NCEES Electrical Circuits 5 — Questions and Answers
Question 1: The transfer function H(s) = V_out(s)/V_in(s) of a simple RC low-pass filter (R in series, C to ground) is:
- sRC/(1+sRC)
- 1/(1+sRC) (Correct answer)
- sRC
- R/(R+1/sC)
Correct answer: 1/(1+sRC)
V_out = V_in × (1/sC)/(R + 1/sC) = V_in/(1 + sRC), giving H(s) = 1/(1+sRC).
Question 2: The bandwidth of a series RLC circuit with resonant frequency ω₀ = 5000 rad/s and Q = 25 is:
- 125 rad/s
- 200 rad/s (Correct answer)
- 250 rad/s
- 5000 rad/s
Correct answer: 200 rad/s
Bandwidth BW = ω₀/Q = 5000/25 = 200 rad/s.
Question 3: In AC circuit analysis, the apparent power S is related to real power P and reactive power Q by:
- S = P + Q
- S = P − Q
- |S|² = P² + Q² (Correct answer)
- S = P/Q
Correct answer: |S|² = P² + Q²
The power triangle gives |S|² = P² + Q², where S is in VA, P in W, and Q in VAR.
Question 4: A 10 Ω resistor and a 10 Ω inductive reactance are connected in parallel. What is the magnitude of the equivalent impedance?
- 20 Ω
- 5 Ω
- 7.07 Ω (Correct answer)
- 14.14 Ω
Correct answer: 7.07 Ω
Z_eq = (10 × j10)/(10 + j10) = j100/(10+j10); |Z_eq| = 100/|10+j10| = 100/(10√2) = 10/√2 ≈ 7.07 Ω.
Question 5: Kirchhoff's Voltage Law (KVL) is a consequence of:
- Conservation of charge
- Conservation of energy (Correct answer)
- Faraday's law of induction
- Ampere's circuital law
Correct answer: Conservation of energy
KVL states that the algebraic sum of voltages around any closed loop is zero, which follows from conservation of energy (work done around a closed path is zero).
Question 6: For an ideal transformer with turns ratio n = N₁/N₂ = 4, if the secondary voltage is 30 V, the primary voltage is:
- 7.5 V
- 120 V (Correct answer)
- 30 V
- 480 V
Correct answer: 120 V
V₁/V₂ = N₁/N₂ = n, so V₁ = n × V₂ = 4 × 30 = 120 V.
Question 7: The Fourier series of a periodic waveform represents it as a sum of:
- Exponentially decaying sinusoids
- Sinusoids at the fundamental frequency and its harmonics (Correct answer)
- Step functions
- Impulse functions at each period
Correct answer: Sinusoids at the fundamental frequency and its harmonics
The Fourier series decomposes a periodic signal into DC plus sinusoidal components at the fundamental frequency and integer multiples (harmonics).
NCEES Electrical Circuits 5
The transfer function H(s) = V_out(s)/V_in(s) of a simple RC low-pass filter (R in series, C to ground) is: