simple first order circuit

Discussion in 'Homework Help' started by squirby, Sep 29, 2009.

  1. squirby

    Thread Starter Member

    Aug 21, 2009
    hey guys. i haf a simple first order circuit here and i have solved for t less greater than or equal to zero and less than or equal to 1 (subject to the voltage source). (1-exp(-2t)) V.

    i have solved using classical differential technique and laplace transform. the answers both agree with each other.

    however, for t greater than 1, they disagree.

    when using differential technique, i get [(exp(2) - 1)]exp(-2t) V, while using laplace transform the answer is [1 - exp(2)]exp(-2t) V.

    i might have made an error in the setting up of the laplace transform (done both using voltage source and current source and still get same answer) but i have checked n double checked to no avail.

    any input would be greatly appreciated.
    p.s if you cannot open the schematic, the circuit is a 1ohm resistor in series with a 0.5 farad capacitor, excited by a voltage source = u(t) - u(t-1) where u(t) is the unit step function
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    Using Laplace I have

    v(t)=(exp(2)-1)exp(-2t) {the capacitor voltage}

    Which was found from the Laplace equation for the output {cap voltage}

    V(s)=2(1-exp(-s))/[s(s+2)]=2/[s(s+2)] - 2exp(-s)/[s(s+2)]

    giving the general equation in the time domain

    v(t)=(1-exp(-2t))u(t) - (1-exp(-2(t-1)))u(t-1) etc .....