A parallel plate capacitor with air between the plates has a capacitance of $$9$$ pF. The separation between its plates is d. The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant $$k1$$ $$=$$ $$3$$ and thickness $$d/3$$ while the other one has dielectric constant $$k2$$ $$=$$ $$6$$ and thickness $$2d/3$$. Capacitance of the capacitor is now

Question

Infinity Learn · Accepted Answer

$$C=$$ϵ$$0Ad=9pF$$ $$C1=k1$$ϵ$$0Ad/3=3k1$$ϵ$$0Ad$$      $$=3$$×$$3$$×$$9=81pF$$ $$C2=k2$$ϵ$$0A2d/3=3k2$$ϵ$$0A2d$$      $$=3$$×$$6$$×$$92=81pF$$

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