The two metallic plates of radius r are placed at a distance d apart and its capacity is C. If a plate of radius r $$/$$ $$2$$ and thickness d of dielectric constant $$6$$ is placed between the plates of the condenser, then its capacity will be

Question

Infinity Learn · Accepted Answer

Area of the given metallic plate $$A=$$π$$r2Area$$ of the dielectric plate A′$$=$$π$$r22=A4Uncovered$$ area of the metallic plates A′′$$=A$$−A′$$=A$$−$$A4=3A4The$$ given situation is equivalent to a parallel combination of two capacitor. One capacitor (C$$'$$) is filled with a dielectric medium (K$$ $$=$$ $$6) having area $$A4$$ while the other capacitor (C$$''$$) is air filled having area $$3A4Hence$$ $$Ceq=C$$'$$+C$$"$$=K$$ε$$0$$ $$(A/4)d+$$ε$$0(3A/4)d=$$ε$$0AdK4+34=$$ε$$0Ad64+34=94C$$ ∵$$C=$$ε$$0Ad$$

The two metallic plates of radius r are placed at a distance d apart and its capacity is C. If a plate of radius r / 2 and thickness d of dielectric constant 6 is placed between the plates of the condenser, then its capacity will be

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material