Subelement A: — Topic :
Question 6A349
Element 6 (Radiotelegraph)What is the line current of a 7 HP motor operating on 120 V at full load, a power factor of 0.8, and 95%efficiency?
Explanation
To calculate the line current, we first need to determine the electrical input power consumed by the motor.
1. **Convert Horsepower (HP) to Mechanical Output Power (Watts):**
One horsepower is equivalent to 746 watts.
Output Power (Po) = 7 HP * 746 W/HP = 5222 W
2. **Calculate Electrical Input Power (Pin) using Efficiency:**
Efficiency (Eff) = Output Power / Input Power. So, Input Power (Pin) = Output Power / Efficiency.
Pin = 5222 W / 0.95 = 5496.84 W
3. **Calculate Line Current (I) using the AC Power Formula:**
For an AC circuit, the true power (Pin) is given by Pin = Voltage (V) * Current (I) * Power Factor (PF).
Rearranging to solve for current: I = Pin / (V * PF)
I = 5496.84 W / (120 V * 0.8)
I = 5496.84 W / 96 V
I = 57.25875 A
Rounding to one decimal place, the line current is approximately 57.2 A. This calculation demonstrates the fundamental relationship between mechanical power, electrical power, efficiency, voltage, current, and power factor, concepts crucial for understanding power requirements in amateur radio equipment and station design. Options A and C result from incorrect application of these formulas.