1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Capacitor and dielectriscs

  1. Jan 10, 2010 #1
    1. The problem statement, all variables and given/known data

    A parallel plate capacitor has a capacitance C when there is a vacuum between teh plates. How does this change if the gap between the plates is half filled with a dielectric with dielectri constant [tex]\epsilon[/tex]r

    Calculate the change in energy stored in the capacitor if the dielectric is inserted while the capacitor is connected to a battery of fixed voltage V.

    2. Relevant equations

    C=C1+C2
    C=[tex]\stackrel{\epsilon_0 A}{d}[/tex]
    3. The attempt at a solution

    For the first part, i assumed it was equivalent to 2 capacitors (one with the dielectric and one without in parallel)

    C=[tex]\stackrel{\epsilon_0 0.5A}{d}[/tex] =0.5C

    C2= [tex]\epsilon_r[/tex]*[tex]\stackrel{\epsilon_0 0.5A}{d}[/tex] - 0.5[tex]\epsilon_[/tex]C

    C(total) = 0.5C+0.5[tex]\epsilon_r[/tex]C.

    Second part, not really sure how to start...

    V is fixed, and U=0.5CV2.. So if C increases by (1+[tex]\epsilon[/tex]r) U increases by the same factor??
     
  2. jcsd
  3. Jan 10, 2010 #2

    ideasrule

    User Avatar
    Homework Helper

    Why in parallel? The battery's voltage is being applied across the 2 capacitors, not across each capacitor individually.

    Yes, except C doesn't increase by (1+[tex]\epsilon[/tex]r).
     
  4. Jan 10, 2010 #3

    Not entirely sure, just seen other examples where they said this



    C(total)=C(0.5+0.5[tex]\epsilon[/tex]r) so it increases by a factor of (0.5+0.5[tex]\epsilon[/tex]r)?
     
    Last edited: Jan 10, 2010
  5. Jan 10, 2010 #4
    tried it again...

    [itex] U_0 =1/2 C_0 V^2 [/itex] and [itex] U_1 =1/2 C_1 V^2 [/itex]

    [itex] C_1 = 1/2 \epsilon[/tex]r so

    [itex] U_1 =1/2 *1/2 C_0 \epsilon[/tex]r V^2 [itex] =1/2 \epsilon[/tex]r *U_0 ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Capacitor and dielectriscs
  1. Capacitors in ? (Replies: 6)

Loading...