Two parallel plate capacitors are connected together with a conductor \"in serie

Question

Two parallel plate capacitors are connected together with a conductor "in series" as shown. The system starts with no charge on any of the surfaces. Then, the whole apparatus is charged up with an external battery so that V_D - V_A = Delta V_total How are V_B and V_C related? If Delta V_1 is the potential across the first capacitor, and DeltaV_2 is the potential across the second capacitor, find the relationship between Delta V_total, V_1, and V_2. How is the charge on plate B related to the charge on plate C, if all the plates started out neutrally charged? If there is a charge +Q on plate D, find the charge on each of the other plates. We can treat this entire apparatus as though it were a single capacitor of capacitance C_total and charge Q (which is the same as the charge on plate D). Find C_total in terms of C_1 and C_2, using the information above.

Explanation / Answer

a) Due to charge transformation B and C are at same potential So VB = VC

b) dV_total = dV1 + dV2

C) opposite and same quantity of charges are present on B and C

D) -Q on C ,+Q on B and -Q on A

E) in series combination

Ctotal = C1*C2/(C1+C2)

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