# simple first order circuit

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

1. ### squirby Thread Starter Member

Aug 21, 2009
15
0
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

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2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
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 .....