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Suppose an ideal case where an ideal voltage source is connected to an ideal inductor with no resistance.

Everytime the voltage changes from the source the electric field in the circuit changes. The change in electric field will cause a changing magnetic field in the circuit and this change in magnetic field (according to Faraday's and Lenz law) will induce equal and opposite voltage in the inductor.

So everytime the voltage change from the voltage source there will be an equal and opposite voltage change in the inductor as well.

My question is that if there is always equal and opposite voltage to the applied voltage then how the current will flow in this case in the circuit as the net voltage will always remain zero in the circuit.

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All circuits have a net voltage of zero around them. That’s Kirchoff’s voltage law.

In a circuit, a battery, generator or other voltage source will provide whatever current is needed for that voltage.

A resistor has a proportional relation between voltage and current; attached to a voltage source, that will determine current in the circuit.

An inductor has a different relation between voltage and current, but the principle is the same: the voltage source puts a voltage across the inductor, and the inductor responds to the voltage across it by drawing a current.

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