309A Circuit Theory and Calculations 2 — Questions and Answers
Question 1: What is the resonant frequency of a series RLC circuit with L = 10 mH and C = 100 µF?
- 79.6 Hz
- 159.2 Hz (Correct answer)
- 318.3 Hz
- 500 Hz
Correct answer: 159.2 Hz
Resonant frequency f = 1/(2π√(LC)) = 1/(2π√(0.01 × 0.0001)) = 1/(2π × 0.001) = 159.2 Hz. At resonance, XL = XC.
Question 2: A three-phase balanced load draws 30 A per phase at 600 V line-to-line. What is the total apparent power?
- 18 kVA
- 31.18 kVA (Correct answer)
- 36 kVA
- 54 kVA
Correct answer: 31.18 kVA
For a three-phase system: S = √3 × VL × IL = 1.732 × 600 × 30 = 31,176 VA ≈ 31.18 kVA.
Question 3: What happens to the total capacitance when capacitors are connected in parallel?
- It decreases
- It stays the same
- It increases (values add) (Correct answer)
- It becomes the reciprocal sum
Correct answer: It increases (values add)
When capacitors are connected in parallel, the total capacitance is the sum of individual capacitances: Ct = C1 + C2 + C3. This is opposite to how resistors behave.
Question 4: A motor draws 25 A at 480 V three-phase with a power factor of 0.85. What is the real power consumed?
- 10.2 kW
- 17.66 kW (Correct answer)
- 20.78 kW
- 24.48 kW
Correct answer: 17.66 kW
Real power P = √3 × V × I × PF = 1.732 × 480 × 25 × 0.85 = 17,658 W ≈ 17.66 kW.
Question 5: What is the time constant of a circuit with a 500 µF capacitor and a 2 kΩ resistor?
- 0.1 s
- 0.5 s
- 1.0 s (Correct answer)
- 2.5 s
Correct answer: 1.0 s
The time constant τ = R × C = 2000 Ω × 0.0005 F = 1.0 second. After one time constant, a capacitor charges to approximately 63.2% of the supply voltage.
Question 6: In a delta-connected three-phase system, what is the relationship between line current and phase current?
- IL = IP
- IL = IP × √3 (Correct answer)
- IL = IP / √3
- IL = IP × 3
Correct answer: IL = IP × √3
In a delta connection, the line current is √3 (1.732) times the phase current: IL = √3 × IP. Line voltage equals phase voltage in a delta connection.
309A Circuit Theory and Calculations 2
What is the resonant frequency of a series RLC circuit with L = 10 mH and C = 100 µF?