Question

False steps will be reported. Thorough explanation and no sloppy writing, as I need to understand the problem. Please, no sloppy writing

2. A coil that has a resistance of 80 Ω has an impedance of 200 Ω when the driven at a frequency of 1 kHz. What is the inductance of the coil?

Answer 1

R = 80 ohm, Z = 200 ohm r = 1 K Hz inductance = L = ? As coil has resistance and inductance, it can be shown as we know that impedance of R - L circuit is Z = squareroot R^2 + X_c^2 Where X_c rightarrow inductive reactance and X_L = wL = 2 pi rL Z = squareroot R^2 + (2 pi r L)^2 Z^2 = R^2 + 4 pi^2 r^2 L^2 (200)^2 = (80)^2 + 4 pi^2 times (1000)^2 L^2 40000 - 6400 = 4 pi^2 times 10^6 L^2 33600/4 pi^2 times 10^6 = L^2 851.098 times 10^-6 = L^2 L = 29.2 times 10^-3 H implies L = 29.2 mH