Understanding Current Flow in Parallel Circuits with Inductors and Resistors

[semc]

Hi, I was wondering am I correct to say that in a circuit, more current will flow in the path where the resistance is the least? If an inductor and a resistor are connected in parallel to a battery with the inductor initially uncharged. The current passing through the inductor will rise slowly to a certain value correct? But how do we find the current passing through the inductor? I tried using Kirchoff's law and got these three equations-
I₂R=E
I₃+I₂=I₁
-I₂R+L(dI₃/dt)=0

After some algebra I got -I₁R+I₃R+L(dI₃/dt)=0 which gives me I₃(t)=-I₁[1-e^-(Rt/L)]. Is this correct? This equation suggests after the inductor is charged up the current will not flow through the resistor?

 

[Matterwave]

Because of conservation of charge, you can't have current moving at different rates across a resistor and an inductor in a series. Currents can only differ if the circuit is in parallel (or for a capacitor...since capacitors store charge - currents don't actually move across capacitors).

 

[semc]

Sorry I meant to say parallel circuit.