A real battery with unknown electromotive force \(\mathcal{E}\) and unknown internal resistance \(r\) is connected in a circuit with resistor \(R_1 = 6.0\text{ }\Omega\), resistor \(R_2 = 12\text{ }\Omega\), and switch \(S\). An ideal voltmeter connected directly across the battery terminals reads \(9.0\text{ V}\) when switch \(S\) is open. When switch \(S\) is closed, the voltmeter reading drops to \(8.0\text{ V}\). What is the internal resistance \(r\) of the battery?