Finding the time constant given % of max value

[Katsmed23]

Homework Statement

After how many time constants does the current in the figure below ( http://www.webassign.net/gianpse3/30-06.gif ) reach the following values?

(a) within 67 percent of its maximum value


(b) within 6.7 percent of its maximum value


(c) within 0.67 percent of its maximum value

Homework Equations

tao (time constant) = L (inductor) /R (resistance)
I = Vo/R (1 - e^-time/tao)
Vc = V(1-e^-t/RC)

The Attempt at a Solution

Ok so I know that tao is the time required for the current (I) to reach the % of max value (1-1/e). However, given NO numerical values and just constants, I can't figure out how to find how many time constants. I tried taking the natural log of both sides and figuring out tao that way, but then I don't know the time t. I know that it is discharging because it isn't connected to the voltage anymore. please help!

 

[anorlunda]

All you need is a table of values of e^-x versus x.

 

[haruspex]

given NO numerical values and just constants

So consider ratios. For case a), what is the ratio between Vc and V?

Vc = V(1-e^-t/RC)

How are you defining V and Vc? In what context does this equation apply? What does it say for t tending to infinity? Does that match the question?

 

[LastScattered1090]

So consider ratios. For case a), what is the ratio between Vc and V?

How are you defining V and Vc? In what context does this equation apply? What does it say for t tending to infinity? Does that match the question?

Or a more direct way to ask this question: why are you considering the equation for the voltage on a capacitor when no capacitor appears in the circuit?