If c1=c2=4.00μf and c4=8.00μf, what must the capacitance c3 be if the network is to store 2.70×10−3 j of electrical energy?

Missing detail in the text: total voltage of the circuit 
Missing figure: https://www.physicsforums.com/attachments/prob-24-68-jpg.190851/

Solution:

1) The energy stored in a circuit of capacitors is given by

where  is the equivalent capacitance of the circuit. We can find the value for  by using  and the energy of the system, 


2) Then, let's calculate the equivalente capacitance of C1 and C2. The two capacitors are in series, so their equivalente capacitance is given by

from which we find 

3) Then let's find , the equivalent capacitance of  and C3.  is in series with C4, therefore we can write

Since we already know  and , we find


4) Finally, we can find , because it is in parallel with , and the equivalent capacitance of the two must be equal to :

So, using  and , we find

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