3 17-1: Alternating Current in a Capacitive Circuit Current flows with ac voltage applied to a series connected capacitor and light bulb.There is NO current through the capacitor’s dielectric.While the capacitor is being charged by increasing applied voltage, the charging current flows in one direction in the conductors to the plates.While the capacitor is discharging, when the applied voltage decreases, the discharge current flows in the reverse direction.With alternating voltage applied, the capacitor alternately charges and discharges.
5 17-1: Alternating Current in a Capacitive Circuit Summary:Alternating current flows in a capacitive circuit with ac voltage applied.A smaller capacitance allows less current, which means more XC with more ohms of opposition.Lower frequencies for the applied voltage result in less current and more XC.With a steady dc voltage source (zero frequency), the capacitor’s opposition is infinite and there is no current. In this case the capacitor is effectively an open circuit.
6 17-1: Alternating Current in a Capacitive Circuit Summary, cont.XC depends on the frequency of the applied voltage and the amount of capacitance.XC is less for more capacitance.XC is less for higher frequencies.
7 17-2: The Amount of XC Equals 1/(2π f C) Factors Affecting XCThe value of XC is inversely proportional to the value of capacitance:Increasing C decreases XCDecreasing C increases XCThe value of XC is inversely proportional to the frequency:Increasing f decreases XCDecreasing f increases XC
8 17-2: The Amount of XC Equals 1/(2π f C) Summary of the XC Formulas:When f and C are known:When XC and f are known:When XC and C are known:XC =12π f CC =12π f XCf =12π C XC
9 17-3: Series or Parallel Capacitive Reactances Capacitive reactance is an opposition to AC, so series or parallel reactances are combined in the same way as resistances.Combining capacitive reactances is opposite to the way capacitances are combined. The two procedures are compatible because of the inverse relationship between XC and C.
10 17-3: Series or Parallel Capacitive Reactances Series Capacitive Reactance:Total reactance is the sum of the individual reactances.XCT = XC1 + XC2 + XC etc.All reactances have the same current.The voltage across each reactance equals current times reactance.VC1 = I × XC1
11 17-3: Series or Parallel Capacitive Reactances Total reactance is found by the reciprocal formula:All reactances have the same voltage.The current through each reactance equals voltage divided by reactance.IC = VC / XC1XCT=XC1XC2XC3+etc.
13 17-5: Applications of Capacitive Reactance The general use of XC is to block direct current but provide low reactance for alternating current.Ohms of R remain the same for dc or ac circuits, but XC depends on frequency.The required C becomes smaller for higher frequencies.
14 17-5: Applications of Capacitive Reactance Table 17-1Capacitance Values for a Reactance of 100 ΩC (Approx.)FrequencyRemarks27 μF60 HzPower-line and low audio frequency1.6 μF1000 HzAudio frequency0.16 μF10,000 Hz1600 pF1000 kHz (RF)AM radio160 pF10 MHz (HF)Short-wave radio16 pF100 MHz (VHF)FM radio
15 17-5: Applications of Capacitive Reactance Summary of Capacitance vs. Capacitive Reactance:CapacitanceSymbol is CUnit is FValue depends on constructioniC = C(dv/dt)Capacitive ReactanceSymbol is XCUnit is ΩValue depends on C and fXC = vc / ic or 1/(2πfC)
16 17-5: Applications of Capacitive Reactance Summary of Capacitive Reactance vs. Resistance:Capacitive ReactanceSymbol is XCUnit is ΩValue decreases for higher fCurrent leads voltage by 90° (Θ = 90°).ResistanceSymbol is RUnit is ΩValue does not change with fCurrent and voltage are in phase (Θ = 0°).
18 17-6: Sine Wave Charge and Discharge Current Charge and discharge current of a capacitor can be found if we know two factors:The capacitance value of the capacitorThe rate of voltage change across the capacitorCapacitive current, iC depends on the rate of voltage change across its plate
19 17-6: Sine Wave Charge and Discharge Current Calculating the Values of iC.The greater the voltage change, the greater the amount of capacitive current.Capacitive current is calculatedi is in amperesC is in faradsdv/dt = volts per second.ic =Cdvdt
20 17-6: Sine Wave Charge and Discharge Current 90° Phase AngleiC leads vC by 90°.ICEThe difference results from the fact that iC depends on the dv/dt rate of change, not v itself.The ratio of vC / iC specifies the capacitive reactance in ohms.
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