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Electric Current in Conductors — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsElectric Current in Conductors3 Marks
Question
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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Answer

$\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, $1\times10^{-3}\text{Q}=\text{Q}\times\text{e}^{\frac{-\text{t}}{\text{RC}}}$
$\Rightarrow\text{e}^{\frac{-\text{t}}{\text{RC}}}=\text{In}\ 10^{-3}$
$\Rightarrow\frac{\text{t}}{\text{RC}}=-(-6.9)=6.9$

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