Answer: the absolute value of the phase angle is 28°
Explanation:
taking a look at expression for the instantaneous electric power in an AC circuit;
P = VI -------let this be equation 1
p is power, v is voltage and I is current;
for maximum power
P_max = V_rms × I_rms --------let this be equ 2
where P_max is the maximum power, V_rms is the rms value of voltage and I_rms is the rms value of current.
Also for average electric power in an AC circuit
P_avg = V_rms × I_rms × cos²∅ -------let this be equ 3
where P_avg is the average power and cos∅ is the power factor
now from equation 2; P_max = V_rms × I_rms
so p_max replaces V_rms × I_rms in equation 3
we now have
P_avg = P_max × cos²∅
so we substitute
expression for the given value of the average power is
P_avg = P_max × 75%
p_avg = P_max.78/100
for the expression of the average electricity in an AC circuit
P_max.78/100 = P_max × cos²∅
78/100 = cos²∅
to get the absolute value of phase angle
∅ = cos⁻¹ ( √(78/100))
∅ = cos⁻¹ ( 0.8832)
∅ = 27.969 ≈ 28°
Therefore the absolute value of the phase angle is 28°
