Answer:
0.000140530327543 s
Explanation:
V = Voltage = 1.5 V
r = Resistance = [tex]7.69\ \Omega[/tex]
c = Capacitance = [tex]4.85\ \mu F[/tex]
Initial current
[tex]i_i=\dfrac{V}{r}\\\Rightarrow i_i=\dfrac{1.5}{7.69}\\\Rightarrow i_i=0.195058517555\ A[/tex]
Time constant
[tex]t_1=rc\\\Rightarrow t_1=7.69\times 4.85\times 10^{-6}\\\Rightarrow t_1=0.0000372965\ s[/tex]
The current is
[tex]i=i_ie^{\dfrac{-t}{t_1}}\\\Rightarrow -\ln\dfrac{i}{i_i}=\dfrac{t}{t_1}\\\Rightarrow t=-t_1\times \ln\dfrac{i}{i_i}\\\Rightarrow t=-0.0000372965\times \ln 0.0231\\\Rightarrow t=0.000140530327543\ s[/tex]
The elapsed time is 0.000140530327543 s
