In a laboratory experiment on a series LCR circuit, the current amplitude reaches a maximum value of 0.50 A when the applied source has angular frequency 2000 rad s⁻¹. It is observed that the current falls to 0.353 A at 1800 rad s⁻¹ and again at 2200 rad s⁻¹.
a. (i) Identify the half-power (−3 dB) angular frequencies and write the numerical bandwidth Δω.
b. (ii) Determine the quality factor Q of the circuit.
c. (iii) If the inductance of the coil is 50 mH, calculate the resistance R of the circuit.
d. (iv) Convert the bandwidth obtained in part (i) to ordinary frequency Δf (in Hz).