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Units problem

  1. Sep 13, 2006 #1
    I have this problem I just can't figure out.

    Current = A (Ampere)

    i(t)=z(e^t/(RC))

    where z is the initial current at t=0, R is the resistance in Ohms and C is the capacitance expressed in secondary units as F (Farad)

    - Express the units of F in terms of seconds and ohms

    So, this is what I tried to do, tell me where I went wrong

    A = A e^(s/F-Ohms)

    1 = e^(s/F-Ohms)

    ln(1) = s/F-Ohms

    0 = s/F-Ohms

    F = 0

    I obviously did something wrong, so any help would be apreciated, thank you!
     
  2. jcsd
  3. Sep 13, 2006 #2
    If you think of an RC circuit as a second order differential equation you will see

    dQ/dT + 1/(R*C)*Q = Junk

    Where junk = 0 for a loop of a circuit without any external components. Otherwise it can also be some forcing function driven by batteries, power sources, etc. But anyways, Q is the charge here so...

    dQ/dT = charge/time (amps)

    thus Q*1/(R*C) = charge/time since Q = charge, R*C has dimension [T]

    Thus an Ohm-Farad has dimension [T] and the quantity in the exponent in your equation is dimensionless then - as it should be
     
  4. Sep 14, 2006 #3
    thank you, I got it now.
     
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