Capacitive Reactance Help

Capacitive Reactance—Capacitors and Current

Inductive reactance has its counterpart in the form of capacitive reactance, denoted X _C . In many ways, inductive and capacitive reactance are alike. They’re both forms of “electrical inertia.” But in a capacitive reactance, the voltage has trouble keeping up with the current—the opposite situation from inductive reactance.

Capacitors And Current

Imagine two gigantic, flat, parallel metal plates, both of which are excellent electrical conductors. If a source of DC, such as that provided by a large battery, is connected to the plates (with the negative pole on one plate and the positive pole on the other), current begins to flow immediately as the plates begin to charge up. The voltage difference between the plates starts out at zero and builds up until it is equal to the DC source voltage. This voltage buildup always takes some time, because the plates need time to become fully charged. If the plates are small and far apart, the charging time is short. But if the plates are huge and close together, the charging time can be considerable. The plates form a capacitor, which stores energy in the form of an electric field.

Suppose the current source connected to the plates is changed from DC to AC. Imagine that you can adjust the frequency of this AC from a few hertz to many megahertz. At first, the voltage between the plates follows almost exactly along as the AC polarity reverses. As the frequency increases, the charge, or voltage between the plates, does not have time to get well established with each current cycle. When the frequency becomes extremely high, the set of plates behaves like a short circuit.

Capacitive reactance is a quantitative measure of the opposition that a capacitor offers to AC. It, like inductive reactance, varies with frequency and is measured in ohms. But X _C is, by convention, assigned negative values rather than positive values. For any given capacitor, the value of X _C increases negatively as the frequency goes down, and approaches zero from the negative side as the frequency goes up.

X _C Vs Frequency

Capacitive reactance behaves, in some ways, like a mirror image of inductive reactance. In another sense, X _C is an extension of X _L into negative values. If the frequency of an AC source is given (in hertz) as f, and the value of a capacitor is given (in units called farads ) as C, then the capacitive reactance (in ohms), X _C , can be calculated using this formula:

X _C = –1/(2πfC )

Capacitive reactance varies inversely with the negative of the frequency. The function of X _C versus f appears as a curve when graphed, and this curve “blows up negatively” (or, if you prefer, “blows down”) as the frequency nears zero. Capacitive reactance varies inversely with the negative of the capacitance, given a fixed frequency. Therefore, the function of X _C versus C also appears as a curve that “blows up negatively” as the capacitance approaches zero. Relative graphs of these functions are shown in Fig. 9-10.

Fig. 9–10. Capacitive reactance varies inversely with the negative of the frequency. It also varies inversely with the negative of the capacitance, given a fixed frequency.