Answer:
[tex]C = 2.48 \times 10^{-4} Farad[/tex]
Explanation:
As per the equation of voltage on capacitor we know that
[tex]V = V_{max}(1 - e^{-\frac{t}{\tau}})[/tex]
now we know that voltage reached to its 80% of maximum value in 4 second time
so we will have
[tex]0.80 V_{max} = V_{max}(1 - e^{-\frac{4}{\tau}})[/tex]
[tex]0.20 = e^{-\frac{4}{\tau}}[/tex]
[tex]-\frac{4}{\tau} = ln(0.20)[/tex]
[tex]-\frac{4}{\tau} = -1.61[/tex]
[tex]\tau = 2.48[/tex]
as we know that
[tex]\tau = RC[/tex]
[tex](10 k ohm)(C) = 2.48[/tex]
[tex]C = 2.48 \times 10^{-4} Farad[/tex]
