calculate the capacitance of a capacitor when dielectric slab is inrtoduced between the plates of capacitors
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Answer:
As the plates are square so length (l)= widith (w).
here, A=lw=l
2
→l=
A
There are two capacitors - one is air filled and other is dielectric filled and they are in parallel.
For air filled capacitor: area A
1
=(l−x)l=(
A
−x)
A
=(A−
A
x) and
Capacitance, C
1
=
d
A
1
ϵ
0
=
d
(A−
A
x)ϵ
0
For dielectric field capacitor: area A
2
=lx=
A
x and
Capacitance , C
2
=
d
A
2
ϵ
r
ϵ
0
=
d
A
xϵ
r
ϵ
0
The net capacitance is C=C
1
+C
2
=
d
(A−
A
x)ϵ
0
+
d
A
xϵ
r
ϵ
0
=
d
ϵ
0
(A−
A
x+ϵ
r
A
x)
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