Ohm's Law states that voltage equals current times resistance. For an AC circuit with only a capacitor, voltage equals current times capacitive reactance. The document provides the equations to calculate capacitive reactance (XC) from voltage and current, and then calculate capacitance (C) from capacitive reactance, frequency, and standard equations. It includes an example problem where the capacitance of a capacitor in a 50V, 400Hz AC circuit with a 10mA current is calculated to be 79.6nF or 0.08μF.

1. Ohm’s Law = V = I R
In a purely capacitive
AC circuit, V = I XC

2. V
I=
R

3. V
I=
Xc

4. V
Xc =
I

5. Example 1:
A capacitor connected across a 50V AC 400Hz
supply causes a current of 10mA. What is
it’s capacitance value?
XC
=
V / I
= 50 / 10 x 10-3
=
5 kΩ

6. XC
1 / 2 π f C
=
∴
C
=
1 / 2 π f XC
=
1 / 2 x 3.1416 x 400 x (5 x 103)
=
7.96 x 10-8 F
=
79.6nF or 0.08 μF