solve for R

Discussion in 'Homework Help' started by Spakle, Jan 21, 2010.

  1. Spakle

    Thread Starter New Member

    Jan 21, 2010
    4
    0
    RC Circuit
    30 volt source
    0.1 μf capacitor
    Capacitor charges to 22 volts after 65μs

    The only unknown is the Resistance Value

    I'm fairly certain that the formula for Capacitor Voltage is the one to use to solve for R

    But i cannot recall how to manipulate the formula

    Formula:
    Vcap = Vsource(1-e(-t/RC))

    The solution is 492Ω, but the closest i get is 477Ω

    22/30 * (0.1μs/65μs) = 476.666Ω
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    If you correctly substitute the values into the equation, re-arrange and solve you will get the right answer. Since you have an exponential term involved you are going to have to find a natural logarithm somewhere in the solution process.

    Vcap=Vsource(1-exp(-t/RC))

    22=30*(1-exp(-(65e-6)/(R*0.1e-6)))

    R is the unknown.

    It might be preferable (for me anyway) to rearrange the equation first to obtain R as the subject and then make the known value substitutions.
     
  3. Spakle

    Thread Starter New Member

    Jan 21, 2010
    4
    0
    That's exactly what I'm trying to do (the 477 answer is just throwing other value together basically) but i cannot remember how to re-arrange that formula to isolate for R
     
  4. AlexR

    Well-Known Member

    Jan 16, 2008
    735
    54
    V_{c} = V_{s}(1-e^{-t/RC})

    e^{-t/RC} = 1-V_{c}/V_{s}

    -t/RC = ln(1-V_{c}/V_{s})

    R = -t/C*ln(1-V_{c}/V_{s})
     
  5. Spakle

    Thread Starter New Member

    Jan 21, 2010
    4
    0
    Thanks Alex, you're the man...

    it's been 2 years since I've done that kind of circuit analysis.
     
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