An e.m.f. of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time \[t=\infty \] and at t = 1 second is [MP PMT 1994]

• A.            \[\frac{{{e}^{1/2}}}{{{e}^{1/2}}-1}\]                              
• B.            \[\frac{{{e}^{2}}}{{{e}^{2}}-1}\]
• C.            \[1-{{e}^{-1}}\]                   
• D.            \[{{e}^{-1}}\]