Combinations of capacitors?

Question

Three identical capacitors are connected so that their maximum equivalent capacitance is 15 micro Farads.

(a) Describe how the capacitors are combined.
(b) There are three other ways to combine all three capacitors in a circuit. What are the equivalent capacitances for each arrangement?

Answer 1

(a)OK, to maximise the combination of individual capacitors you would connect them in parallel. If the 3 caps total 15mf and they are the same, each would be 15/3=5mf.
[(b)1] The 3 caps could be connected in series. In which case the total capacitance would be 5/3=1.67mf
[(b)2] Now it gets a bit tricky. 2 caps can be in series with the 3rd connected in parallel with that combination. The 2 series caps are 5/2=2.5mf. Now you have that 2.5mF parallel with a 5mf. 2.5+5=7.5mf
[(b)3] And finally. A parallel combo of 2 caps in series with a 3rd. 2 caps in parallel, 5+5=10mf. That 10 mf in series with a 5mf. Using product over sum;
(10x5)/(10+5)=3.33mf.
Hope this was helpful. Charley