Thread: Another First Order-RC circuits

RC circuits-
A 10 ohm resistor and 10 microfarad capacitor are attached in series to a 10 volt DC supply. If the current i(0)=1 ampere, what is the current after 0.1 milliseconds (0.0001 seconds)? Round in the thousandths place.

So I worked through this one so carefully! and I was sure I had the correct answer, but didn't! so this is what I did:

10microfarad=0.00001 farads

Rdq/dt+1/Cq=V

10dq/dt+1/10=10

Dividing by R and substituing 0.00001 farads.....

dq/dt+1000q=1

using IF e^1000....I have e^1000t

e^1000tdq=integral[e^-1000t x dt] = 1/1000 e^-1000t + C
q=1/1000+Ce^-1000t
1=1/1000+Ce^-1000(0)
C=0.999

q=1/1000+0.999e^-1000(0.0001)
q=0.905

Where did I go wrong?

10dq/dt+1/10=10

should be 10dq/dt + 10^5 q = 10

Once you fix this

q=1/1000+Ce^-1000t

even if this were correct

dq/dt = i(t) use this to compute C from i(0) = 1 q(0) is not 1