# series RC current with AC source

• Jan 24th 2009, 06:40 PM
mhyann
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
• Jan 24th 2009, 09:15 PM
mr fantastic
Quote:

Originally Posted by mhyann
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.