RC circuit

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This is a model of the AC and transient signal behavior of an RC series circuit. The AC characteristics include the attenuation factors (ratio of AC output to input voltage) and phase shifts for both high-pass and low pass outputs. The variables Et, Eo, t, and Tr refer to the transient behavior of the low-pass output to a step input of zero to Eo volts at t=0. 

Variable Sheet
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St Input     Name    Output    Unit      Comment
             Xc      10        KOhm      capacitive reactance (Ohm, KOhm, MOhm)
   60        f                 Hz        frequency (Hz, KHz)
             C       .26525824 µF        capacitor value (F,µF)
   10        R                 KOhm      Resistor (Ohm, KOhm, MOhm)
             Z       14142.136 Ohm       Impedance (Ohm, KOhm, MOhm)
   60        fo                Hz        corner frequency (Hz, KHz)
             alphaL  .70710678           Low-pass attenuation factor (unitless)
             alphaH  .70710678           High-pass attenuation factor (unitless)
             ThetaL  45        degrees   Low pass phase angle (radians, degrees)
             ThetaH  45        degrees   High pass phase angle (radians, degrees)
             Tc      .00265258 sec       Time constant (sec, msec, µsec)
             Et      .98994816 volts     Voltage at time t (volts, mV,µV)
   1         Eo                volts     Steady-state voltage (volts, mV,µV)
   .01220188 t                 sec       time after step input (sec, msec, µsec)
             Tr      .01220188 sec       1 % response time (sec, msec, µsec)

Rule Sheet
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S Rule
  Xc=1/(2*Pi()*f*C)       "Reactance of capacitor
  Z=SQRT((R*R)+(Xc*Xc))   "Impedance of series RC circuit
  fo=1/(2*Pi()*R*C)       "Frequency at which alpha = 0.707
  alphaL=Xc/Z             "ratio of output to input ac voltage (low pass)
  alphaH=R/Z              "ratio of output to input ac voltage (high pass)
  Tan(Pi()/2-ThetaL)=Xc/R "Low pass phase angle
  ThetaH=Pi()/2-ThetaL    "High pass phase angle
  Tc=R*C                  "Time constant
  Et=Eo*(1-exp(-t/Tc))    "Transient response of RC circuit
  Tr=4.6*Tc               "1 percent response time