(a) A parallel plate capacitor has a capacity of `6muF`, with air in between the plates and `60muF` when dielectric medium is introduced. What is the dielectric constant (K) of the medium?
(b) A 900 pF capacitor is charged by 100 V battery.
(i) How much electrostatic energy is stored by the capacitor?
(ii) The capacitor is now disconected from the battery and is connected to another uncharged 900 pF capacitor. How much is the electrostatic energy stored in the system?

Explanation

(a) `K=(C_("medium"))/(C_("air"))=(60)/(6)=10muF`
(b) Given `C_(1)=900pF=900xx10^(-12)F, V=100` volt
(i) Energy stored
`U=(1)/(2)C_(1)V_(1)^(2)=(1)/(2)xx900xx10^(-12)xx10000`
`U=4.5xx10^(-6)J`
(ii) On connecting the charged capacitor to another capacitor. Total capacitance, of capacitance
`C_(2)=900pF`
`C=900+900=1800pF`
Total charge
`q=q_(1)+q_(2)=C_(1)V_(1)+0=9xx10^(-8)C`
`therefore` Common potential
`V=(q)/(C )=(9xx10^(-8))/(1800xx10^(-12))=50V`
`therefore ` Energy stored in the system
`U=(1)/(2)CV^(2)=2.25xx10^(-6)J`