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Circuit Analysis: AC, Linear Circuits and Transients

Which of the following is the s-domain impedance Z(s) of a resistor R and a capacitor C connected in parallel?

  1. AR + 1/(sC)
  2. BsRC/(1 + sRC)
  3. CR/(1 + sRC)
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Answer: C. R/(1 + sRC)

Method 1 (sum of admittances): in the s-domain, the impedance of a capacitor is 1/(sC) and its admittance is sC. In parallel the admittances add, so Y(s) = 1/R + sC = (1 + sRC)/R and Z(s) = R/(1 + sRC). Method 2 (product over sum): multiplying the numerator and denominator of Z = R × (1/(sC))/(R + 1/(sC)) by sC also gives R/(1 + sRC). Setting s = jω gives the AC impedance R/(1 + jωRC); it approaches R as s → 0 (DC) and 0 as s → ∞.

  • A. This is the impedance of R and C connected in series.
  • B. This dimensionless quantity has the form of the transfer function of an RC high-pass filter; it is not an impedance.
  • C. Correct. Z(s) = R/(1 + sRC).
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