The instantenous emf equation is given as;
Ldtdi+Ri=V
dtdi=LV−Ri
dtdi=LR(RV−i)
(RV−i)di=LRdt
Integrating on both sides
∫0i(RV−i)di=∫0tLRdt
∫0i(Ri−V)di=−LR∫0tdt
ln−RV(i−RV)=−LRt
−RV(i−RV)=e−LRt
i=RV(1−e−LRt)
When t=1, i(1)=9
9=10100(1−e−L101)
109=1−eL−10
eL−10=0.1
L−10=ln(0.1)
ln(0.1)=-2.302
L=2.30210
L=4.443H
Current after 0.5s is;
i(0.5)=10100(1−e−4.34410∗0.5)
=6.837A
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