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Pure Capacitance Suppose an ac voltage source is connected across a capacitor. Imagine that the frequency is low enough, and/or the capacitance is small enough, so the absolute value of the capacitive reactance, X C, is extremely large compared with the resistance, R. Then the current leads the voltage by just about 90 (Fig. 14-8). The situation depicted in Fig. 14-8 represents a pure capacitive reactance. The vector in the RC plane in this situation points straight down. Its angle is 90 from the R axis. Capacitance and Resistance When the resistance in a resistance-capacitance circuit is significant compared with the absolute value of the capacitive reactance, the current leads the voltage by something less than 90 (Fig. 14-9). If R is small compared with the absolute value of X C, the difference is almost a quarter of a cycle. As R gets larger, or as the absolute value of X C becomes smaller, the phase difference decreases. A circuit containing resistance and capacitance is called an RC circuit. The value of R in an RC circuit might increase relative to the absolute value of X C because resistance is deliberately put into a circuit. It can also happen if the frequency becomes so high that the absolute value of the capacitive reactance drops to a value comparable with the loss resistance in

Suppose that the source is changed from direct to alternating current (Fig. 14-3). Imagine that you can adjust the frequency of this ac from a low value of a few hertz, to hundreds of hertz, to many kilohertz, megahertz, and gigahertz.

Asynchronous Transfer Mode (ATM)

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the circuit conductors. In either case, the situation can be represented by a resistance, R, in series with a capacitive reactance, X C (Fig. 14-10). If you know the values of X C and R, you can find the angle of lead, also called the RC phase angle, by plotting the point R jX C on the RC plane, drawing the vector from the origin 0 j0 out to that point, and then measuring the angle of the vector clockwise from the R axis. You can use a protractor to measure this angle, as you did in the previous chapter for RL phase angles. Or you can use trigonometry to calculate the angle. As with RL circuits, you need only know the ratio of X C to R to determine the phase angle. For example, if X C = 4 and R = 7 , you ll get the same angle as with X C = 400 and R = 700 , or with X C = 16 and R = 28 . The phase angle will be the same whenever the ratio of XC to R is equal to 4:7.

At first, the voltage between the plates will follow just about exactly along as the ac source polarity reverses over and over. But the set of plates has a certain amount of capacitance, as you have learned. Perhaps they can charge up fast, if they are small and if the space between them is large, but they can t charge instantaneously.

Network architectures often develop in concert with the corporate structures that they serve Companies with centralized management authorities such as utilities, banks, and hospitals often have centralized and tightly controlled hierarchical data-processing architectures to protect their data On the other hand, organizations that are distributed in nature such as research and development facilities and universities often have highly distributed data processing architectures They tend to share information on a peer-to-peer basis and their corporate structures reflect the fact ATM came about not only because of the proliferation of diverse network architectures, but also because of the evolution of traffic characteristics and transport requirements To the well-known demands of voice, we now add various flavors of data, video, MP3, an exponentially large variety of IP traffic, interactive real-time gaming, and a variety of other content types that place increasing demands on the network.

Pure Resistance As the resistance in an RC circuit gets large compared with the absolute value of the capacitive reactance, the angle of lead becomes smaller. The same thing happens if the absolute value of X C gets small compared with the value of R. When R is many times larger than the absolute value of X C , whatever their actual values, the vector in the RC plane points almost along the R axis. Then the RC phase angle is close to 0 . The voltage comes nearly into phase with the current. The plates of the capacitor do not come anywhere near getting fully charged with each cycle. The capacitor is said to pass the ac with very little loss, as if it were shorted out. But it will still have an extremely high X C for any ac signals at much lower frequencies that might exist across it at the same time. (This property of capacitors can be put to use in electronic circuits. An example is when an engineer wants to let radio-frequency signals get through while blocking signals at audio frequencies.) Ultimately, if the absolute value of the capacitive reactance gets small enough, the circuit acts as a pure resistance, and the current is in phase with the voltage.

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