The equivalent capacitance of the capacitor when dielectric material is partially filled, is given as
C=
ε0A
(d−t)+
t
k
=
ε0A
(d−
d
2
)+
d/2
k
=
ε0A
d
2k
+
d
2
where, ε0= absolute electrical permittivity of free space, A= area of the plates of capacitor =2m2 K= dielectric constant =3.2 t= thickness of dielectric material =
d
2
and d= distance between the plates =2m. C=
2ε0A
d
k
+d
=
2×2ε0
1
3.2
+1
=
4×3.2
4.2
ε0 ⇒C=3.04ε0 The required value after rounding off to the nearest integer is 3 .