Series resistor-capacitor circuits

Chapter 4.3 Series resistor-capacitor circuits

Lessons In Electric Circuits Volume II – AC Book
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Lessons In Electric Circuits Volume II – AC Book

  • 4.3.SERIES RESISTOR-CAPACITOR CIRCUITS85• REVIEW:• Capacitive reactance is the opposition that a capacitor offers to alternating current due to itsphase-shifted storage and release of energy in its electric field. Reactance is symbolized by thecapital letter “X” and is measured in ohms just like resistance (R).• Capacitive reactance can be calculated using this formula: XC = 1/(2πfC)• Capacitive reactance decreases with increasing frequency. In other words, the higher thefrequency, the less it opposes (the more it “conducts”) the AC flow of electrons.4.3Series resistor-capacitor circuitsIn the last section, we learned what would happen in simple resistor-only and capacitor-only ACcircuits. Now we will combine the two components together in series form and investigate the effects.(Figure 94,4.10)RCEC-79.3°ETI ER10 V60 Hz5 ΩRC100 µFETIIRVCICI = IR = ICET = ER+ ECFigure 4.10: Series capacitor inductor circuit: voltage lags current by 0o to 90o.The resistor will offer 5 Ω of resistance to AC current regardless of frequency, while the capacitorwill offer 26.5258 Ω of reactance to AC current at 60 Hz. Because the resistor’s resistance is a realnumber (5 Ω0o, or 5 + j0 Ω), and the capacitor’s reactance is an imaginary number (26.5258 Ω-90o, or 0 - j26.5258 Ω), the combined effect of the two components will be an opposition to currentequal to the complex sum of the two numbers. The term for this complex opposition to currentis impedance, its symbol is Z, and it is also expressed in the unit of ohms, just like resistance andreactance. In the above example, the total circuit impedance is: