A battery with electromotive force \(\mathcal{\varepsilon}\) and internal resistance \(r\) is connected in a closed circuit to an external resistor of resistance \(R\). A voltmeter connected across the terminals of the battery measures a terminal voltage of \(V_T = \dfrac{3}{4}\mathcal{\varepsilon}\). Which of the following correctly indicates the external resistance \(R\) in terms of \(r\), and the ratio of the power \(P_R\) dissipated by the external resistor to the total power \(P_{\text{total}}\) supplied by the electromotive force?