309A Circuit Theory and Calculations 3 — Questions and Answers
Question 1: What is the inductive reactance of a 50 mH inductor at 60 Hz?
- 3.0 Ω
- 9.42 Ω
- 18.85 Ω (Correct answer)
- 188.5 Ω
Correct answer: 18.85 Ω
Inductive reactance XL = 2πfL = 2 × 3.14159 × 60 × 0.05 = 18.85 Ω. Reactance increases with both frequency and inductance.
Question 2: A 120 V circuit has a load that draws 10 A. What is the power dissipated if the power factor is 0.9?
- 900 W
- 1080 W (Correct answer)
- 1200 W
- 1333 W
Correct answer: 1080 W
Real power P = V × I × PF = 120 × 10 × 0.9 = 1080 W. The power factor accounts for the phase difference between voltage and current.
Question 3: In a wye-connected three-phase system, what is the relationship between line voltage and phase voltage?
- VL = VP
- VL = VP × √3 (Correct answer)
- VL = VP / √3
- VL = VP × 2
Correct answer: VL = VP × √3
In a wye (star) connection, the line voltage is √3 times the phase voltage: VL = √3 × VP. Line current equals phase current in a wye connection.
Question 4: What is the capacitive reactance of a 50 µF capacitor at 60 Hz?
- 18.85 Ω
- 26.53 Ω
- 53.05 Ω (Correct answer)
- 106.1 Ω
Correct answer: 53.05 Ω
Capacitive reactance XC = 1/(2πfC) = 1/(2 × 3.14159 × 60 × 0.00005) = 1/0.01885 = 53.05 Ω.
Question 5: A conductor has a resistance of 2 Ω at 20°C. If its temperature rises to 75°C and the temperature coefficient is 0.00393/°C, what is the new resistance?
- 2.22 Ω
- 2.43 Ω (Correct answer)
- 2.59 Ω
- 3.06 Ω
Correct answer: 2.43 Ω
R2 = R1 × [1 + α(T2 - T1)] = 2 × [1 + 0.00393(75 - 20)] = 2 × [1 + 0.216] = 2 × 1.216 = 2.43 Ω.
Question 6: What is the efficiency of a motor that outputs 7.5 HP while consuming 6500 W from the supply?
- 76.5%
- 82.1%
- 86.1% (Correct answer)
- 91.5%
Correct answer: 86.1%
First convert HP to watts: 7.5 × 746 = 5595 W. Efficiency = (Output/Input) × 100 = (5595/6500) × 100 = 86.1%.
309A Circuit Theory and Calculations 3
What is the inductive reactance of a 50 mH inductor at 60 Hz?