These two capacitors are connected in series.
To find out the capacitance, let us consider a small capacitor of
differential width dx at a distance x from
the left end of the capacitor.
The two capacitive elements of dielectric
constants K1 and K2 are with plate
separations as -
and in series,
respectively as seen from fig.
Also, differential plate areas of the capacitors are adx.
We know, capacitance c is given by-
A= Plate Area
d= separation between the plates,
∈0 = Permittivity of free space = 8.854 × 10-12 m-3 kg-1 s4 A2
k = dielectric strengthof the material
Then, looking into the fig, the capacitances of the capacitive elements of the elemental capacitors are given by –
We know that equivalent capacitance of capacitors connected in
series is given by the expression –
Now, integrating both sides to get the actual capacitance,
Looking back into the fig.
Substituting in the expression for capacitance C,
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