Respuesta :
Answer:
T= 0.167 millisecs (T is time constant)
[tex]I = 1- e^{-6000t}[/tex]
T₉₉ = 0.768 millisecs (T₉₉ is time taken to reach 99% current value)
E = 10⁻³ Joules or 1 milli Joule
Explanation:
Here the expression of Time Constant for a series L-R circuit is[tex]T =\frac{L}{R}[/tex]
Thus [tex]T = \frac{2* 10^{-3} }{12}[/tex] = 0.167 millisecs
The current flowing in series L-R circuit is given by the expression
[tex]I = \frac{V}{R} (1 - e^{-\frac{t}{T} } )[/tex]
Substituting required values we get
[tex]I = 1- e^{-6000t}[/tex]
Final current is when t -> ∞ I(final) -> 1
Thus when I = 0.99 then t = T₉₉
[tex]0.99 = 1- e^{-6000T_{99} }[/tex]
Solving we get
T₉₉ = 0.768 millisecs
Energy stored in inductor is [tex]\frac{1}{2} Li^{2}[/tex]
Here final current is I(final)->1
[tex]E = \frac{1}{2}* 2*10^{-3} *1^{2}[/tex]
Thus,
E = 10⁻³ Joules or 1 milli Joule
