The given figure can be shown with capacitors as
Let
C0 be the capacitance of each capacitor.
In the above figure capacitance
C1 is in series combination with equivalent of parallel combination of capacitance
C2 and
C3.
Ceq′=C2+C3⇒Ceq′=C0+C0=2C0 ⇒=+=+= ⇒Ceq =....(i)
As,
C0=...(ii)
From Eqs. (i) and (ii), we get
⇒Ceq =...(iii)
According to question, the equivalent capacitance between
A and
C is
.
So, comparing it with Eq. (iii), we get
x=2