Reactance and frequency

Chapter Reactance and frequency

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

  • As you increase the frequency of the ac voltage source, there will come a point atwhich the plates do not get charged up very much before the source polarity reverses.The set of plates will be “sluggish.” The charge won’t have time to get established witheach ac cycle.At high ac frequencies, the voltage between the plates will have trouble followingthe current that is charging and discharging them. Just as the plates begin to get a goodcharge, the ac current will pass its peak and start to discharge them, pulling electronsout of the negative plate and pumping electrons into the positive plate.As the frequency is raised, the set of plates starts to act more and more like a shortcircuit. When the frequency is low, there is a small charging current, but this quickly tailsoff and drops to zero as the plates become fully charged. As the frequency becomes high,the current flows for more and more of every cycle before dropping off; the charging timeremains constant while the period of the charging/discharging wave is getting shorter.Eventually, if you keep on increasing the frequency, the period of the wave will be muchshorter than the charging/discharging time, and current will flow in and out of the platesin just about the same way as it would flow if the plates were shorted out.The opposition that the set of plates offers to ac is the capacitive reactance. It ismeasured in ohms, just like inductive reactance, and just like resistance. But it is, byconvention, assigned negative values rather than positive ones. Capacitive reactance,denoted XC, can vary, just as resistance and inductive reactance do, from near zero(when the plates are huge and close together, and/or the frequency is very high) to afew negative ohms, to many negative kilohms or megohms.Capacitive reactance varies with frequency. But XC gets larger (negatively) as thefrequency goes down. This is the opposite of what happens with inductive reactance,which gets larger (positively) as the frequency goes up.Sometimes, capacitive reactance is talked about in terms of its absolute value,with the minus sign removed. Then you might say that XC is increasing as the frequencydecreases, or that XC is decreasing as the frequency is raised. It’s best, however, if youlearn to work with negative XC values right from the start. This will be important later,when you need to work with inductive and capacitive reactances together in the samecircuits.Reactance and frequencyIn many ways capacitive reactance behaves like a mirror image of inductive reactance.But in another sense, XC is an extension of XL into negative values—below zero.If the frequency of an ac source is given in hertz as f and the capacitance of a ca-pacitor in farads as C, then the capacitive reactance isXC 1/(6.28fC)This same formula applies if the frequency, f, is in megahertz and the capacitance,C, is in microfarads (µF). Just remember that if the frequency is in millions, the capac-itance must be in millionths.Capacitive reactance varies inversely with the frequency. This means that thefunction XC vs f appears as a curve when graphed, and this curve “blows up” as the fre-quency nears zero.Reactance and frequency249