\(i = I _{\max }\left(1- e ^{- Rt / L }\right)\)

For \(U\) to be \(\frac{ U _{\max }}{ n } ;\) i has to be \(\frac{ I _{ max }}{\sqrt{ n }}\)

\(\frac{I_{\max }}{\sqrt{n}}=I_{\max }\left(1-e^{-R t / L}\right)\)

\(e ^{- Rt / L }=1-\frac{1}{\sqrt{ n }}=\frac{\sqrt{ n }-1}{\sqrt{ n }}\)

\(-\frac{ Rt }{ L }=\ln \left(\frac{\sqrt{ n }-1}{\sqrt{ n }}\right)\)

\(t =\frac{ L }{ R } \ln \left(\frac{\sqrt{ n }}{\sqrt{ n }-1}\right)\)