Question

Starting with V=Voe^(-t/RC) show that t(.5)= RCln2. This is an analysis question for a lab on RC circuits w/ AC. I don't quite understand the question.

Answer 1

It's asking you for what time, t, is \( V = V_0/2 \).

Answer 2

So what I plug in the Voltage, Vo/2 and it should be the same as RCln(2)?

Answer 3

No, you want the value of \( t \) for which \( V = V_0/2 \). In other words, the value of \( t \) for which

\[ \frac{V_0}{2} = V_0 e^{-t/RC} \]
Solve that equation for \( t \).

Answer 4

So something like .5= e^-t/RC -> ln(.5) =-t/RC -> -(1/t) = 1/RCln(.5) -> t=RCln(.5)?

Answer 5

From here,
ln(.5) =-t/RC
remember that ln(1/2) = -ln(2)

Answer 6

Oh yea, thanks got it.