Practice Problems: Network Theorems
Question 1
A power system engineer is analyzing a transmission line circuit to determine the current through a critical load resistor. The circuit consists of a 120 V DC source with an internal resistance of 2 Ω connected to a network of resistors: 8 Ω in series with the source, followed by two parallel branches - one branch has 12 Ω and the other has a 6 Ω resistor in series with the load resistor of 4 Ω. Using Thevenin's theorem to analyze the circuit from the perspective of the 4 Ω load resistor, what is the Thevenin equivalent voltage?
(a) 24 V
(b) 30 V
(c) 36 V
(d) 40 V
Question 2
An electrical engineer is designing a control circuit for an industrial automation system. The circuit has a voltage source of 48 V with internal resistance 1 Ω, connected through a 5 Ω resistor to a junction. From this junction, three branches exist: Branch 1 has 10 Ω, Branch 2 has 15 Ω, and Branch 3 has a 20 Ω resistor in series with a variable load. To determine the Norton equivalent circuit as seen by the variable load, what is the Norton equivalent current?
(a) 1.6 A
(b) 2.0 A
(c) 2.4 A
(d) 3.0 A
Question 3
A facilities engineer is troubleshooting a lighting circuit in a commercial building. The circuit can be modeled as two voltage sources: Source 1 is 24 V with 3 Ω series resistance, and Source 2 is 18 V with 2 Ω series resistance, both connected to a common load of 10 Ω. Using the superposition theorem, what is the contribution of Source 1 alone to the load current (with Source 2 replaced by its internal resistance)?
(a) 0.96 A
(b) 1.20 A
(c) 1.60 A
(d) 2.00 A
Question 4
A test engineer is validating a power supply circuit that delivers power to a communication device. The circuit has a 60 V source with 4 Ω internal resistance connected to a load. According to the maximum power transfer theorem, what load resistance will extract maximum power from this source?
(a) 2 Ω
(b) 4 Ω
(c) 8 Ω
(d) 12 Ω
Question 5
A circuit design engineer is analyzing a DC network for a battery management system. The network contains a 36 V battery with 0.5 Ω internal resistance, connected through a 2.5 Ω resistor to a node. From this node, two branches exist: one with 6 Ω and another with 3 Ω in series with a sensor load of 9 Ω. What is the Thevenin resistance seen by the 9 Ω sensor when it is removed from the circuit?
(a) 3.0 Ω
(b) 4.5 Ω
(c) 5.0 Ω
(d) 6.0 Ω
Question 6
A control systems engineer is designing a sensor interface circuit. The circuit has two current sources in parallel: I₁ = 3 A with parallel resistance 12 Ω, and I₂ = 2 A with parallel resistance 18 Ω, both feeding a 6 Ω load resistor. Using Norton's theorem, what is the Norton equivalent current for this combined network as seen by the load?
(a) 3.4 A
(b) 4.0 A
(c) 4.6 A
(d) 5.0 A
Question 7
An automotive electronics engineer is analyzing the electrical system of an electric vehicle. A complex network supplies power to a motor controller through multiple paths. The network can be simplified to a Thevenin equivalent with VTH = 288 V and RTH = 0.8 Ω. If the motor controller presents a load resistance of 3.2 Ω, what is the actual power delivered to the controller?
(a) 16.4 kW
(b) 18.2 kW
(c) 20.7 kW
(d) 25.9 kW
Question 8
A power electronics engineer is testing a solar inverter circuit. The circuit contains three voltage sources in a mesh network: V₁ = 100 V with 5 Ω resistance in the first mesh, V₂ = 80 V with 4 Ω resistance in the second mesh, and a common 10 Ω resistor between meshes. A 15 Ω load connects the second mesh to ground. Using the superposition theorem, what is the current through the 15 Ω load due to V₁ only (with V₂ set to zero)?
(a) 2.89 A
(b) 3.45 A
(c) 4.17 A
(d) 5.26 A
Question 9
A telecommunications engineer is designing a signal distribution network for a cellular base station. The network has a 50 V DC source with 2 Ω internal resistance feeding a bridge circuit. The bridge consists of four arms: 8 Ω, 12 Ω, 10 Ω, and 15 Ω arranged clockwise. A detector with 5 Ω resistance is connected across the bridge diagonal. What is the Thevenin voltage across the detector terminals when it is removed?
(a) 1.2 V
(b) 2.5 V
(c) 3.8 V
(d) 5.0 V
Question 10
A circuit protection engineer is analyzing fault currents in an industrial distribution panel. The system can be represented by two parallel current sources: Source A provides 15 A through an 8 Ω parallel resistance, and Source B provides 10 A through a 12 Ω parallel resistance. Both sources feed a critical 4 Ω load. What is the Norton equivalent resistance seen by the 4 Ω load?
