Answer:
The time constant is [tex]\tau = 1.265 s[/tex]
Explanation:
From the question we are told that
the time take to charge is [tex]t = 2.4 \ s[/tex]
The mathematically representation for voltage potential of a capacitor at different time is
[tex]V = V_o - e^{-\frac{t}{\tau} }[/tex]
Where [tex]\tau[/tex] is the time constant
[tex]V_o[/tex] is the potential of the capacitor when it is full
So the capacitor potential will be 100% when it is full thus [tex]V_o =[/tex]100% = 1
and from the question we are told that the at the given time the potential of the capacitor is 85% = 0.85 of its final potential so
V = 0.85
Hence
[tex]0.85 = 1 - e^{-\frac{2.4}{\tau } }[/tex]
[tex]- {\frac{2.4}{\tau } } = ln0.15[/tex]
[tex]\tau = 1.265 s[/tex]
