Answer:
0.2854
Explanation:
The Energy stored in coil is given by
U=[tex]\frac{1}{2}[/tex]L[tex]I^{2}[/tex]
U=0.565Uo
[tex](\frac{1}{2} )L(i^{2} )=(0.565)(\frac{1}{2} )L(io^{2} )[/tex]
[tex](i^{2} )=(0.565)(io^{2} )[/tex]
[tex](ioe^{-t/T} )^{2}=(0.565) (io)^{2}[/tex]
[tex](io)^{2}e^{-2t/T}=(0.565)(io)^{2}[/tex]
[tex]e^{-2t/T}=0.565[/tex]
Apply log: both sides we get
[tex]\frac{-2t}{T}=-0.5709[/tex]
[tex]\frac{t}{T}=0.2854[/tex]
