1.If a capacitor is disconnected from the battery, what will be the energy stored in the capacitor when 1. separation between plates is doubled and 2. an uncharged and identical capacitor is connected across it.
 
2.A parallel plate capacitor with plate area A and separation d is charged to a potential difference V. The battery used to charge it is then disconnected. A dielectric slab of thickness d and dielectric constant K is placed between the plates. What changes will take place in 1. Charge on plates, 2. electric field intensity between plates and 3. capacitance.

Asked by JASKAMAL KAUR | 1st Jun, 2015, 06:46: PM

Expert Answer:

1. 
 
begin mathsize 14px style Let space straight C space be space the space capacitance space of space the space capacitor. The space charge space on space the space plates space remain space the space same space if space the space battery space is space disconnected but space the space potential space difference space between space the space plates space will space change. space We space know space that space capacitance space straight C space equals fraction numerator straight epsilon subscript 0 straight A over denominator straight d end fraction comma space where space straight d space is space the space seperation space and space straight A space the space area space of space crossection When space the space seperation space between space the space plates space is space doubled comma space capacitance space becomes colon straight C apostrophe equals fraction numerator straight epsilon subscript 0 straight A over denominator 2 straight d end fraction equals straight C over 2 Then space the space potential space difference space between space the space plates space will space space be colon straight V apostrophe equals fraction numerator straight Q over denominator straight C apostrophe end fraction equals fraction numerator 2 straight Q over denominator straight C end fraction where space straight Q space is space charge space and space straight C apostrophe space the space capacitance space Therefore space Energy space stored space will space be comma space straight U apostrophe equals 1 half straight C apostrophe straight V apostrophe squared space straight U apostrophe space equals 1 half cross times straight C over 2 cross times open parentheses fraction numerator 2 straight Q over denominator straight C end fraction close parentheses squared straight U apostrophe equals straight Q squared over straight C end style
2. 
 
begin mathsize 14px style If space straight C space is space the space capacitance space initially space when space charged space to space potential space straight V. space Energy space stored space at space that space time comma space straight U equals 1 half CV squared Charge space aquired space by space the space capacitor space initially space will space be comma space straight Q equals CV On space disconnecting space from space battery space the space charge space remains space the space same. If space an space uncharged space identical space capacitor space of space capacitance space straight C space is space connected space across space the space first space capacitor comma The space total space capacitance space of space the space parallel space combination space will space be comma space straight C plus straight C space equals 2 straight C The space total space charge space on space the space two space capacitors space will space remains space straight Q comma space the space potential space across space each space will space be colon straight V apostrophe equals fraction numerator straight Q over denominator 2 straight C end fraction equals fraction numerator CV over denominator 2 straight C end fraction equals straight V over 2 Since space two space capacitors space are space identical comma space equal space amount space of space energy space will space be space stored space in space them. The space final space energy space stored space in space each space of space the space two space capacitors space will space be colon straight U apostrophe space equals 1 half CV apostrophe squared straight U apostrophe equals 1 half cross times straight C cross times open parentheses straight V over 2 close parentheses squared straight U apostrophe equals 1 fourth cross times 1 half CV squared straight U apostrophe equals straight U over 4 end style

Answered by Jyothi Nair | 2nd Jun, 2015, 10:21: AM