A dielectric of dielectric constant 3 fill up three fourths of the space between the plates of a paralleled plate capacitor. The fraction of total energy that is stored in the dielectric is

Answer

`00.50`

Explanation

Eneirgy of the capacitor
`U=(Q^(2))/(2C)=(Q^(2))/(2xx(epsilon_(0)A)/((d-3/4xd((3d//4))/3)))=(Q^(2))/((2epsilon_(0)A)/((d//2))`
`=(Q^(2)d)/(4epsilon_(0)A)`
Energy in the dielectric = energy of capacitor of same area, charge and with plate separation equal to the thickness of the dielectric
`:.U.=(Q^(2))/(2xxC.)=(Q^(2))/(2xx(epsilon_(0)epsilon_(r)A)/t)=(Q^(2))/(2xx(epsilon_(0)xx3A)/((3d//4)))`
`=(Q^(2)d)/(8epsilon_(0)A)`
...........`( :.t=3/4d)`
`:.` Fraction of energy stored `=(U.)/U`
`=((Q^(2)d)/(8epsilon_(0)a))/((Q^(2)d)/(4epsilon_(0)A))`
`=0.5`