Parallel resistor-capacitor circuits

Chapter 4.4 Parallel resistor-capacitor circuits

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

  • 90CHAPTER 4. REACTANCE AND IMPEDANCE – CAPACITIVEZ = arctangent(-30/40) = -36.87oZ = 40 - j30 = 50 36.87o• REVIEW:• Impedance is the total measure of opposition to electric current and is the complex (vector)sum of (“real”) resistance and (“imaginary”) reactance.• Impedances (Z) are managed just like resistances (R) in series circuit analysis: series impedancesadd to form the total impedance. Just be sure to perform all calculations in complex (notscalar) form! ZT otal = Z1 + Z2 + . . . Zn• Please note that impedances always add in series, regardless of what type of componentscomprise the impedances. That is, resistive impedance, inductive impedance, and capacitiveimpedance are to be treated the same way mathematically.• A purely resistive impedance will always have a phase angle of exactly 0o (ZR = R Ω0o).• A purely capacitive impedance will always have a phase angle of exactly -90o (ZC = XC Ω-90o).• Ohm’s Law for AC circuits: E = IZ ; I = E/Z ; Z = E/I• When resistors and capacitors are mixed together in circuits, the total impedance will have aphase angle somewhere between 0o and -90o.• Series AC circuits exhibit the same fundamental properties as series DC circuits: current isuniform throughout the circuit, voltage drops add to form the total voltage, and impedancesadd to form the total impedance.4.4Parallel resistor-capacitor circuitsUsing the same value components in our series example circuit, we will connect them in parallel andsee what happens: (Figure 99,4.14)RC10 V60 Hz5 ΩRC100µFEIIR ICE = ER = ECI = IR+ ILIR10.7°IICEFigure 4.14: Parallel R-C circuit.Because the power source has the same frequency as the series example circuit, and the resistorand capacitor both have the same values of resistance and capacitance, respectively, they must also