45. A parallel plate capacitor with plate area  and plate separation  has a capacitance of . The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant  (as shown in figure) will be:                                                                                                             

A capacitor plates are charged by a battery with '  ' volts. After charging battery is disconnected and a dielectric slab with dielectric constant '  ' is inserted between its plates, the potential across the plates of a capacitor will become                 

A parallel plate air capacitor has a capacitance of . The plates are at a distance  apart. If a slab of thickness  ) and dielectric constant 5 is introduced between the parallel plates, then the capacitance will be

A parallel plate capacitor having a separation between the plates , plate area  and material with dielectric constant  has capacitance . Now one-third of the material is replaced by another material with dielectric constant , so that effectively there are two capacitors one with area , dielectric constant and another with area  and dielectric constant . If the capacitance of this new capacitor is  then  is           

A parallel plate cápacitor with air between the plates is charged to a potential difference of  and then insulated. A plastic plate is inserted between the plates filling the whole gap. The potential difference between the plates now becomes 75V. The dielectric constant of plastic is

Two parallel plate capacitors of capacitance  and  are connected in parallel and charged to a potential difference . The battery is then disconnected, and the region between the plates of  is filled completely with a material of dielectric constant . The common potential difference across the combination becomes 

An uncharged paralle plate capacitor having a dielectric of dielectric constant  is connected to a similar air cored parallel plate capacitor charged to a potential . The two share the charge, and the common potential becomes . The dielectric constant  is

A parallel plate capacitor with air between the plates is charged to a potential difference of  and then insulated.
A plastic plate is inserted between the plates filling the whole gap. The potential difference between the plates now becomes . The dielectric constant of plastic is              

A parallel-plate capacitor is filled by a dielectric whose permittivity varies with the applied voltage according to the law , where . The same (but containing no dielectric) capacitor charged to a voltage  is connected in parallel to the first "nonlinear" uncharged capacitor. Determine the final voltage  across the capacitors.