First need find the impedance the circuit impedance the circuit given the sum the resistive

Solved Step by Step With Explanation- Power Analysis: Values and PF

Questions

The impedance of the circuit is given by the sum of the resistive (R), inductive (XL), and capacitive (XC) impedances:

Z = R + XL + XC

where Vrms is the RMS voltage, I is the current, and θ is the phase angle between the voltage and current.

Apparent Power (S):

Q = Vrms * I * sin(θ)

Power Factor (PF):

Z = R + XL + XC

Z = 6 + j7 - j15

I = Vrms / Z

I = 100 / (6 + j22)

P ≈ 100 * 4.347 * cos(θ) [Neglecting the imaginary component for real power]

P ≈ 434.7 * cos(θ)

Step 5: Calculate the reactive power (Q):

Q = Vrms * I * sin(θ)

PF = P / S

PF ≈ (434.7 * cos(θ)) / (434.7 - j1565.2)

θ ≈ arccos(114.304 / 0.263) [In radians]

Power (P) is approximately 434.7 * cos(θ) W