Current in a branch containing both resistor inductor?
Express the series L/C/R branch as a complex impedance - either via Laplace transfom: \$\small Z(s)=R+sL+\frac{1}{sC}\$, or the equivalent in the frequency domain: \$\small Z(j\omega)=R+j\omega L+\frac{1}{j\omega C}\$. As the source is a direct voltage, Laplace is the way to go.