Final answer:
The impedance of an RLC series circuit with a 200 Ω resistor and a 25.0 mH inductor at 8000 Hz and a phase angle of 45.0° is 200 Ω.
Step-by-step explanation:
The impedance of an RLC series circuit can be calculated using the formula:
Z = sqrt(R^2 + (Xl - Xc)^2)
Where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance. In this case, the resistor has a value of 200 Ω and the inductor has an inductive reactance of ωL = 2πfL = 2π(8000 Hz)(25.0 mH) = 1.26 Ω. The phase angle of 45.0° indicates that the inductive and capacitive reactances are equal. Therefore, the capacitive reactance, Xc, can be calculated using:
Xc = Xl = 1.26 Ω
Substituting the values into the impedance formula:
Z = sqrt(200^2 + (1.26 - 1.26)^2) = 200 Ω
Therefore, the impedance of the RLC series circuit is 200 Ω.