BEE DC and AC Circuit Analysis 3 — Questions and Answers
Question 1: What is the resonant frequency of a series RLC circuit with L = 10 mH and C = 10 μF?
- 503 Hz (Correct answer)
- 159 Hz
- 1000 Hz
- 250 Hz
Correct answer: 503 Hz
f₀ = 1/(2π√LC) = 1/(2π√(0.01 × 10⁻⁵)) ≈ 503 Hz.
Question 2: In a parallel RLC circuit, resonance occurs when the circuit exhibits:
- Maximum impedance and minimum current (Correct answer)
- Minimum impedance and maximum current
- Zero impedance and infinite current
- Equal voltage and current magnitudes
Correct answer: Maximum impedance and minimum current
At parallel resonance, the susceptances of L and C cancel, yielding maximum impedance and minimum line current drawn from the source.
Question 3: Applying the superposition theorem, what must be done with independent sources not under consideration?
- Voltage sources are short-circuited; current sources are open-circuited (Correct answer)
- Voltage sources are open-circuited; current sources are short-circuited
- Both are short-circuited
- Both are open-circuited
Correct answer: Voltage sources are short-circuited; current sources are open-circuited
Superposition requires deactivating all other independent sources: replace voltage sources with short circuits and current sources with open circuits.
Question 4: What is the reactance of a 100 μF capacitor at 60 Hz?
- 26.5 Ω (Correct answer)
- 37.7 Ω
- 53.1 Ω
- 10.6 Ω
Correct answer: 26.5 Ω
Xc = 1/(2πfC) = 1/(2π × 60 × 100×10⁻⁶) ≈ 26.5 Ω.
Question 5: In a DC circuit, if two resistors R1 = 4 Ω and R2 = 6 Ω are connected in parallel, what is the equivalent resistance?
- 2.4 Ω (Correct answer)
- 10 Ω
- 5 Ω
- 1.67 Ω
Correct answer: 2.4 Ω
Req = (R1 × R2)/(R1 + R2) = (4 × 6)/(4 + 6) = 24/10 = 2.4 Ω.
Question 6: What is reactive power measured in?
- VAR (volt-ampere reactive) (Correct answer)
- Watts
- VA (volt-ampere)
- Joules
Correct answer: VAR (volt-ampere reactive)
Reactive power, Q, is the power stored and released by reactive elements (inductors/capacitors) and is measured in volt-amperes reactive (VAR).
Question 7: In nodal analysis, what is chosen as the reference (datum) node?
- The node with the most connections (often ground) (Correct answer)
- The node with the highest voltage
- Any node with a voltage source attached
- The node connected to the load
Correct answer: The node with the most connections (often ground)
The reference node, typically ground (0 V), is usually chosen as the node with the most branch connections to simplify the system of equations.
BEE DC and AC Circuit Analysis 3
What is the resonant frequency of a series RLC circuit with L = 10 mH and C = 10 μF?