(a) 2.4 Ω
(b) 3.6 Ω
(c) 4.8 Ω
(d) 6.0 Ω
Question 11
A renewable energy engineer is analyzing a hybrid power system combining solar and wind sources. The solar array provides 200 V with 1.5 Ω series resistance, and the wind turbine provides 180 V with 2.0 Ω series resistance. Both sources are connected in parallel to supply a 12 Ω battery charging load. Using superposition theorem, what is the total current through the load?
(a) 12.8 A
(b) 14.5 A
(c) 16.2 A
(d) 18.9 A
Question 12
A data center engineer is optimizing power delivery to server racks. A UPS system can be modeled with Thevenin equivalent parameters: VTH = 240 V and RTH = 0.4 Ω. To achieve maximum power transfer to a server rack, what load resistance should be designed, and what maximum power will be transferred?
(a) RL = 0.4 Ω, Pmax = 36 kW
(b) RL = 0.4 Ω, Pmax = 72 kW
(c) RL = 0.8 Ω, Pmax = 36 kW
(d) RL = 0.8 Ω, Pmax = 48 kW
Question 13
An instrumentation engineer is designing a measurement circuit for a strain gauge bridge. The circuit has a 12 V precision source with 0.2 Ω resistance, feeding a Wheatstone bridge. After removing the strain gauge (initially 350 Ω), the open-circuit voltage measured across the gauge terminals is 0.48 V, and the resistance looking back into the circuit is 175 Ω. If the strain gauge is reconnected, what current flows through it?
(a) 0.91 mA
(b) 1.37 mA
(c) 2.74 mA
(d) 4.11 mA
Question 14
A power quality engineer is analyzing harmonic currents in a three-phase distribution system. For a single-phase equivalent circuit analysis, the system has two current sources in different branches: I₁ = 25 A at a node with 6 Ω parallel resistance, and I₂ = 18 A at another node with 9 Ω parallel resistance. These are connected through a 3 Ω series impedance to a common 18 Ω load. What is the Norton current for the equivalent circuit seen by the 18 Ω load?
(a) 28.3 A
(b) 32.7 A
(c) 37.4 A
(d) 43.0 A
Question 15
A manufacturing plant engineer is troubleshooting a DC motor control circuit. The circuit consists of a 440 V supply with 3 Ω line resistance, connected to a complex network of resistors: 12 Ω and 18 Ω in parallel, in series with 8 Ω, then connected to the motor armature of 22 Ω. Using Thevenin's theorem from the motor terminals, what is the Thevenin equivalent resistance?
(a) 13.2 Ω
(b) 15.6 Ω
(c) 18.2 Ω
(d) 20.8 Ω
Question 16
A research engineer is developing a biomedical sensor circuit. The circuit has three voltage sources forming a complex network: V₁ = 5 V with 1 kΩ resistance, V₂ = 3.3 V with 1.5 kΩ resistance, and V₃ = 2.5 V with 2 kΩ resistance, all connected at different nodes with a common 10 kΩ sensor load. Using superposition, what is the contribution of V₂ to the load voltage when V₁ and V₃ are replaced by their internal resistances?
(a) 1.42 V
(b) 1.89 V
(c) 2.24 V
(d) 2.67 V
Question 17
An aerospace engineer is analyzing a satellite power distribution system. The battery system provides 28 V with 0.15 Ω internal resistance to a payload. The payload can operate with variable resistance from 1 Ω to 10 Ω. At what load resistance will the efficiency of power transfer be exactly 90%?
(a) 1.35 Ω
(b) 2.25 Ω
(c) 3.00 Ω
(d) 4.50 Ω
Question 18
A grid integration engineer is analyzing the connection of a wind farm to the utility grid. The equivalent circuit has two voltage sources: Grid voltage = 13.8 kV with 0.5 Ω impedance, and Wind farm voltage = 13.5 kV with 0.8 Ω impedance. Both connect through a tie line to supply a 50 Ω load representing local industries. Using Norton's theorem, what is the Norton equivalent current for this combined system at the load terminals?
(a) 20.7 kA
(b) 24.2 kA
(c) 27.6 kA
(d) 30.4 kA
Question 19
A protection relay engineer is calculating fault currents for a substation. The system can be represented as a Thevenin equivalent with VTH = 69 kV and RTH = 2.5 Ω feeding a transformer with equivalent impedance of 7.5 Ω. During a fault, the transformer impedance drops to 1.5 Ω. What is the percentage increase in current through the transformer during the fault compared to normal operation?
(a) 150%
(b) 200%
(c) 300%
(d) 400%
Question 20
An electric vehicle charging station engineer is designing a fast-charging system. The charging station has a complex DC distribution network that can be simplified using Thevenin's theorem. The network consists of a 480 V source with 0.3 Ω resistance, connected through a 0.7 Ω cable to a junction. From the junction, two parallel paths exist: Path 1 has 4 Ω, and Path 2 has 2 Ω in series with the vehicle battery connection point. What is the maximum current available at the battery connection terminals under short-circuit conditions?
(a) 320 A
(b) 384 A
(c) 432 A
(d) 480 A
