Basic Formulas

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Basic Formulas

Ohms Law | Capacitance | Inductance | Legend

The following pages of formulas, some derivations and discussions are intended to assist in designing and applying capacitor banks properly.

1. Ohm’s Law

I = V (1)
or V = I

(2)

Then Z =

(3)

and I =

(4)

P=I

(5)

From (4)

This becomes

V =

(6)

Let P = VAR

Then Z =

(7)

or Z =

(8)

Or Z =

(9)

Letting Z = X_C Or X_L

(10)

We have X_C (Or X_L) =

(11)

This will allow you to determine the reactance of a capacitor or reactor when voltage and KVAR is given.

Example:

A three-phase 600KVAR capacitor bank at 12,470 will yield

Xc = = = 259.168 Ohms

A three-phase shunt reactor of 150KVAR, at 13.8KV will yield

X_L = = = 1269.6 Ohms

2. Capacitance

X_C=
(12)

But, as stated VAR = (6)

VAR =

(13)

Or =

(14)

Then VAR =

(15)

^{KVAR =

(16)}

Example:

From above 600KVAR at 12.47KV equals 259.168 Ohms and from (12)

X_C= . Then C =

Let f = 60 Hertz

Then C = 0.000010235 farads or 10.235 microfarads.

From (16) KVAR =

KVAR = 600

3. Inductance

(17)

VAR = from (6) =
(18)

KVAR =
(19)

From above 150KVAR at 13.8KV equals 1269.6 Ohms and from (17)

. Let f = 60 Hertz

Then L = = = 3.36773 Henries

Or 3367.73 millihenries.

From (19) KVAR ==

KVAR = 150

LEGEND
R	Resistance
I	Amps
V	Volts
Z	Impedance
P	Power (in Watts and/or Vars)
VAR	Reactive Power
K	Kilo (10³)
X_c	Capacitive Reactance
X_L	Inductive Reactance
M	Mega (10⁶)

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