EG1108 Electrical Engineering Sample Problems for Practice

Set 4 1. Write the nodal equations for the circuit below and find V1 and V2.

[Answer: -6.73 V, 1.45 V]

2. Derive the matrix equation [G][V]=[I] for the circuit below and, from there, find the voltage drop across R3.

[Answer: 17 V]

3. Use nodal analysis to find the nodal voltages for the circuit shown below. Use the answers to solve for the current through R1.

Solution:

Convert voltage source into equivalent current source and redraw the circuit. Assign lower end as the ground. Label the nodes and write nodal equations.

5 k R2 3 k

R3 4 k

R4 2 k

2 mA3 mA2 mA

V1 V2

Node V1: mAmAVk

Vkkk

3241

41

31

51

21 −=⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛ ++

Abdullah Al Mamun, Dept. of Electrical & Computer Engineering, NUS Page 1

EG1108 Electrical Engineering Sample Problems for Practice

Set 4

Node V2: mAVkk

Vk

221

41

41

21 =⎟⎠⎞

⎜⎝⎛ ++⎟

⎠⎞

⎜⎝⎛−

After simplification,

Node V1: 141

60152012

21 −=⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛ ++ VV

Node V2: 24

2141

21 =⎟⎠⎞

⎜⎝⎛ +

+⎟⎠⎞

⎜⎝⎛− VV

Or, Node V1: 125.07833.0 21 −=×−× VV Node V2: 275.025.0 21 =×+×− VV Solving these 2 equations for 2 unknowns, we get, V1 = -0.476 V and V2 = 2.51 V Since R1 is in a branch that was changed using source conversion, we must take the original circuit into consideration while finding current through R1.

The current is,

mAk

VVk

VVIR 10.25

)476.0(105

10 11 =

Ω−−

=Ω−

= .

4. Use nodal analysis to find the current through the 10 V source and, hence, determine the

power (delivered or absorbed) by this source.

[Answer: 511.4 watt delivered]

This problem is a good candidate for source conversion method. You can convert the current sources into equivalent voltage sources and apply KVL to the loop to find current. Use this method to verify your answer obtained by nodal analysis.

Abdullah Al Mamun, Dept. of Electrical & Computer Engineering, NUS Page 2

EG1108 Electrical Engineering Sample Problems for Practice

Set 4

5. Use superposition theorem to determine the voltage drop across the resistor R2 of the following circuit.

16V

32V5

mA

R31.6 k

R21.6 k

R12.4 k

[Answer: 11 V]

6. What must be the value of the unknown voltage source in the following circuit to ensure the current through the load IL = 5 mA?

[Answer: 30 V]

7. If the load resistor RLin the following circuit is to dissipate 240 W, determine the value of the unknown voltage source.

[Answer: 640 V]

8. Find Thevenin’s equivalent circuit for the following circuit between nodes ‘a’ and ‘b’ and

use it to find the power dissipated in RL.

8V

R21.2 k

R16.8 k

R31.0 k

RL1.5 k

a b

[Answer: RTh = 2.02 kW, VTh= 1.20 V, Power: 0.17 mW]

9. Find the Thevenin’s equivalent circuit of the following two-terminal circuit. [Hambley, Problem P2.75]

Abdullah Al Mamun, Dept. of Electrical & Computer Engineering, NUS Page 3

EG1108 Electrical Engineering Sample Problems for Practice

Set 4

Abdullah Al Mamun, Dept. of Electrical & Computer Engineering, NUS Page 4

[Answer: VTh = 20/3 V, RTh = 10/3 Ω]

10. Use Thevenin’s equivalent circuit to find current I in the following circuit when RL = 10 kΩ and RL = 50 kΩ.

[Answer: RTh = 60 kΩ, VTh= 25 V, I: -0.357 mA, -0.227 mA]

11. Find Norton’s equivalent circuit between nodes ‘a’ and ‘b’ of the circuit shown below. Use

this equivalent circuit to determine IL when RL = 20 Ω and when RL = 50 Ω.

[Answer: IN = 0.35 A, RN = 16 Ω, IL = 0.156 A and 0.085 A]

12. For this circuit, find the value of R so that RL = RTh. Calculate power dissipated by RL.

[Answer: 31.58 Ω, 7.81 mW]

13. If R1+R2 = 200 kΩ in the circuit below, determine their individual values such that the load resistance is equal to the Thevenin’s resistance (RTh) of the remaining circuit. What is the maximum power received by the load?

R1

RL32 kR2

25 V

[Answer: (R1= 40 kΩ, R2= 160 kΩ) or (R1= 160 kΩ, R2= 40 kΩ), 3.125 W]