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A 0.12-mu or micro FF capacitor, initially uncharged, is connected in series with a 10-kohm resistor and a 12-V battery of negligible internal resistance. Approximately how long does it take the capacitor to reach 90% of its final charge?
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The formula for a charging capacitor in a RC circuit is

$Q=Q_{0}(1-e^{-\frac{t}{RC}})$

So, to find the time to charge to 90% of $Q_{0}$:

$0.9Q=Q(1-e^{-\frac{t}{RC}})\Rightarrow 0.9=1-e^{-\frac{t}{RC}}\Rightarrow -0.1=-e^{-\frac{t}{RC}}$

$0.1=e^{-\frac{t}{RC}}\Rightarrow \ln0.1=-\frac{t}{RC}\Rightarrow t=-RC\cdot\ln 0.1=-(10k\Omega )(0.12\mu F)\ln 0.1={\color{Red} 0.00276seconds}$

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