# Deriving expressions for total capacitance

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**

C_{total} = C_{1}+C_{2} + C_{3}… ( for capacitors in parallel)

1/C_{total} = 1/C_{1} + 1/C_{2} + 1/C_{3} … (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 C_{total} = C_{1}+C_{2} + C_{3}

**Circuit (ii)**

Capacitor 3 and 4 are in series with one another, so add to give 1/C_{3,4} = 1/C_{3} + 1/C_{4}

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

Capacitor 1 and Capacitor 2,3,4 are in series with one another so 1/C_{1,2,3,4} = 1/C_{1} + 1/C_{2,3,4}

**Circuit (iii)**

Capacitors 1, 2 and 3 are all in parallel so add as C_{1,2,3} = C_{1} + C_{2} + C_{3}

Similarly Capacitors 4, 5 and 6 add to give C_{4,5,6} = C_{4} + C_{5} + C_{6}

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 ðŸ™‚

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