What is the Equivalent Capacitance of a Single Capacitor Setup?

[Sami Lakka]

Homework Statement

What is the equivalent capacitance of the arrangement shown in figure. (Answer is C1)

Homework Equations

Cparallel = C1+C2+...Cn
Cseries = 1/(1/C1+1/C2+...+1/Cn)

The Attempt at a Solution

 

[Andrew Mason]

Homework Statement

What is the equivalent capacitance of the arrangement shown in figure. (Answer is C1)

Homework Equations

Cparallel = C1+C2+...Cn
Cseries = 1/(1/C1+1/C2+...+1/Cn)

The Attempt at a Solution

It is easier to see what is happening if you change the drawing to a square with 2 C1s on each side in series and a C2 attached across the middle (from points between the C1s).

By the symmetry of the circuit, you can see that there is 0 voltage across the C2 capacitor. So the C2 really does nothing to change the capacitance of the circuit - ie. it never stores charge. So the capacitance is the same as the circuit without C2.

AM