## Power

The
power P dissipated by a resistance R carrying a current I with a voltage
drop V is:

P = V^{2} / R = VI = I^{2}R

Similarly,
the power P dissipated by a conductance G carrying a current I with a
voltage drop V is:

P = V^{2}G = VI = I^{2} / G

The power P
transferred by a capacitance C holding a changing voltage V with charge Q is:

P = VI = CV(dv/dt) = Q(dv/dt) = Q(dq/dt) / C

The power P transferred by an inductance L carrying a changing current I
with magnetic linkage
Y is:

P = VI = LI(di/dt) =
Y(di/dt) =
Y(dy/dt) / L

####
Complex
Power

When
a voltage V causes a current I to flow through a reactive load Z, the
complex power S is:

S = VI* where I* is the conjugate of the complex current I.

Inductive Load

Z = R + jX_{L}

I = I_{P} - jI_{Q}

cosf = R / |Z|
(lagging)

I* = I_{P} + jI_{Q}

S = P + jQ

An inductive load is a sink of lagging VArs (a source of leading VArs).

Capacitive Load

Z = R - jX_{C}

I = I_{P} + jI_{Q}

cosf = R / |Z|
(leading)

I* = I_{P} - jI_{Q}

S = P - jQ

A capacitive load is a source of lagging VArs (a sink of leading VArs).

**
**

####
Three
Phase Power

For
a balanced star connected load with line voltage V_{line} and line
current I_{line}:

V_{star} = V_{line} / Ö3

I_{star} = I_{line}

Z_{star} = V_{star} / I_{star} = V_{line} / Ö3I_{line}

S_{star} = 3V_{star}I_{star} = Ö3V_{line}I_{line}
= V_{line}^{2} / Z_{star} = 3I_{line}^{2}Z_{star}

**
For
a balanced delta connected load with line voltage V _{line} and line
current I_{line}:**

V_{delta} = V_{line}

I_{delta} = I_{line} / Ö3

Z_{delta} = V_{delta} / I_{delta} = Ö3V_{line} / I_{line}

S_{delta} = 3V_{delta}I_{delta} = Ö3V_{line}I_{line} = 3V_{line}^{2} / Z_{delta} = I_{line}^{2}Z_{delta}

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

S^{2} = P^{2} + Q^{2}

P = Scosf

Q = Ssinf

where cosf is the power factor and sinf
is the reactive factor

**
Note that
for equivalence between balanced star and delta connected loads:
Z _{delta} = 3Z_{star} **