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RC Circuits and time constants

  1. Feb 5, 2008 #1
    RC Circuits!!

    A capacitor in a single-loop RC circuit is charged to 63 % of its final voltage in 1.5 s. Find (a) the time constant for the circuit and (b) the percentage of the circuit's final voltage after 3.5 s.








    Given that V/Vo = 63%, t = 1.5 sec , Time constant =τ
    Now,
    V/Vo =63%
    We have, V/Vo = 1 - e –t/ τ
    0.63 = 1 - e –t/ τ
    e –t/ τ = 1-0.63
    e t/ τ = 1/0.37
    t/ τ = log 1/ 0.37
    = 2.3026 x log 2.7027
    1.5 /τ =2.3026 x log 2.7027
    τ = 0.77???

    Now to find the percentage of the circuit’s final
    voltage after 3.5 sec,
    V/Vo = 1- e^-3.5/.77
    3.5/.77 = 2.3026 log Vo/ (Vo – V)
    Or Vo/ (Vo – V) = antilog of 3.5/(.77 x 2.3026)
    = 0.0106
    1- (V/Vo) = 0.0106
    Or V/Vo = 0.98
    Therefore the percentage of the circuit’s final voltage
    after 3.5 sec is 98%???
     
  2. jcsd
  3. Feb 5, 2008 #2
    Yeah, I don't see any immediate discrepancies, and you know that 5 time constants give approximately 98% of the initial voltage, which yours does. If you made a mistake is one I can't see, but you put in numbers way too soon for me to really tell what you did. Physics rule: algebra first, numbers later.
     
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