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Pure capacitance
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Imagine placing an ac voltage source across a capacitor. Suppose that the frequency is high enough, and/or the capacitance large enough, so that the capacitive reactance, XC, is extremely small compared with the resistance, R. Then the current leads the voltage by a full 90 degrees (Fig. 14-8). At very high frequencies, it doesn t take very much capacitance for this to happen. Small capacitors usually have less leakage resistance than large ones. At lower frequencies, the capacitance must be larger, although high-quality, low-loss capacitors are not too difficult to manufacture except at audio frequencies and at the 60-Hz utility frequency. The situation depicted in Fig. 14-8 represents an essentially pure capacitive reactance. The vector in the RC plane points just about straight down. Its angle is 90 degrees from the R axis or zero line.
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Currents leads voltage 255
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14-8 In a pure capacitance, the current leads the voltage by 90 degrees.
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Capacitance and resistance
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When the resistance in a resistance-capacitance circuit is significant compared with the capacitive reactance, the current leads the voltage by something less than 90 degrees (Fig. 14-9). If R is small compared with XC, the difference is almost a quarter of a cycle. As R gets larger, or as XC becomes smaller, the phase difference gets less. A circuit containing resistance and capacitance is called an RC circuit.
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14-9 In a circuit with capacitance and resistance, the current leads the voltage by less than 90 degrees.
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256 Capacitive reactance The value of R in an RC circuit might increase relative to XC because resistance is deliberately put into a circuit. Or, it might happen because the frequency becomes so low that XC rises to a value comparable with the leakage resistance of the capacitor. In either case, the situation can be represented by a resistor, R, in series with a capacitor, C (Fig. 14-10).
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14-10 Schematic representation of an RC circuit.
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If you know the values of Xc and R, you can find the angle of lead, also called the RC phase angle, by plotting the point R jXC 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 resistance 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 only need to know the ratio of XC to R to determine the 4 and R 7 , you ll get the same angle as with phase angle. For example, if XC 400 and R 700 , or with XC 16 and R 28 . The phase angle will XC be the same for any ratio of XC :R 4:7.
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Pure resistance
As the resistance in an RC circuit gets large compared with the capacitive reactance, the angle of lead becomes smaller. The same thing happens if the value of XC gets small compared with the value of R. When you call XC large, you mean large negatively. When you say that XC is small, you mean that it is close to zero, or small negatively. When R is many times larger than XC, whatever their actual values, the vector in the RC plane will be almost right along the R axis. Then the RC phase angle will be nearly zero, that is, just a little bit negative. The voltage will come nearly into phase with the current. The plates of the capacitor will not come anywhere near getting fully charged with each cycle. The capacitor will be said to pass the ac with very little loss, as if it were shorted out. But it will still have an extremely high XC 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, for example when an engineer wants to let radio signals get through while blocking audio frequencies.) Ultimately, if the capacitive reactance gets small enough, the circuit will act as a pure resistance, and the current will be in phase with the voltage.
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