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!

Can somebody tell my where I am going to wrong.

  1. Jan 23, 2008 #1
    W=work(energy) in joules
    C=capacitance in farads
    Q=charge in coulombs
    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?

  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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook