DP 8-1 Design the circuit in Figure DP 8.1 so that v(t) makes the transition from v(t) = 6 V to v(t) = 10 V in 10 ms after the switch is closed. Assume that the circuit is at steady state before the switch is closed. Also assume that the transition will be complete after 5 time constants.

Figure DP 8.1

For time before t = 0 assuming circuit is in steady state we have

The voltage across the capacitor is equal to voltage across R₃ since they are in parallel. We can determine that by simple voltage division

So one condition we have is

So

At a later time the circuit is

Again we can use current division and find our next condtion.

And

Plug this back into first equation and we get

or

Using time constant condition

Deactivating power supply to find Thevenin resistance we have

So we have R₁ and R₃ in parallel

Using relation

Solve for C

So our circuit will work as required changing from 6 V to 10 V in 10 ms if the following equations hold:

There are clearly many Possible answers choose a particular value of R₁ and then calculate the rest. So one answer can be found by choosing R₁ to be 1 kΩ

Dr. Donovan's Classes Page	Dr. Donovan's PH 320 Homework Page	PH 320 Homework Chapter 8 Page
Dr. Donovan's Main Web Page	NMU Physics Department Web Page	NMU Main Page

Please send any comments or questions about this page to ddonovan@nmu.edu

This page last updated on July 26, 2019