A circuit consists of an ideal battery of emf \(\mathcal{E}\), an open switch \(S\), an ideal inductor of inductance \(L\), and a resistor of resistance \(R\), all connected in series. At time \(t = 0\), switch \(S\) is closed. Consider the following four quantities:

• \(P_1\): The rate at which energy is delivered by the battery immediately after the switch is closed (\(t = 0^+\))
• \(P_2\): The rate at which energy is stored in the magnetic field of the inductor when the current is \(I = \dfrac{\mathcal{E}}{2R}\)
• \(P_3\): The rate at which energy is dissipated in the resistor when the current is \(I = \dfrac{\mathcal{E}}{2R}\)
• \(P_4\): The rate at which energy is delivered by the battery long after the switch is closed (\(t \to \infty\))

Which of the following correctly ranks these four power values?