Understanding Current Flow in Parallel Circuits with Inductors and Resistors

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In a parallel circuit with an inductor and a resistor, current tends to flow more through the path with lower resistance. When the inductor is initially uncharged, the current through it rises gradually to a steady state. The user derived equations using Kirchhoff's law to analyze the current flow, ultimately arriving at an expression for the current through the inductor over time. This expression indicates that once the inductor is fully charged, current will primarily flow through the inductor rather than the resistor. The discussion emphasizes the principles of conservation of charge and the behavior of currents in parallel circuits.
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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?
 

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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).
 
Sorry I meant to say parallel circuit.
 
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