Final answer:
The inductance of the coil is approximately 0.278 H. The RMS voltage of the source should be approximately 265.2 V.
Step-by-step explanation:
Part A: To find the inductance of the coil, we can use the formula XL = 2πfL, where XL is the inductive reactance and f is the frequency. Given that the inductive reactance is 230 Ω and the frequency is 130 Hz, we can rearrange the formula to solve for L. Plugging in these values, we get:
230 Ω = 2π(130 Hz)L
L = 230 Ω / (2π(130 Hz)) ≈ 0.278 H
Therefore, the inductance of the coil is approximately 0.278 H.
Part B: To find the RMS voltage of the source, we can use the formula P = V(rms)^2 / R, where P is the average power, V(rms) is the RMS voltage, and R is the resistance. Given that the average power is 830 W and the resistance is 410 Ω, we can rearrange the formula to solve for V(rms). Plugging in these values, we get:
830 W = V(rms)^2 / 410 Ω
V(rms) = √(830 W * 410 Ω) ≈ 265.2 V
Therefore, the RMS voltage of the source should be approximately 265.2 V.