Answer :

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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