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