Finding possible combinations of capacitors given circuit capacitance

[ChiralSuperfields]

Homework Statement

Please see below

Relevant Equations

Please see below

For this problem,

The solution is,

Is the only way of finding the possible combinations is by drawing out circuit diagrams?

Many thanks!

 

[kuruman]

Homework Statement:: Please see below
Relevant Equations:: Please see below

For this problem,
View attachment 322007
The solution is,
View attachment 322008
Is the only way of finding the possible combinations is by drawing out circuit diagrams?

Many thanks!

Drawing a circuit diagram surely helps when you are trying to figure out the capacitance for each particular configuration. However, if you intensely dislike drawing circuit diagrams, you can always look at the list that you posted above.

 

[Omega0]

Homework Statement:: Please see below
Relevant Equations:: Please see below

For this problem,
View attachment 322007
The solution is,
View attachment 322008
Is the only way of finding the possible combinations is by drawing out circuit diagrams?

Many thanks!

I think so. For such a small case a closed formula doesn't make sense to me and for very many passive circuit elements like resistors, capacitors or coils I am quite sure to not have a closed mathematical formula at all - plus, there is no usage for such a general case.

 

[ChiralSuperfields]

Thank you for your help @kuruman and @Omega0 !