Halliday, Resnick & Walker — Electromagnetic Oscillations and Alternating Current: Problem 30

30 An alternating emf source with a variable frequency \( f_d \) is connected in series with a \( 50.0\text{ }\Omega \) resistor and a \( 28.0\text{ }\mu\text{F} \) capacitor. The emf amplitude is \( 12.0\text{ V} \). (a) Draw a phasor diagram for phasor \( V_R \) (the potential across the resistor) and phasor \( V_C \) (the potential across the capacitor). (b) At what driving frequency \( f_d \) do the two phasors have the same length? At that driving frequency, what are (c) the phase angle in degrees, (d) the angular speed at which the phasors rotate, and (e) the current amplitude?