Question

A capacitor and resistor are in parallel. When operated at 105 V, they consume 7.4 A of current at a power factor of 0.74 leading. (Assume the system is operated at 60 Hz.)

(a) Determine the apparent power (in VA), real power (in W), and reactive power (in VAR) consumed by the combination.

Answer 1

The apparent power consumed by the parallel combination is 777 VA, the real power is 575.18 W, and the reactive power is 522.27 VAR.

Step-by-step explanation:

To determine the apparent power, real power, and reactive power consumed by a capacitor and resistor in parallel at 105 V with 7.4 A of current and a power factor of 0.74 leading, we can use the following formulas:

• 
  
• Apparent Power (S) = Voltage (V) × Current (I)
• 
  
• Real Power (P) = Apparent Power (S) × Power Factor (pf)
• 
  
• Reactive Power (Q) = √(S² - P²)

(a) The apparent power is calculated as S = 105 V × 7.4 A = 777 VA.

(b) The real power is calculated as P = 777 VA × 0.74 = 575.18 W.

(c) The reactive power is calculated using the Pythagorean theorem for the power triangle, which results in Q = √(777² - 575.18²) = √(603729 - 330957.47) = √(272771.53) = 522.27 VAR.