# Deriving expressions for total capacitance

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!

1. The problem statement, all variables and given/known data

Derive expressions for the total capacitance expected in part 2.3.3

(Circuit diagrams attached)

2. Relevant equations

Ctotal = C1+C2 + C3… ( for capacitors in parallel)

1/Ctotal = 1/C1 + 1/C2 + 1/C3 … (for capacitors in series)
3. The attempt at a solution

Circuit (i)

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

Circuit (ii)

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

Capacitor 2 and ‘capacitor 3,4’ are in parallel so add to give C2,3,4 = (C3,4) + C2

Capacitor 1 and Capacitor 2,3,4 are in series with one another so 1/C1,2,3,4 = 1/C1 + 1/C2,3,4

Circuit (iii)

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

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

These two grouping add to give 1/C1,2,3,4,5,6 = 1/(C1,2,3) + 1/(C4,5,6)

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 🙂

Attached Images cappf.jpg (30.6 KB)

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