# Step-by-Step Solution ## Given Data - Resistance, \( R = 20\,\Omega \) - Inductance, \( L = 0.1\,\text{H} \) - Frequency, \( f = 50\,\text{Hz} \) - Supply Voltage, \( V = 200\,\text{V} \) (not needed for impedance calculation) ## Step 1: Calculate Inductive Reactance (\( X_L \)) Inductive reactance is given by: \[ X_L = 2\pi f L \] Substitute the values: \[ X_L = 2 \times \pi \times 50 \times 0.1 \] \[ X_L = 2 \times 3.1416 \times 50 \times 0.1 \] \[ X_L = 6.2832 \times 5 \] \[ X_L = 31.416\,\Omega \] ## Step 2: Calculate Total Impedance (\( Z \)) The impedance of a coil (series combination of \( R \) and \( L \)) is: \[ Z = \sqrt{R^2 + X_L^2} \] Substitute the values: \[ Z = \sqrt{(20)^2 + (31.416)^2} \] \[ Z = \sqrt{400 + 987.77} \] \[ Z = \sqrt{1387.77} \] \[ Z \approx 37.28\,\Omega \] ## Final Answer **The impedance of the coil is \( \boxed{37.3\,\Omega} \) (rounded to one decimal place).**