Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd

10.11 
problemS
1. What is the differential equation describing i
L
for t 
≥
0
+ 
in the circuit in Fig. 10.11-1?
+
R
L
i
L
u
(
t
) – 
u
(
t 
– 1)
t 
= 2 s
–
Fig. 10.11-1
2. A series RL circuit with non-zero initial energy is driven by a unit step voltage source. The circuit 
current is found to reach 75% of its steady-state value in one time constant. Express the initial 
current in the inductor as a percentage of its steady-state value.
3. A DC voltage source of 1V is switched on to a series RL circuit at t 
= 
0. i
L
is found to be 
50% at t 
= 
t
. Was there any initial current in the inductor? If so, what is its magnitude and 
direction?
4. Find the ratio E/V such that i
L
in Fig. 10.11-2 becomes V/R at t 
= 
0.5 
+ 
t
where 
t
= 
L/R.
+
R
L
E
i
L
V u
(
t
)
t 
= 0.5 s
–
+
–
Fig. 10.11-2 
5. What is the time required for the energy stored in the inductor in a series RL circuit to reach 90% 
of its steady-state value in step response?
6. i
L
in the circuit in Fig. 10.11-3 is –2A at t 
= 
0
-
due to other sources that are not shown, but are 
switched out at t 
= 
0. It is found that i
L
(t) 
= 
0 for t 
≥
0
+
.
What is the value of L?
+
R
L
i
L
(
t
)
–
δ
Fig. 10.11-3

---

10.60
First-Order 
RL
Circuits
7. i
L
in the circuit in Fig. 10.11-4 at t 
= 
0
-
is –2A. It is found that i
L
(t) 
= 
0 for t 
≥
0
+
.
What is the value 
of time constant of the circuit?
R
L
i
L
2
(
t
)
δ
Fig. 10.11-4 
8. A series RL circuit with non-zero initial energy is driven by a 1V DC switched source. The 
inductor current is found to be (2 
- 
e
-
t
) A. What are the values of inductance, resistance and initial 
current?
9. A series RL circuit with non-zero initial energy is driven by a 1V DC switched source. The 
inductor current is found to be 3A for t 
≥
0
+
.
What is the value of initial current and what is its 
direction relative to the 3A current?
10. An AC voltage source 
= 
V sin (
w
t) is applied to a series RL circuit from t 
= 
0.The circuit current 
is found to be 
= 
0.7sin (
w
t 
- 
p
/3) A. Was there any initial current in the inductor? If yes, what is 
its magnitude and relative direction?
11. A series RL circuit with non-zero initial energy is driven by a 1V DC switched source. The 
inductor current is found to be 2A. What is the new i
L
in the circuit if (i) the initial condition is 
doubled and (ii) if a 2V DC switched source is applied with no change in initial condition?
12. The inductor current 
= 
0 for t 
≥
0
+ 
in the circuit in Fig. 10.11-5. Find the values of I
0
and I
S
.