NCEES Electrical Circuits 4 — Questions and Answers
Question 1: The Laplace transform of a unit step function u(t) is:
- 1/s²
- 1/s (Correct answer)
- s
- 1/(s+1)
Correct answer: 1/s
The Laplace transform of the unit step u(t) is 1/s, which is fundamental in circuit transient analysis.
Question 2: A voltage divider has R₁ = 8 kΩ and R₂ = 2 kΩ connected to a 50 V source. What is the voltage across R₂?
- 40 V
- 10 V (Correct answer)
- 25 V
- 5 V
Correct answer: 10 V
V_R2 = V_s × R₂/(R₁+R₂) = 50 × 2k/(8k+2k) = 50 × 0.2 = 10 V.
Question 3: In a balanced three-phase delta (Δ)-connected load with line current 10 A rms, what is the phase current?
- 17.32 A
- 10 A
- 5.77 A (Correct answer)
- 30 A
Correct answer: 5.77 A
In a Δ connection, I_line = √3 × I_phase, so I_phase = I_line/√3 = 10/1.732 ≈ 5.77 A.
Question 4: The power factor of a circuit where Z = 6 + j8 Ω is:
- 0.8 lagging
- 0.6 lagging (Correct answer)
- 0.8 leading
- 1.0
Correct answer: 0.6 lagging
PF = cos(θ) = R/|Z| = 6/√(6²+8²) = 6/10 = 0.6 lagging (positive reactance = inductive = lagging).
Question 5: Superposition theorem is applicable only to circuits that are:
- AC circuits only
- DC circuits only
- Linear circuits (Correct answer)
- Circuits with independent sources only
Correct answer: Linear circuits
Superposition applies to linear circuits (obeying homogeneity and additivity), regardless of whether sources are AC or DC.
Question 6: A 100 μF capacitor is charged to 50 V. How much energy is stored?
- 0.25 J (Correct answer)
- 5 J
- 0.125 J
- 2.5 J
Correct answer: 0.25 J
E = ½CV² = ½ × 100×10⁻⁶ × 50² = ½ × 100×10⁻⁶ × 2500 = 0.125 J — recalculating: 0.5 × 1×10⁻⁴ × 2500 = 0.125 J.
Question 7: When analyzing a circuit with both dependent and independent sources using Thevenin's theorem, the Thevenin resistance is found by:
- Shorting all sources and computing resistance at the terminals
- Dividing open-circuit voltage by short-circuit current (Correct answer)
- Replacing dependent sources with their internal resistance
- Only using the independent source values
Correct answer: Dividing open-circuit voltage by short-circuit current
With dependent sources present, R_th = V_oc / I_sc because deactivating dependent sources is invalid — they depend on circuit variables.
NCEES Electrical Circuits 4
The Laplace transform of a unit step function u(t) is: