If I have the following AC circuit:

.. .. .. ||||--( V )---/\/\/-------((((()-------||------||||
'' '' ''

I can describe it with the following equations

V_L + V_R + V_C = V L dq^2/dt^2 + R dq/dt + (1/C) q = V

I now have to deal with the following AC circuit:

.---((((()---. .. | | .. .. ||||--( V )---/\/\/---| |---||------|||| '' | .. | '' '' '----||------' ''

How do I treat the inductor and capacitor that are in parallel? My guess is that I have a term representing the inductor and capacitor together, but I'm not sure. How do I represent this with a differential, or coupled differential equation?

Thanks for any help.

.. .. .. ||||--( V )---/\/\/-------((((()-------||------||||

I can describe it with the following equations

V_L + V_R + V_C = V L dq^2/dt^2 + R dq/dt + (1/C) q = V

I now have to deal with the following AC circuit:

.---((((()---. .. | | .. .. ||||--( V )---/\/\/---| |---||------|||| '' | .. | '' '' '----||------' ''

How do I treat the inductor and capacitor that are in parallel? My guess is that I have a term representing the inductor and capacitor together, but I'm not sure. How do I represent this with a differential, or coupled differential equation?

Thanks for any help.