# What Formality Am I Using To Isolate This Portion Of The Circuit?

If I have this circuit in which the switch opens at t = 0 (after being closed for an infinite time, making the circuit steady state), for which I'm trying to find the voltage across R2 as a function of time, I need to determine the current through the inductor as a function of time first. To do this, I need to find the initial current through the inductor. (ignore element values) simulate this circuit – Schematic created using CircuitLab

I can replace the inductor with a short circuit and use circuit simplifications to reduce the circuit to the following. This is before the switch is opened at t = 0, and use the current through this circuit as the initial current through the inductor. simulate this circuit

After t = 0, my gut tells me I can simplify the circuit into two parts, one containing the inductor, and the other without. simulate this circuit

What law states I can do this? Is it because opening the switch means there are no current loops between either side of the circuit?

• Could you shrink the size of your second and third diagrams? They make the question hard to follow. Also, please clarify whether you are saying that the second and third diagrams are before switch closure, or after? – gwideman Apr 8 '14 at 0:43
• Also, is there supposed to be some correspondence between the resistor names in the first diagram, and those in the second and third? To be honest, I'm not seeing much valid reasoning I can latch onto here. – gwideman Apr 8 '14 at 0:49