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Capacitance question help

  1. Feb 3, 2013 #1
    1. The problem statement, all variables and given/known data
    A capacitor with C = 4600 μ F is fully charged using a 12 V power supply.
    At time t = 0, you start discharging the capacitor via a 50 k Ω resistor.
    Calculate the initial charge Q max (in mC) and the initial energy E max (in mJ) stored in the capacitor.

    Then, calculate the residual charge Q, the potential difference V across the capacitor and its energy E content after 49 seconds.
    Q=mC
    V=V
    E=mJ

    Have to answer in decimal numbers to 2 sig fig.

    2. Relevant equations



    3. The attempt at a solution
    Here’s my attempt:
    Q max = CV = 4600 uF * 12 V = 55200 u coulomb = 55.2 mC
    E max = 1/2 CV^2 = 1/2 4600 uF (12 V)^2 = 331.2 mJ

    tau = RC = 50e3*4600e-6 = 230 S.

    Q = Q max exp(-t/tau) = 55.2 mC * exp(-49/230) = 55.2 mC * 0.808121 = 44.6 mC.
    V = V power supply * 0.808121 = 12 * 0.808121 = 9.697 V
    E = 1/2 CV^2 = 1/2 4600 uF (9.697 V)^2 = 216.3 mJ


    Is this looking correct?
    The only thing i cant do (stupid i know) is convert these to 2 sig fig whilst also in decimal form. For example V = 9.697 is 9.7
    Is it 55.2 = 50.2
    331.2 = 330.0
    44.6 = 45.0
    216.3 = 210.0
     
  2. jcsd
  3. Feb 3, 2013 #2

    marcusl

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  4. Feb 3, 2013 #3

    tiny-tim

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