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Unformatted text preview: loses at t = 0. Interesting things start tp happen.
t=0
IS R iL +
L vL
– 1. Because the through an inductor cannot change instantaneously, iL
will maintain the value that it had initially. iL (t = 0) = iLi (= 0).
2. Inductor voltage current has no such restriction, and it’s value will
instantaneously jump to a value determined by the voltage across the
parallel resistor.
vL (t = 0) = vR = IS R
EE 442 RC and RL transients – 16 As we observe how the situation progresses for t > 0:
t>0
IS R iL
increasing +
L vL decreasing
– 3. Current will begin to ﬂow into the inductor so iL (t > 0) > iLi, (> 0) (and
increasing).
4. As the inductor takes more of the current from the source, less current
ﬂows through the resistor, and the voltage across the inductor (and
inductor) drops. (We might say that the inductor is becoming “amped
up”.) EE 442 RC and RL transients – 17 IS R iL = IS +
L vL = 0
– after a sufﬁciently long time
5. Eventually, the inductor current will increase until it is equal to
IS – it is taking all of the current from the source. Since no current is
left to go through the resistor, the parallel voltage drops to zero. From
that time nothing changes anymore.
This is a transient effect. Initially, the inductor current was at some ﬁxed,
steady value ( = 0 in our example) and the inductor voltage was zero.
When the switch closed, the voltage jumped up to a value determined the
initial voltage across the resistor. The voltage across the inductor caused
the inductor to begin increasing from its initial value. When the inductor
current equaled the source current, the voltage dropped to zero, and the
circuit returned to a static (quiescent) state with the inductor having a
new, higher current, with no voltage across it.
EE 442 RC and RL transients – 18 IS R iL (t) +
L vL (t)
– Now, let’s do the math. For t > 0 (after the switch has closed):
vR = vL
vR = (IS − iL ) R diL
vL = L
dt
diL
( I S − iL ) R = L
dt Another differential equation. This is pret...
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This document was uploaded on 04/05/2014.
 Fall '09
 Volt

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