NCEES Electrical Circuits 3 — Questions and Answers
Question 1: Using the node voltage method, how many independent equations are needed for a circuit with 5 nodes (including the reference node)?
- 5
- 4 (Correct answer)
- 3
- 6
Correct answer: 4
The node voltage method requires (N − 1) equations for N nodes, so 5 nodes yield 4 independent node equations.
Question 2: A 120 V rms source delivers power to a load with impedance Z = 3 + j4 Ω. What is the real power consumed?
- 1440 W
- 2880 W
- 1728 W (Correct answer)
- 864 W
Correct answer: 1728 W
I_rms = 120/|Z| = 120/5 = 24 A; P = I²R = (24)²×3 = 576×3 = 1728 W.
Question 3: Which theorem states that maximum power is transferred to a load when the load impedance equals the complex conjugate of the source impedance?
- Superposition theorem
- Reciprocity theorem
- Maximum power transfer theorem (Correct answer)
- Compensation theorem
Correct answer: Maximum power transfer theorem
The Maximum Power Transfer Theorem states Z_L = Z_S* (complex conjugate) for maximum power delivery in AC circuits.
Question 4: The time constant of an RL circuit with R = 50 Ω and L = 0.25 H is:
- 12.5 s
- 200 s
- 0.005 s (Correct answer)
- 0.2 s
Correct answer: 0.005 s
Time constant τ = L/R = 0.25/50 = 0.005 s (5 ms).
Question 5: In a balanced three-phase Y-connected system, if the line voltage is 208 V rms, the phase voltage is approximately:
- 208 V
- 360 V
- 120 V (Correct answer)
- 416 V
Correct answer: 120 V
For a Y-connected system, V_phase = V_line/√3 = 208/1.732 ≈ 120 V rms.
Question 6: The mesh current method is most efficiently applied when:
- The circuit has many nodes but few loops (Correct answer)
- The circuit has many loops but few nodes
- The circuit contains only current sources
- The circuit is non-planar
Correct answer: The circuit has many nodes but few loops
Mesh analysis is preferred when the number of meshes (loops) is less than the number of nodes minus one, reducing the number of equations needed.
Question 7: What is the impedance of a 10 mH inductor at a frequency of 60 Hz?
- 0.6 Ω
- 3.77 Ω (Correct answer)
- 6.28 Ω
- 376.8 Ω
Correct answer: 3.77 Ω
X_L = 2πfL = 2π(60)(0.010) = 3.77 Ω; impedance Z = j3.77 Ω, with magnitude 3.77 Ω.
NCEES Electrical Circuits 3
Using the node voltage method, how many independent equations are needed for a circuit with 5 nodes (including the reference node)?