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Math Help - series RC current with AC source

  1. #1
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    series RC current with AC source

    Vm w/s^+w^2- VR-VC=0
    Vm w/s^2+w^2-iR-Q/C=0
    i=dQ/dt
    Vm w/s^2+w^2-RdQ/dt-Q/C=0
    Vm w/s^2+w^2-R laplce of [sQ(s)-Q(0)]-1/C Q(0)=0
    Vmw/s^2+w^2-Q(s)[SR+1/C]=0
    divide both side by R:
    Vm/R w/s^2+w^2-Q(s)[s+1/RC]=0
    Vm/R w/s^2+w^2=Q(s) [s+1/RC]
    Q(s)=(w/R)Vm/(s^2+w^2)(s+1/RC)
    Q(t)=L^-1 Q(s)
    Q(t)=L^-1 (w/R)Vm/(s^2+w^2)(s+1/RC)

    applied partial fraction:
    wVm/R=(A+C)s^2+(A/RC+B)s
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  2. #2
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    Quote Originally Posted by mhyann View Post
    Vm w/s^+w^2- VR-VC=0
    Vm w/s^2+w^2-iR-Q/C=0
    i=dQ/dt
    Vm w/s^2+w^2-RdQ/dt-Q/C=0
    Vm w/s^2+w^2-R laplce of [sQ(s)-Q(0)]-1/C Q(0)=0
    Vmw/s^2+w^2-Q(s)[SR+1/C]=0
    divide both side by R:
    Vm/R w/s^2+w^2-Q(s)[s+1/RC]=0
    Vm/R w/s^2+w^2=Q(s) [s+1/RC]
    Q(s)=(w/R)Vm/(s^2+w^2)(s+1/RC)
    Q(t)=L^-1 Q(s)
    Q(t)=L^-1 (w/R)Vm/(s^2+w^2)(s+1/RC)

    applied partial fraction:
    wVm/R=(A+C)s^2+(A/RC+B)s
    Can you please state clearly what it is you're trying to do and where you get stuck.
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