# PROBLEM # 7.34 ```PROBLEM # 7.34
a) Use component values fromAppendix H to create a first-order RL circuit (see
Fig. 7.16) with a time constant of 8 μs. Use a single inductor and a network of
resistors, if necessary. Draw your circuit.

R
L
R
L

L  1mH
1103
R
 125
8 106
For a 125 Ω resistor, use a 100 Ω, a 15 Ω, and a 10Ω resistor in series.
J1
V1
12 V
R1
R2
R3
100Ω
15Ω
10Ω
Key = Space
L1
1mH
b) Suppose an inductor you chose in part (a) has no iitial stored energy. At t = 0,
a switch connects a voltage source with a value of 25 V in series with the
inductor and equivalent resistance. Write an epression for the current through
the inductor for t &gt;= 0.
J1
R1
R2
R3
100Ω
15Ω
10Ω
Key = Space
L1
1mH
V1
25 V
i (t )  i ()  [i (0)  i()]e
i (0)  0
25
i ( ) 
 0.2 A
125
i (t )  0.2  [0  0.2]e

125
t
0.001
R
 t
L
 0.2  0.2e 125000t
i (t )  0.2 1  e 125000t  A, t  0
c) Using your result from part (b), calculate the time at which the current through
the inductor reaches 75 % of its final value.
i (t1 )  (0.75)(0.2)  0.2(1  e 125000t1 )
0.75  1  e 125000t1
0.25  e125000t1
ln(0.25)  125000t1
1.38629  125000t1
t1 
1.38629
 11 s
125000
```