Answer:
0.5 seconds
Explanation:
Charge
[tex]Q=CV\\\Rightarrow Q=0.1\times 10^{-6}\times 10\\\Rightarrow Q=0.000001\ F[/tex]
Resistance
[tex]R=\dfrac{V}{I}\\\Rightarrow R=\dfrac{10}{2\times 10^{-6}}\\\Rightarrow R=5000000\ \Omega[/tex]
We have the relation
[tex]Q=CV\left(1-e^{-\dfrac{t}{RC}}\right)\\\Rightarrow 0.000001=0.000001\left(1-e^{-\dfrac{t}{5000000\times 0.1\times 10^{-6}}}\right)\\\Rightarrow \dfrac{0.000001}{0.000001} = \left(1-e^{-\dfrac{t}{5000000\times 0.1\times 10^{-6}}}\right)\\\Rightarrow \dfrac{0.000001}{0.000001}-1=-e^{-\dfrac{t}{5000000\times 0.1\times 10^{-6}}}\right)\\\Rightarrow 0=e^{-\dfrac{t}{0.5}\right)\\\Rightarrow -\dfrac{t}{0.5}=1\\\Rightarrow -t=0.5\ s[/tex]
The time taken is 0.5 seconds
