An ideal battery of electromotive force \(\mathcal{E}\) is connected in series at time \(t = 0\) with an ideal switch S, a resistor of resistance \(R\), and an inductor of inductance \(L\). At a specific time \(t_1\), the rate at which thermal energy is dissipated in the resistor equals the rate at which energy is being stored in the magnetic field of the inductor. What are the potential difference across the inductor \(V_L\) and the time \(t_1\) at which this equality occurs?