Pulse response of rc circuits

Discussion in 'Homework Help' started by newtoelectronics, Jan 11, 2009.

  1. newtoelectronics

    Thread Starter New Member

    Jan 11, 2009

    I am new to electronics and am trying to learn on my own from a textbook. A lot of times I get stuck and have no one to ask. Hopefully the online community can help me when needed. I appreciate all of your help in advance!

    Here are the questions:

    1. Derive a formula for finding time at any point on an increasing exponential voltage curve. Use this formula to find the time at which the voltage is at 6 V after switch is close.

    The applied voltage is 12 and the time constant is .02 ms.

    I know the formula for an increasing exponential curve is Vf +(Vi-Vf e^-t/rc), but am unsure what to do here.

    2. For a circuit with 15V applied and time constant = .01 ms, how long does it take for the cap to charge to 8V.

    I know the formula for finding the time it takes for the cap to discharge is -rc*in(v/vi), but am unsure how to solve for the time it takes to charge.

    Thanks again!
  2. vvkannan

    Active Member

    Aug 9, 2008
    hello newtoelectronics,
    The formula for the voltage across the capacitor is Vc = V(1-e^(-t/rc)) as there is no initial voltage given here.
    rearranging this equation Vc /V = 1 - e^(-t/rc).
    e^(-t/rc) = 1 -(Vc/V)
    -t/rc = ln (1- (Vc/V))

    t = -rc x ln (1 - ( Vc/V))
    substituting the supply voltage for V and capacitor voltage at any point for Vc and the time constant we can get the time.
    hope this helps