How much lead?

Chapter How much lead?

Teach Yourself Electricity and Electronics Third Edition Book
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Teach Yourself Electricity and Electronics Third Edition Book

  • The value of R in an RC circuit might increase relative to XC because resistance isdeliberately put into a circuit. Or, it might happen because the frequency becomes solow that XC rises to a value comparable with the leakage resistance of the capacitor. Ineither case, the situation can be represented by a resistor, R, in series with a capacitor,C (Fig. 14-10).256 Capacitive reactance14-10Schematicrepresentation of anRC circuit.If you know the values of Xc and R, you can find the angle of lead, also called the RCphase angle, by plotting the point RjXC on the RC plane, drawing the vector from theorigin 0 – j0 out to that point, and then measuring the angle of the vector, clockwise fromthe resistance axis. You can use a protractor to measure this angle, as you did in the pre-vious 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 thephase angle. For example, if XC4Ω and R7Ω, you’ll get the same angle as withXC400Ω and R700Ω, or with XC16Ω and R28Ω. The phase angle willbe the same for any ratio of XC:R4:7.Pure resistanceAs 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 smallcompared 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 inthe RC plane will be almost right along the R axis. Then the RC phase angle will benearly zero, that is, just a little bit negative. The voltage will come nearly into phase withthe current. The plates of the capacitor will not come anywhere near getting fullycharged 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 atmuch lower frequencies that might exist across it at the same time. (This property ofcapacitors can be put to use in electronic circuits, for example when an engineer wantsto let radio signals get through while blocking audio frequencies.)Ultimately, if the capacitive reactance gets small enough, the circuit will act as apure resistance, and the current will be in phase with the voltage.How much lead?If you know the ratio of capacitive reactance to resistance, or XC /R, in an RC circuit,then you can find the phase angle. Of course, you can find this angle of lead if you knowthe precise values.