reactive power Q are:

S = V|I| = |I|^{2} / |Y| = V^{2}|Y|

P = VI_{P} = I_{P}^{2} / G = |I|^{2}G / |Y|^{2}
= V^{2}G

Q = VI_{Q} = I_{Q}^{2} / B = |I|^{2}B / |Y|^{2}
= V^{2}B

The power factor cosf
and reactive factor sinf
are:

cosf = I_{P} / |I| = P / S
= G / |Y|

sinf = I_{Q} / |I| = Q / S
= B / |Y|