Find the potential difference \(v_{X}(t)\), its amplitude \(V_{X}\), and current \(i_{X}(t)\), its amplitude \(I_{X}(X=R, C, L)\), if you are given a

(a) purely resistive load with resistance \(R=100 \Omega\),

(b) purely capacitive load with \(C=20 \mu \mathrm{F}\), and

(c) purely inductive load with inductor \(L=300 \mathrm{mH}\). In all cases, the sinusoidal alternating emf device operates at amplitude \(\mathscr{E}_{\text {max }}=40.0 \mathrm{~V}\) and frequency \(f_{d}=50.0 \mathrm{~Hz}\).