BEE DC and AC Circuit Analysis 5 — Questions and Answers
Question 1: What is the bandwidth of a series RLC resonant circuit with f₀ = 1000 Hz and Q = 50?
- 20 Hz (Correct answer)
- 50 Hz
- 500 Hz
- 100 Hz
Correct answer: 20 Hz
Bandwidth BW = f₀/Q = 1000/50 = 20 Hz, representing the range of frequencies within 3 dB of the resonant peak.
Question 2: In an AC circuit, the complex power S is defined as:
- S = V × I* (voltage times conjugate of current) (Correct answer)
- S = V × I (voltage times current)
- S = |V|² / Z
- S = I² × Z*
Correct answer: S = V × I* (voltage times conjugate of current)
Complex power S = V_rms × I*_rms gives the full power triangle: S = P + jQ, where P is real power and Q is reactive power.
Question 3: When analyzing a circuit using Norton's theorem, what is the Norton current (IN)?
- The short-circuit current at the output terminals (Correct answer)
- The open-circuit voltage divided by the load resistance
- The Thevenin voltage divided by Thevenin resistance
- The current through the internal resistance
Correct answer: The short-circuit current at the output terminals
Norton current IN is found by short-circuiting the output terminals and calculating the resulting current through that short.
Question 4: In phasor notation, multiplying a phasor by j (the imaginary unit) results in:
- A 90° phase lead (Correct answer)
- A 90° phase lag
- Doubling the magnitude
- Halving the magnitude
Correct answer: A 90° phase lead
Multiplying by j = 1∠90° rotates a phasor counterclockwise by 90°, corresponding to a 90° phase advance (lead).
Question 5: The impedance of a series circuit with R = 3 Ω, XL = 6 Ω, and XC = 2 Ω is:
- 5 Ω at 53.13° (Correct answer)
- 7 Ω at 90°
- 3 Ω at 0°
- 11 Ω at 45°
Correct answer: 5 Ω at 53.13°
Z = R + j(XL - XC) = 3 + j4, so |Z| = √(9+16) = 5 Ω and θ = arctan(4/3) ≈ 53.13°.
Question 6: What does Millman's theorem allow engineers to calculate directly?
- The common voltage across parallel branches with different sources (Correct answer)
- The equivalent resistance of a ladder network
- The resonant frequency of a multi-loop circuit
- The Thevenin resistance of a bridge circuit
Correct answer: The common voltage across parallel branches with different sources
Millman's theorem provides a direct formula for the voltage at a node where multiple branches (each with a source and impedance) connect in parallel.
Question 7: In a purely capacitive AC circuit, which statement correctly describes current and voltage?
- Current leads voltage by 90° (Correct answer)
- Voltage leads current by 90°
- Current and voltage are in phase
- Current lags voltage by 45°
Correct answer: Current leads voltage by 90°
In a pure capacitor, the current leads the voltage by 90° because current flows as the capacitor charges before the voltage across it fully develops.
BEE DC and AC Circuit Analysis 5
What is the bandwidth of a series RLC resonant circuit with f₀ = 1000 Hz and Q = 50?