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New capacitance when dielectric material covers bottom half

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  1. Mar 28, 2016 #1
    1. The problem statement, all variables and given/known data

    The plates of a parallel plate capacitor of capacitance C0 are
    horizontal. Into the gap a slab of dielectric material with K=2 is placed,
    filling the bottom half of the gap between the plates. What is the
    resulting new capacitance?
    2. Relevant equations

    C = Q/V = κɛ0A/d

    3. The attempt at a solution

    Co = ɛ0A/d
    Cf = kɛ0A/d = ((ɛ0)(0.5A)/d) + ((2ɛ0)(1/2a)/(d)) = (ɛ0A/2d) +(ɛ0A/d) = (ɛ0A/d) + (2ɛ0A/2d) = (3ɛ0A/2d)
    Cf = 3/2 Co

    The correct answer is 4/3 Co. Guys, can anyone help me out? I have no idea how to derive the correct answer.
     
  2. jcsd
  3. Mar 28, 2016 #2

    cnh1995

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    The new capacitance is a series combination of two capacitors, one with k=2 and the other with k=1(upper half). If the original capacitance was C, what values do you get for these new series capacitances?
     
  4. Mar 28, 2016 #3
    Do you need to change A to 1/2A?
     
  5. Mar 28, 2016 #4

    cnh1995

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    A remains the same. Distance between the plates is halved..
     
  6. Mar 28, 2016 #5
    Thanks! I solved it already!
     
  7. Apr 1, 2016 #6
    Hey guys, can you tell me how exactly can I get?
     
  8. Apr 2, 2016 #7

    cnh1995

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