Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A shop sells only capacitors. You need a combination of and want to use as few capacitors as you can. How many do you need? Find the value of the parallel part and of the series part of your combination.
In parallel the voltage is shared and the capacitances add: In series the charge is shared and For two capacitors in series, . In a series chain, the capacitor that reaches its rating first sets the limit.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. Only capacitors. The target is .
Plan. Parallel parts add, so write as a sum of values that can be made.
Step 1. Three capacitors are not enough. Three can make , , or and so on. None of these is .
Step 2. Four capacitors. Write . Two capacitors in parallel give . Two in series give .
Step 3. Join the two parts in parallel. .
Answer: capacitors. The parallel part is and the series part is .
Check. The series pair, , is a small part of the total. It is a good guess that it adds only a little to the large parallel pair.
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