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A series $RC$ circuit is connected to a $DC$ voltage source at time $t= 0$. The relation between the source voltage $V_{s},$ the resistance $R$, the capacitance $C$, and the current $i(t)$ is given below.

$V_{s}= R \: i(t)+\frac{1}{c}\int ^{t}_{o}i(u)du$.

Which one of the following represents the current $i(t)$?

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