EETC Circuit Theory 5 — Questions and Answers
Question 1: In a delta-connected three-phase load, the relationship between line current and phase current is:
- IL = IP
- IL = √3 × IP (Correct answer)
- IL = IP / √3
- IL = 3 × IP
Correct answer: IL = √3 × IP
In a delta connection, IL = √3 × IP because each line carries the phasor sum of two phase currents displaced by 60°.
Question 2: The bandwidth (BW) of a series resonant circuit is related to its Q-factor and resonant frequency (f₀) by:
- BW = Q × f₀
- BW = f₀ / Q (Correct answer)
- BW = f₀ × Q²
- BW = Q / f₀
Correct answer: BW = f₀ / Q
Bandwidth BW = f₀/Q; a higher Q-factor produces a narrower bandwidth and sharper selectivity.
Question 3: When two inductors are magnetically coupled with a mutual inductance M, the total inductance when connected series-aiding is:
- L1 + L2 - M
- L1 + L2 - 2M
- L1 + L2 + 2M (Correct answer)
- L1 × L2 / M
Correct answer: L1 + L2 + 2M
For series-aiding coupled inductors, LT = L1 + L2 + 2M, because the mutual inductance adds to both coils.
Question 4: A wattmeter in an AC circuit measures:
- Apparent power (VA)
- Reactive power (VAR)
- True (real) power (W) (Correct answer)
- Peak power
Correct answer: True (real) power (W)
A wattmeter measures true (real) power in watts, which accounts for the phase angle between voltage and current.
Question 5: Applying mesh analysis, a mesh current is assumed to flow:
- Through only resistors in the circuit
- Around a closed loop (mesh) in one direction (Correct answer)
- Into each node of the circuit
- Through the voltage source only
Correct answer: Around a closed loop (mesh) in one direction
In mesh analysis, a mesh current is assigned to each independent closed loop (mesh) and is assumed to circulate around that loop.
Question 6: A capacitor fully charged to 100V is discharged through a 1 MΩ resistor. The RC time constant is 2 seconds. After one time constant, the voltage is approximately:
- 100V
- 63.2V
- 36.8V (Correct answer)
- 50V
Correct answer: 36.8V
After one time constant, the voltage decays to V₀ × e⁻¹ ≈ 100 × 0.368 = 36.8V.
Question 7: Apparent power (S) in an AC circuit is the vector sum of real power (P) and reactive power (Q). The correct relationship is:
- S = P + Q
- S = P - Q
- S = √(P² + Q²) (Correct answer)
- S = P × Q
Correct answer: S = √(P² + Q²)
Apparent power S = √(P² + Q²), forming the hypotenuse of the power triangle with real and reactive power as legs.
EETC Circuit Theory 5
In a delta-connected three-phase load, the relationship between line current and phase current is: