☑ Inductor At Time Zero

If the circuit had just a resistor the current would drop immediately to zero. However if the current flowing through an inductor changes very rapidly such as with the operation of a switch high voltages can be induced across the inductors coil.

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Therefore the long time equivalence of an inductor is a wire ie.

Inductor at time zero. We now know that the current can not change instantaneously in an inductor because for this to occur the current would need to change by a finite amount in zero time which would result in the rate of current change being infinite didt making the induced emf infinite as well and infinite voltages do no exist. To see why apply kirchoffs loop rule. This time constant t is measured by t lr in seconds where r is the value of the resistor in ohms and l is the value of the inductor in henries.

This is in keeping with the intuitive point that the inductor will only have a voltage across as long as the current in the circuit is changing as the circuit reaches its steady state there is no further current change and ultimately no inductor voltage. The time required for the current flowing in the lr series circuit to reach its maximum steady state value is equivalent to about 5 time constants or 5t. Thus the voltage across the inductor tends towards 0 as time passes while the voltage across the resistor tends towards v as shown in the figures.

It is considered to reach zero in five time constant periods. The exponential curve the change of current in an inductor in response to a step change in input is exponential. At the exact instant the switch is closed the current through the inductor goes from nothing to something in a difference in time of zerothat exact instant thus the voltage across the.

The current does eventually reach zero but it takes some time to get there. In the long time limit after the magnetic flux through the inductor has stabilized no voltage would be induced between the two sides of the inductor. Once the inductors terminal voltage has decreased to a minimum zero for a perfect inductor the current will stay at a maximum level and it will behave essentially as a short circuit.

Short circuit or 0 v battery. With the inductor the change in current means a change in magnetic flux so the inductor opposes the change. Over time the inductors current rises to the maximum value allowed by the circuit and the terminal voltage decreases correspondingly.