Deriving expressions for total capacitance

[BOAS]

Hello,

my timetabled experiments for lab work are a week or two ahead of my E&M course which means I'm doing the experiments before being introduced to the theory.

As part of my prep work I need to come up with an expression for the total capacitance of a number of different circuits involving a combination of parallel and in-series circuits.

I would really appreciate it if someone could look at what I have done so far and offer some help with the last one that I am stuck on.

Thanks!

Homework Statement

Derive expressions for the total capacitance expected in part 2.3.3

(Circuit diagrams attached)

Homework Equations

C_total = C₁+C₂ + C₃... ( for capacitors in parallel)

1/C_total = 1/C₁ + 1/C₂ + 1/C₃ ... (for capacitors in series)

The Attempt at a Solution

Circuit (i)

Capacitor 1, 2 and 3 are in parallel with one another and therefore add to give C_total = C₁+C₂ + C₃

Circuit (ii)

Capacitor 3 and 4 are in series with one another, so add to give 1/C_3,4 = 1/C₃ + 1/C₄

Capacitor 2 and 'capacitor 3,4' are in parallel so add to give C_2,3,4 = (C_3,4) + C₂

Capacitor 1 and Capacitor 2,3,4 are in series with one another so 1/C_1,2,3,4 = 1/C₁ + 1/C_2,3,4

Circuit (iii)

Capacitors 1, 2 and 3 are all in parallel so add as C_1,2,3 = C₁ + C₂ + C₃

Similarly Capacitors 4, 5 and 6 add to give C_4,5,6 = C₄ + C₅ + C₆

These two grouping add to give 1/C_1,2,3,4,5,6 = 1/(C_1,2,3) + 1/(C_4,5,6)

Circuit (iv)

I'm really struggling to figure out how to break apart the capacitors into groups and which ones to consider etc.

I know it's asking a lot to pick through the above but i'd really appreciate some help here.

Thanks :)

 

[BvU]

You are doing just fine. In iv you make life easier by drawing A higher and B lower. Then you see 2,3,4 in series and 1 in parallel with that.

Four in series caused a problem in an earlier thread today. I don't think you will stumble, though.