Solve the following problems. Use the applicable method$/$s of solutions standard notations and express answers, when necessary, to at least $3$ decimal places.

$1.$ A constant inductance of $1$ henry and a variable resistance of $\backslash ($ R$=1/5+$t $\backslash )$ ohms are connected in series with a constant e$.$m$.$f$.$ E volts. If at time $\backslash ($ t $\backslash )\backslash (=0\backslash ),$ the current I $=0$ ampere, what is the value of the constant e$.$m$.$f $\backslash ($ E $\backslash )$ if at $\backslash ($ t$=5\backslash$mathrm$\{$sec$\}\backslash ),$ the current $\backslash ($ I$=30\backslash )$ amperes.