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The resistance r is the dc resistive value of the wire turns or loops that goes into making up the inductors coil. The rl parallel circuit is a first order circuit because its described by a first order differential equation where the unknown variable is the inductor current it.

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This equation is valid only a a single frequency f and must be calculated for each frequency of interest.

Circuit inductor equation. Written by willy mcallister. Written by willy mcallister. We look at the inductor i v equations and notice how important it is to give inductor current a place to flow.
At a certain point a high enough frequency its practically as if the inductor is an open circuit being that it offers such high impedance. Alternating current in a simple inductive circuit is equal to the voltage in volts divided by the inductive reactance in ohms just as either alternating or direct current in a simple resistive circuit is equal to the voltage in volts divided by the resistance in ohms. We look at the inductor i v equations and notice how important it is to give inductor current a place to flow.
So this formula calculates impedance. A lr series circuit consists basically of an inductor of inductance l connected in series with a resistor of resistance r. A circuit containing a single equivalent inductor and an equivalent resistor is a first order circuit.
Since the q of an inductor is the ratio of the reactive component to the resistive component an equivalent circuit can be defined with a resistor in parallel with the inductor. The last equation computes the time constant of an rl circuit a circuit composed of a single resistor and indctor.

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