# Simple RC circuit question

#### secondhandloser

Joined Sep 30, 2008
7
Question attached in PDF form.

As far as what I've done, I wrote up the condition required while the voltage across the SCR is less than 5v
x(t)=6V+(0-6)e^-t/τ

after the switchover, I'm having difficulty writing the equation, as I don't understand what the voltage difference would be across the SCR at t=∞.
At t=0, I know it will be 5v, because that's what it is before the changeover.

Any help on even how to set up the equation will be appreciated- I know it's simple, and I'm just blanking on it.

#### beenthere

Joined Apr 20, 2004
15,819
Do you have the values for R and C?

#### secondhandloser

Joined Sep 30, 2008
7
Do you have the values for R and C?

That's what I'm trying to solve for.

#### Ratch

Joined Mar 20, 2007
1,070
secondhandloser,

That's what I'm trying to solve for.
I will give it a try, but the hour is late and I might make a mistake.

The voltage across C when first powered up is (6/s)(1/Cs)/(R+1/Cs) . Cleaning it up and finding the inverse Laplace we get 6(1-exp(-t/RC)) . Equating the expression to 5 volts and substituting t=1 sec we get a RC constant of 1/ln6 . Now we write a node equation (V-6)/R +VCs-5C+50E-6 = 0 . Cleaning it up and separating out V we get V = (5RC - R*50E-6 +6)/(RCs+1) . Finding the inverse and substituting t=0.1, and RC = 1/ln6, and equating the voltage to 0.1, I get R = 174 kohms. Then C = 3.2E-6 farads. I hope I did everything correctly.

Ratch