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I need to calculate systematic error for $\tau$ in capacitor's charging formula($V_c(t)=V_s\left(1-e^{-t\over\tau}\right)$ )

I converted it to : $\tau=-{t \over \ln(1-{V_c \over V_s})}$
and continued by doing: $\ln(\tau)=\ln(-t)-\ln\left(\ln\left(1-{V_c \over V_s}\right)\right)$
then tried to derivative: ${d\tau \over \tau}={dt \over t}- ...$
I can't go ahead any more!
How should i continue and get result for $d\tau \over \tau$?

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What are your uncertain parameters in this formula? Is it all of $t,V_c$ and $V_s$? – Pantelis Sopasakis Nov 25 '11 at 12:12
@PantelisSopasakis: t is uncertain parameter. But as the first formula $V_c$ itself is a function of t – Snigger Nov 25 '11 at 12:15
Is $\tau$ also a function of $t$...? – Tapu Nov 25 '11 at 12:34
@Swapan: No. It is a constant in formula that has it's own formula ($\tau=RC$) and doesn't depends to t – Snigger Nov 25 '11 at 12:40

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