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A resistor-inductor circuit (RL circuit) is one of the simplest analogue infinite impulse response electronic filters. It consists of a resistor and an inductor, either in series or in parallel, driven by a voltage source.
If a circuit is switched on, the current cannot instantly rise to the value determined by its resistance because of the opposing emf produced by its inductance. If an emf є, a resistance R, and an inductance L are connected together in series, the loop rules can be used to find the differential equation that determines the way the current rises from zero up to its final value:
The solution of this equation for a circuit with zero current at time t = 0 is
The quantity L/R is called the inductive time constant of the circuit.
If we just open a switch and very quickly stop the current, Faraday's law says that an enormous emf should be produced because of the very short time involved. Very often this enormous emf is large enough to cause the air to break down and spark. This is just Lenz's law at work again, fighting the change in the current, and it is easy to produce this effect. To avoid a flash, it is necessary to design a special kind of switch that gives the current a conducting path through which to flow while it decreases. If this has been done, then the loop rules applied to a circuit with inductance L and resistance R to give
The solution of this equation is given as:
where I0 is the initial current.
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Electromagnetism