If a dielectric slab of thickness t and area A is inserted in between the plates of a parallel plate capacitor of plate area A and distance between the plates `d(d gt t)` then find out capacitance of system. What do you predict about the dependence of capacitance on location of slab?

Explanation

`C=(Q)/(v)=(sigmaA)/(v)" " V=(sigmat_(1))/(in_(0))+(sigmat)/(K in_(0))+(sigmat_(2))/(in_(0))" " (.:'t_(1)+t_(2)=d-t)`
`=(sigma)/(in_(0))[t_(1)+t_(2)+(t)/(k)] rArr " " V=(sigma)/(in_(0))[d-t+(t)/(k)]=(Q)/(C)=(sigma A)/(C)=(sigma A)/(C) rArr C=(in_(0)A)/(d-t+t//K)`
Note :
(i) Capacitance does not depend upon the position of dielectric (it can be shifted up or down still capacitance does not change).
(ii) If the slab is of metal then : `C=(A in_(0))/(d-t)` (for metal k `rarr oo`)