Relationship Between Different Capacitors for Different Applied Voltages

[malindenmoyer]

In the arrangement shown, find the necessary relationship between the capacitances of the four capacitors in order that when a voltage is applied across terminals a and b, no voltage difference is set up between terminals c and d. Would this arrangement work for the case of the voltage applied to terminals c and d to give no voltage across a and b?

http://malindenmoyer.com/fig.gif

I am rather confused as the concept was just introduced to me, so any help and guidance would be appreciated.

 

[ehild]

C1 an C2 are connected in series. They carry the same charge q.
C3 and C4 are also connected in series, they both carry the charge Q.

The voltage across the capacitor C1 is Vac=Q1/C1=q/C1.
The voltage across the capacitor C2 is Vcb=q/C2.

The same holds for capacitors C3 and C4: Vad=Q/C3, Vdb=Q/C4

No voltage between c and d means that Vac=Vad and Vcb=Vdb.

Write down the equations for the voltages and eliminate the charges.

ehild