Walker, Halliday & Resnick — Electromagnetic Oscillations and Alternating Current: Problem 20

20 An ac generator with emf amplitude \(\mathcal{E}_m = 180 \text{ V}\) and operating at frequency \(400 \text{ Hz}\) causes oscillations in a series \(RLC\) circuit having \(R = 220 \ \Omega\), \(L = 150 \text{ mH}\), and \(C = 24.0 \ \mu\text{F}\). Find (a) the capacitive reactance \(X_C\), (b) the impedance \(Z\), and (c) the current amplitude \(I\). A second capacitor of the same capacitance is then connected in series with the other components. Determine whether the values of (d) \(X_C\), (e) \(Z\), and (f) \(I\) increase, decrease, or remain the same.