Inductors -
UNDER CONSTRUCTION - Barely Started
The
inductor is a peculiar electrical element. Ideally, it only exhibits its'
behavior when things are changing. Keep the status quo and it is well
behaved. Change things and you may see some effect you may consider to be
truly wierd.
Consider this. The inductor has a relationship between voltage and
current:
INSERT V = L di/dt
where:
v(t) =
Voltage across the inductor
i(t) =
Current through the inductor
L =
Inductance (in henries)
So, if
the current through the inductor is not changing, there is no voltage across the
inductor. However, if the current changes then things start to happen.
When you try to force the current through an inductor to change, then you can
have problems.
Consider this simple circuit:
INSERT V-R-L CIRCUIT
At some point in time the switch is opened.
Prior to opening the switch, an equilibrium is achieved. The current is
constant and is simply Vs
/ RL.
That's because there is no voltage across the inductor. Remember the
current is constant so di/dt = 0 and there is no voltage across the inductor.
It's almost as though the circuit doesn't know that the inductor is there.
Now,
consider what happens when the switch is opened. You probably want to
believe that opening the switch causes the current to go to zero. Here's a
little exercise for you then.
At the
moment the switch is opened, write KVL and be sure to include the voltage across
the switch. Assume that the current drops from Vs
/ RL
at the instant that the switch opens and becomes zero instantaneously.
Now, answer the following questions:
What is the voltage across the inductor?
What is the voltage across the source?
What is the voltage across the resistor?
What is the voltage across the switch?
In each case, as you answer the question, be sure to
supply reasons for your conclusions.
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