# Current in a branch containing both resistor inductor?

simulate this circuit – Schematic created using CircuitLab There is a switch in the circuit which has been closed recently so the circuit is now in transient state and we are applying KCL at node 1. Also we cannot use Laplace transform. Is there a method for this?

WE have to apply KCL at NODE1 , How can we write the expression for current in the branch containing capacitor and inductor? As we have for left and right branches i.e $$(V_1 - 1)/100$$ and $$(V_1 - 0)/100$$

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.