Recall that when DC is placed across
a capacitor it will conduct for a
short time then stop conducting. Therefore, a capacitor is said to
block DC. However, AC repeatedly reverses direction. Every time this
happens the capacitor starts to conduct again. The more frequently the
AC reverses direction the more time the capacitor spends in its
conducting state. Unless the frequency is very low—or
the
capacitor is
of a very low value—the capacitor never goes out of its conducting
state when AC is applied to it. Therefore, AC passes through a
capacitor.
Capacitive Reactance
As the frequency of AC applied to a capacitor increases the capacitor
appears to become a better and better conductor. More formally, the
opposition to current flow decreases. A capacitor appears to become a
lower resistance as frequency goes up. For example, if a capacitor has
10 ohms of opposition to current flow at 100 Hz it will have 5 ohms at 200 Hz. A capacitor's opposition to
current flow is called capacitive reactance and, like resistance, is
measured in ohms.
At a given frequency, a larger capacitor will have less opposition to
current flow than a smaller capacitor. This means that a larger
capacitor has less capacitive reactance than a smaller capacitor. More
capacitance leads to less capacitive reactance.
Calculating Capacitive Reactance
Since the reactance of a capacitor is different at different
frequencies you need to be able to calculate the reactance based on the
frequency and the size of the capacitor.
The formula to calculate capacitive reactance is:
Where:

X_{C} 
=

capacitive reactance in ohms 

2π 
=

6.28 

ƒ

=

frequency in hertz 

C 
=

capacitance in farads 
The steps to solve this formula are:
 Multiply the frequency by 6.28.
 Multiply the resulting product by the capacitance.
 Find the reciprocal of this final product (divide 1 by the final
product)
For example, if you have a capacitance of 100 microfarads (0.0001
farads) and a frequency of 60 Hz, you would calculate capacitive
reactance with the following keystrokes on a typical calculator:
6


.


2


8


X


6


0


X


.


0


0


0


1


=


^{1}/χ


26.54




press these keys

displayed
answer

This gives a result of 26.54 ohms.
Note:
There are several styles of entry used by calculators. The above
example works for calculators with a reciprocal button that is labeled
as ^{1}/_{X}. Scientific calculators may label
the reciprocal button as X^{1}. You may also have to use the =
button after using the reciprocal
button on some calculators. Be sure to familiarize yourself with your
particular calculator.
In the following circuit the capacitive reactance is calculated as
below:
The source voltage has a frequency of 60 hertz and the capacitance is
66 microfarads (0.000066 farads). Plugging these numbers into the above
formula we get:
X_{C
= }

1

——————————————— 
6.28 x 60 x 0.000066

This gives a capacitive reactance (X
_{C}) of 40.2 ohms.
The keystrokes to perform this calculation are:
6


.


2


8


X


6


0


X


.


0


0


0


0


6


6


=


^{1}/χ


40.2

Voltage Division in Capacitive AC Circuits
Voltage division in AC circuits is the same as voltage division in DC
circuits. However, since more capacitance leads to less capacitive
reactance—i.e., a higher value capacitor acts like a lower value
resistor—
in a capacitive voltage
divider, the capacitor with the
greater capacitance will have the lesser voltage.
In the above circuit one capacitor is twice the value of the other. At
first glance you might expect the 33 microfarad capacitor to have 1/3
of the voltage (33.3 volts) and the 66 microfarad capacitor to have 2/3
of the voltage (66.6 volts). However, with capacitors the opposite is
true. The 33 microfarad capacitor will have the greater voltage (66.6
volts) and the 66microfarad capacitor will have the lesser voltage
(33.3 volts).
Voltage and Current in a Capacitor
Voltage and current are always synchronized with resistors. This means
if the voltage across a resistor increases, the current through the
resistor increases with it, and viceversa. If the voltage across a
resistor is steady, the current also remains steady. Voltage and
current don't synchronize with a capacitor. If the voltage across a
capacitor remains steady the current will stop flowing. If you increase
the voltage applied to a capacitor, the current will jump to a high
value then gradually drop to zero while the voltage gradually climbs to
the new higher value.
If you apply a square wave to a capacitor, then observe the voltage
across the capacitor and the current through the capacitor on an
oscilloscope, you will see something like the following diagram. Notice
that when the voltage is at zero, the current is at its maximum. Once
the voltage has reached its maximum value the current has reached
zero.. When the applied voltage reverses the current suddenly jumps to
its maximum negative value (negative current simply means that the
current has reversed direction). While the voltage is changing to its
mostnegative value, the current is approaching zero again. Once the
voltage has reached its greatest negative value, the current has once
again reached zero.
When a sine wave is applied to a capacitor the voltage is
constantly changing. As when a square wave is applied, when the
voltage is highest the current is zero. However, since the voltage
applied to the capacitor is a sine wave, so is the current. The voltage
and current simply peak at different times.
ICE
The following illustration shows the voltage and current with a capacitor
when a sine wave is applied. Notice that regardless of the frequency, the
current will peak 90 degrees before the voltage peaks. It has to because
when the current peaks, the voltage must be at zero and vice versa. The
current peaks and the voltage is at zero, then the voltage peaks and the
current is at zero. This phenomenon results in the voltage reaching its peak
90 degrees after the current reaches the same peak. Recall that in
electronic formulas the letter I represents current and E represents voltage. A
memory aid to help remember that current leads voltage in a capacitor
is "ICE". I comes before E with a C in the middle. This reminds you that current comes before voltage in a
capacitor.
Voltage and current of a
capacitor with a sine wave applied. Notice that when one peaks the other is
always at zero. This causes the voltage to follow the current by 90
degrees. 