Calculating Equivalent Capacitance for C1, C2 & C3

[magnifik]

for what values of C1, C2, and C3 make the terminal pairs equivalent?

i know the 2f and 1f capacitance are in series:
(1*2)/(1+2) = 2/3

and i know the 1/2 f is parallel to the preceding capacitors:
2/3 + 1/2 = 7/6

but i am unsure where to go from here...
any help would be appreciated. thx.

 

[berkeman]

for what values of C1, C2, and C3 make the terminal pairs equivalent?

i know the 2f and 1f capacitance are in series:
(1*2)/(1+2) = 2/3

and i know the 1/2 f is parallel to the preceding capacitors:
2/3 + 1/2 = 7/6

but i am unsure where to go from here...
any help would be appreciated. thx.

I believe you will need to solve 3 simultaneous equations (no big deal). The capacitances have to be equal for the two circuits, as seen at the left and right ports, and across the top leg.

So if you call the bottom rail Ground, then you have to find C1, C2, C3, so that you match the left circuit's capacitances:

C(left to ground)
C(right to ground)
C(left to right)

You've already found the C(left to right) that needs to be matched. Calculate the other two capacitances for the left circuit, and then write the equations for the capacitances of the right circuit, and solve for the values of C1, C2, C3.

 

[magnifik]

from what you said...

C(left to ground) = 1*2/(1+2) = 2/3
C(right to ground) = 1+1 = 2
C(left to right) = 7/6

i'm a little confused on what you're saying should be the last step