Answer: cosθ = 0.7531
Explanation: the phase angle cosθ is given as
cosθ = R/Z
Where R = resistive reactance = 14.5 ohms
Z = impeadance = √R^2 +(Xl - Xc)^2
Where Xl = inductive reactance = 16.5 ohms and Xc= capacitive reactance = 9.41 ohms
By substituting the parameters, we have that
Z = √14.5^2 + (16.5^2 - 9.41^2)
Z = √210.25 + (272.25 - 88.5481)
Z = √210.25 + 183.7019
Z = √393.9519
Z = 19.85 ohms
Z = 19.85 ohms, R = 14.5 ohms
cosθ = R/Z = 14.5/19.85
cosθ = 0.7531
26.06°
Given an RLC circuit [a circuit containing a capacitor, inductor and resistor], the phase angle (Φ), which is the difference in phase between the voltage and the current in the circuit, is given by;
Φ = tan⁻¹ [ [tex]\frac{X_{L} - X_{C}}{R}[/tex]] --------------------------(i)
Where;
[tex]X_{L}[/tex] = inductive reactance of the circuit
[tex]X_{C}[/tex] = capacitive reactance of the circuit
R = resistance of the circuit
From the question;
[tex]X_{L}[/tex] = 16.5 Ω
[tex]X_{C}[/tex] = 9.41 Ω
R = 14.5 Ω
Substitute these values into equation (i) as follows;
Φ = tan⁻¹ [ [tex]\frac{16.5 - 9.41}{14.5}[/tex]]
Φ = tan⁻¹ [ [tex]\frac{7.09}{14.5}[/tex]]
Φ = tan⁻¹ [ 0.4890]
Φ = 26.06°
Therefore the phase angle of the AC series circuit is 26.06°
