Engineering First-Order Circuit Transient Response Question that i with

[spoonjabba]

The switch in the diagram below has been open for a long time prior to t = 0; then it closes at t = 0 and opens again at t = 105 µs. Find:

1. Ix(75 µs),
2. Vx(75 µs),
3. Ix(190 µs),
4. Vx(190 µs).

Attached is the diagram of the circuit and its answers.

so i understand how to get questions 1 and 2, but for 3 and 4 I am stuck.

i found the voltage of the capacitor at time 105µs so I am assuming I use that voltage as the initial condition to questions 3 and 4. I also know that the time constant(tau2) will be different as it will only be the C and R1.

these are the values i am calculating thus far.
vx(105us) = 7.1467V
Tau2 = 33n*3900
vx(190us) = 7.1467e^(-190us/tau2) << i have a feeling i have done something wrong here

thanks guys!

 

[gneill]

The switch in the diagram below has been open for a long time prior to t = 0; then it closes at t = 0 and opens again at t = 105 µs. Find:

1. Ix(75 µs),
2. Vx(75 µs),
3. Ix(190 µs),
4. Vx(190 µs).

Attached is the diagram of the circuit and its answers.

so i understand how to get questions 1 and 2, but for 3 and 4 I am stuck.

i found the voltage of the capacitor at time 105µs so I am assuming I use that voltage as the initial condition to questions 3 and 4. I also know that the time constant(tau2) will be different as it will only be the C and R1.

these are the values i am calculating thus far.
vx(105us) = 7.1467V
Tau2 = 33n*3900
vx(190us) = 7.1467e^(-190us/tau2) << i have a feeling i have done something wrong here

thanks guys!

Hi spoonjabba, Welcome to Physics Forums.

The time constant $\tau$ will depend upon both of the resistances. I suggest that you "remove" the capacitor from the circuit and find the Thevenin equivalent of the remaining network (resistors and voltage supply). This will be the equivalent circuit that the capacitor will "see", and will consist of a single resistance in series with a voltage supply. It will then be a trivial matter to calculate the effective time constant and other values.