Answer:
[tex]0.35[/tex] sec
Explanation:
[tex]i_{o}[/tex] = maximum value of the current
[tex]i[/tex] = value of the current after time "t" = 0.63 [tex]i_{o}[/tex]
[tex]R[/tex] = resistance of the resistor = 6 ohm
[tex]L[/tex] = Inductance of the inductor = 2.1 H
Time constant of the circuit is given as
[tex]T = \frac{L}{R}[/tex]
[tex]T = \frac{2.1}{6}[/tex]
[tex]T = 0.35[/tex] sec
Using the equation
[tex]i = i_{o}(1 - e^{\frac{-t}{T}})[/tex]
Inserting the values
[tex](0.63) i_{o} = i_{o}(1 - e^{\frac{-t}{0.35}})[/tex]
[tex](0.63) = (1 - e^{\frac{-t}{0.35}})[/tex]
[tex]t = 0.35[/tex] sec
