Statement 1: The quantity L/R possesses dimensions of time.

Statement 2: To reduce the rate of increases of current through a solenoid, one should increase the time constant (L/R).

The  current i is given by $$\begin{gathered} i=\frac{E}{R}(1-e^{\frac{-Rt}{L}} )=\frac{E}{R}(1-e^{\raisebox{1ex}{$-t$}\!\left/ \!\raisebox{-1ex}{$\tau $}\right.} ) \\ \Rightarrow \frac{di}{dt}=\frac{E}{R\tau } e^{\frac{-t}{\tau }} \end{gathered}$$ 

In order to decreases the rate of increase of current through solenoid, we have to increase the time constant $\frac{L}{R}.$

Also $\frac{L}{R}=\frac{\varphi /i}{v/i}=\frac{\phi }{v}=\raisebox{1ex}{$volt sec$}\!\left/ \!\raisebox{-1ex}{$volt$}\right.=sec$