A real battery with an electromotive force (emf) of \(\varepsilon = 6.0\text{ V}\) and an unknown internal resistance \(r\) is connected in a single closed loop to an external resistor of resistance \(R = 4.0\text{ }\Omega\). During circuit operation, a net charge of \(180\text{ C}\) passes through the resistor in a time interval of \(3.0\text{ min}\). What is the internal resistance \(r\) of the battery?