 ## Capacitors in AC Circuits

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:

 XC    = 1 ————— 2πƒC

Where:

 XC = capacitive reactance in ohms 2π = 6.28 ƒ = frequency in hertz C = capacitance in farads

The steps to solve this formula are:
1. Multiply the frequency by 6.28.
2. Multiply the resulting product by the capacitance.
3. 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:

 XC    = 1 ——————————————— 6.28 x 60 x 0.000066

This gives a capacitive reactance (XC) 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 66-microfarad 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 vice-versa. 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 most-negative 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.