Example 9.
For the circuit shown below, the switch has been in position a for a long time and it is
moved to b at t=0. Determine the initial and final values the inductor voltage and current
i L (0  ) , vL (0  ) , i L () , v L ()
9 kΩ
t=0
1 kΩ
a
b
+
_
10 V
1 kΩ
+
i L (t )
vL
10 mH
_
20 V
+
_
An instantaneously change in inductor current is impossible because the infinite voltage
diL
would be required. This means the inductor current must be continuous. v L  L
dt
10
i L (0  )  i L (0  ) 
 1mA
9 1
v L (0  )  0V
t>0
b
1 kΩ
1 kΩ
+
i L (t )
vL
10 mH
_
20 V
+
_
v L (0  )  20  1 (1  1)  18V
For a circuit with dc source, if the circuit stays for a very long time without any switching
taking place, we say that the circuit is in the steady state. In the steady sate mode, all the
diL
 0 . So the
currents in the circuit are constants and their derivatives are zero. v L  L
dt
inductor behaves as a short circuit.
20
i L () 
 10 mA
11
v L ()  0V