How many time constants will elapse before the charge on a capacitors falls to 0.1% of its maximum value in a discharging RC circuit?
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$\text{q}=\text{Qe}^{\frac{-\text{t}}{\text{RC}}}$
$\text{q}=0.1\%\text{ Q}$
$\text{RC}\Rightarrow\text{Time constant}$
$=1\times10^{-3}\text{Q}$
So, $1\times10^{-3}\text{Q}=\text{Q}\times\text{e}^{\frac{-\text{t}}{\text{RC}}}$
$\Rightarrow\text{e}^{\frac{-\text{t}}{\text{RC}}}=\text{In}\ 10^{-3}$
$\Rightarrow\frac{\text{t}}{\text{RC}}=-(-6.9)=6.9$
$\text{q}=0.1\%\text{ Q}$
$\text{RC}\Rightarrow\text{Time constant}$
$=1\times10^{-3}\text{Q}$
So, $1\times10^{-3}\text{Q}=\text{Q}\times\text{e}^{\frac{-\text{t}}{\text{RC}}}$
$\Rightarrow\text{e}^{\frac{-\text{t}}{\text{RC}}}=\text{In}\ 10^{-3}$
$\Rightarrow\frac{\text{t}}{\text{RC}}=-(-6.9)=6.9$
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