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Energy and Capacitors

  1. Feb 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Two capacitors having values of 10 μF each are connected in parallel and then hooked up to a 9.0 V battery. How much energy must the battery supply to charge the capacitors?

    *a. 8.1 x 10-4 J
    b. 9.0 x 10-5 J
    c. 1.6 x 10-3 J
    d. 2.0 x 10-4 J
    e. 2.3 x 10-5 J


    2. Relevant equations

    ε=ΔW/ΔQ
    Q=CV
    ΔW=ΔE
    C=C1+C2...+Cn (for capacitors in parallel)

    3. The attempt at a solution

    ΔE=ε*ΔQ
    ΔE=ε*CV
    ΔE=9V*(10μF+10μF)*9V
    ΔE=1.62x10-3 J

    the answer key says A is correct...can someone tell my why?
     
  2. jcsd
  3. Feb 9, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    Your calculation made the assumption that the change in potential is the same for all the charges moved onto the capacitor. When an initially uncharged capacitor is connected to a voltage source for charging up, the potential across the capacitor is not immediately equal to that of the source; the capacitor begins with 0V across it which rises to meet the source's potential as current flows and its charge increases.

    What this means is that it takes less work to move charge onto the capacitor early on in the process when the capacitor potential is low than it does later when the potential is higher. If you perform the required integration to calculate the work you'll find that the resulting expression is similar in form to other such expressions for other types of energy. This can make it easier to remember them all! Some examples:

    Spring potential Energy: PE = (1/2)kx2
    Linear Kinetic Energy: KE = (1/2)mv2
    Rotational Kinetic Energy: KE = (1/2)Iω2
    Capacitor Electrical PE: PE = (1/2)CV2
     
  4. Feb 9, 2012 #3
    You had an almostidentical question to this a couple of weeks ago. See the first post on the list at the bottom.
    There are 2 important pieces of information
    1) The energy STORED on the capacitor is (a) 8.1 x 10^-4 J
    2) The energy supplied by the battery is (c) 1.62 x 10^-3 J
    Whichever answer you take to be correct depends on your interpretation of the question.
    For me, this means it is a badly worded question. A multiple choice question must have only one correct answer with no doubt whatsoever.
     
  5. Feb 9, 2012 #4
    OK...thanks to the both of you!
     
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