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-



Where,


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 –


and



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,



Now,





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