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°
We have that for the Question "For what absolute value of the phase angle does a source deliver 71 % of the maximum possible power to an RLC circuit"
It can be said that
Power delivered to RLC circuit is given by
[tex]P = \frac{V^2}{Z}cos\theta\\\\P = I^2Zcos\theta[/tex]
Therefore,
[tex]Z = \sqrt{R^2 + (X_L-X_C)^2}[/tex]
Power delivered is maximum, therefore,
[tex]P_{max} = cos\theta\\\\71\% = cos\theta\\\\cos\theta = 0.71\\\\\theta = cos^{-1}0.71\\\\\theta = 44.76^o\\\\approximately 45^o[/tex]
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