Electrostatic Potential and Capacitance Part 1

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
⇒‌‌‌

1

Ceq

=‌

1

C1

+‌

1

Ceq′

=‌

1

C0

+‌

1

2C0

=‌

3

2C0

⇒‌‌‌‌C‌eq ‌=‌

2C0

3

....(i)
As, C0=‌

ε0A

d

...(ii)
From Eqs. (i) and (ii), we get
⇒‌‌C‌eq ‌=‌

2ε0

d

...(iii)
According to question, the equivalent capacitance between A and C is ‌

xε0

d

.
So, comparing it with Eq. (iii), we get
x=2