# 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 $$(V_1 - 0)/100$$

## 1 Answer

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.

• One thing that I not mentioned is that the circuit is in the transient state, a switch in the circuit is closed recently.@Chu – Sohail Ahmed Dec 26 '15 at 11:14
• See updated answer - use the Laplace transform for transient analysis (unless you want to go down the differential equation route!) – Chu Dec 26 '15 at 11:17
• We have DC source @Chu – Sohail Ahmed Dec 26 '15 at 11:17
• Actually I'm looking for a method other than Laplace, is there anyone?@Chu – Sohail Ahmed Dec 26 '15 at 11:19
• Differential equation – Chu Dec 26 '15 at 11:20