The space between the plates of a parallel plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants 
and 
(as shown in figure). If new capacitance is 
then the value of 
is 
.
Text Solution
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(8)
The initial capacitance is 
.
From the figure, the capacitor is divided into three parts.
The bottom half is divided into two capacitors 
and 
in parallel, each with area 
and thickness 
.
The equivalent capacitance of the bottom part is 
.
The top half is a single capacitor 
with area 
and thickness 
.
.
The total capacitance 
is the series combination of 
and 
.
Comparing with 
, we get 
.
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