Indian Institute of Technology, Delhi
ELL 202: Circuit Theory
Tutorial 1, August 8, 2022
Multiple choice type questions
1. Two inductors of 0.1 H and 0.2 H are coupled to each other through a
coupling coefficient of 0.5. What is the mutual inductance?
(a) 0.05 H
(b) 0.0707 H
(c) 0.1 H
(d) 0.1414 H
2. Two inductors of 10 mH and 2.5 mH are mutually coupled. What is
the maximum mutual inductance?
(a) 2.5 mH
(b) 5 mH
(c) 10 mH
(d) 20 mH
3. A mutual inductance of 2 mH is designed using inductors of 1 mH and
9 mH. What should be the coupling coefficient?
(a) 1/8
(b) 1/6
(c) 1/3
(d) 1/2
4. Which of the following is true for the coupling coefficient, k, of a mutual
inductance?
(a) k ∈ (−∞, ∞)
(b) k ∈ [0, ∞)
(c) k ∈ [−1, 1]
(d) k ∈ [0, 1]
5. Which of the following is the outcome of Tellegen’s theorem?
(a) VI = 0
(b) VT I = 0
(c) VIT = 0
(d) VT IT = 0
Short answer type questions
6. The incidence matrix is guaranteed to be linearly
.
7. Removal of any one row of the incidence matrix gives the
.
is linearly
, which
8. A circuit does not have any dependent sources. While analyzing using
the
method, the G matrix will be
.
9. One should not place two or more voltage sources in
.
10. One should not place two or more current sources in
.
11. If a circuit has 8 nodes and 12 elements, what is the number of equations
in node-voltage analysis?
1
4A
6Ω
3Ω
3V
3Ω
3V
5Ω
8Ω
2Ω
vx
Figure 1: Circuit for question 16
12. In an 8-node 12-element circuit, what is the number of mesh equations
in mesh-current analysis?
13. In the 8-node 12-element circuit, what is the maximum number of independent and dependent current sources? (Answer: 5)
14. In the 8-node 12-element circuit, what is the maximum number of independent and dependent voltage sources? (Answer: 7)
15. In the 8-node 12-element circuit, there are 4 voltage sources and 3
current sources. Which analysis method will have lesser equations node voltage method or mesh current method? Why? (Answer: mesh
method will have 2 equations, while node voltage method will need 3
equations.)
Numericals
16. In the circuit shown in Fig. 1, find the value of vx .
17. Solve the circuits in Fig. 2 using the node voltage method. Arrive at
the matrix equation GV = U for each of the circuits. Invert the matrix
G using Octave.
18. Solve the circuits in Fig. 2 using the mesh method. Arrive at the matrix
equation ZI = U for each of the circuits. Invert the matrix A using
Octave. Cross-check your answers with those obtained earlier in 17.
19. For each of the circuits in Fig. 2 (let us call the circuit as Ca ), come up
with a new circuit Cb , such that (i) the mesh equations of Ca are the
same as the node equations of Cb , and (ii) the node equations of Ca are
the same as the mesh equations of Cb .
2
1A
4Ω
4Ω
4V
(a)
20 Ω
va
−0.1vb
vb
100 Ω
2V
5Ω
100 Ω
3Ω
−0.1va
0
(b)
6Ω
4Ω
4Ω
2Ω
2Ω
va
6Ω
vb
3V
3V
3Ω
2Ω
5Ω
8Ω
4Ω
4V
4Ω
2Ω
3V
1Ω
2Ω
4Ω
2V
2A
5ix
4Ω
ix
2Ω
4vab
(c)
(d)
(e)
Figure 2: Circuits for questions 17, 18, and 19.
20. Schematics are shown in Fig. 3. The component values are to be taken
as 1, 2, 3,. . . 12, numerically. For example, a component R5 will have a
value of 5 Ω, V6 will have a value of 6 V, I7 a value of 7 A, K8 a value
of 8, Z9 a value of 9 Ω, G10 a value of 10 S. Solve the four circuits using
the node-voltage method first and the mesh method next.
21. Consider a current-controlled voltage source (CCVS). Suppose the voltage across this CCVS is defined as 10ix , where ix is the current through
the CCVS itself. Can you simplify the representation of this CCVS?
22. Consider a voltage-controlled current source (VCCS). Suppose the current through this VCCS is defined as 0.1vx , where vx is the voltage
across the VCCS itself. Can you simplify the representation of this
VCCS?
23. Consider a voltage-controlled voltage source (VCVS). Is it possible to
have the value of the voltage source to be proportional to the voltage
across the VCVS itself? Think and decide as to what happens if a
proportionality constant ̸= 1 is used. What happens if a proportionality
constant = 1 is used? Repeat the exercise for a current-controlled
current source (CCCS).
24. A resistive network with unknown resistances was used in two experi3
R1
I3
V4
V8
R2
a
K6 vbc
V12
V2
R7
R6
R8
R12
R7
K9 vxy
R11
Figure 3: Circuits for questions 20.
4
G5 ixy
y
x
G10 vbd
d
R10
K4 vxy
R3
c
R9
I9
R1
R5
b
V7
R11
Z4 iab
R11
R8
R12
R1
R5
R6
I10
R11
R2
I4
R7
R9
V8
V3
R5
V6
I3
R1
R2
I10
R12
i1
v1
vL
RL
Figure 4: Circuit for question 24
50 Ω
Experiment-A
Resistive network
ix
0.1 A
50 Ω
Resistive network
1A
50 Ω
50 Ω
1V
Experiment-B
Figure 5: Schematics for question 25
ments, as shown in Fig. 4. First RL was set to 2 Ω, v1 was 8 V, ii was
measured as −2 A, vL was measured as 2 V. Next RL was changed to
4 Ω, and the applied v1 was changed to 12 V. The measured i1 was
−2.4 A. What would be vL in the second experiment? (Hint: Use
Tellegen’s theorem.)
25. In the schematic of Fig. 5, two experiments are shown with a two-port
network. In experiment-A, a 1-A 50-Ω source is applied on the left side,
and a 50-Ω resistor is connected on the right. The current measured
is 0.1 A. In experiment-B, a 1-V 50-Ω source is applied on the right
side, and a 50-Ω resistor is connected on the left. What will be the
current iX ? (Hint: Use Tellegen’s theorem. Any other method will lead
to significant wastage of time.)
26. If you apply mesh-method to solve the circuit of Fig. 6, what is the
least number of equations you will obtain? What is the least number
of equations you will obtain if you apply node-analysis? Use the more
straightforward method and solve for ix .
5
2Ω
2Ω
2Ω
1V
ix
2V
2Ω
Figure 6: Circuit for question 26
6
1A