A tuning circuit in a radio receiver uses a coil of inductance 0.25 H in series with a variable capacitor and a fixed resistor of 15 Ω. The capacitance can be varied from 50 pF to 450 pF.
a. (i) For a general capacitance C, write an expression for the magnitude of the impedance Z of the circuit when it is driven at angular frequency ω.
b. (ii) The set is tuned to a station broadcasting at 1 MHz with the capacitor adjusted to C=100pF. Calculate the impedance at this setting.
c. (iii) While the station frequency remains at 1 MHz, the listener changes the capacitor to C=300pF. Determine the new value of the impedance.
d. (iv) Which capacitor setting, 100 pF or 300 pF, results in a larger current through the circuit? Give a brief reason based on your calculations.