A series RL circuit consists of a resistor $R=10 \ \Omega$ and an inductor $L=1\text{ H}$, connected to a DC voltage source of $V=20\text{ V}$. The switch is closed at $t=0$, and the initial current is zero. Determine the expression for the current $i(t)$ through the inductor for $t>0$, assuming ideal components.