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Can somebody tell my where I am going to wrong.

  1. Jan 23, 2008 #1
    W=work(energy) in joules
    C=capacitance in farads
    A=Amperes
    V=Voltage
    Q=charge in coulombs
    s=seconds
    P=power in watts

    I know that W=1/2(V^2)C is the correct formula, but I don't know how to derive it.

    I am doing the following: C=Q/V, C=As/V, VC=VAs/V, VC=Ps/V, VC=W/V, W=C(V^2)
    What am i missing?

    --dbernat32
     
  2. jcsd
  3. Jan 23, 2008 #2
    Don't know if you studied integrals.
    When you add a small charge dq to a condenser at potential V and charge q, you have to make the work V*dq. But now V is not the same anylonger because V = q/C and q is now different. So you have to write V(q) and dW = V(q)*dq.
    To get the total work you have to sum all these infinitesimal quantities, that is you have to compute the integral:
    Integral(0;Q) V(q)*dq = Integral(0;Q) (q/c)*dq = (1/2)Q^2/C = (1/2)CV^2.
    The equality coloured in blue requires knowledge of integrals.
     
    Last edited: Jan 23, 2008
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