Three parallel branches are connected across two common junction nodes as shown in the diagram. Each branch contains an ideal battery in series with a resistor, and all three batteries have their positive terminals connected toward the upper node. The battery emfs are \(\mathcal{E}_1 = 16 \text{ V}\), \(\mathcal{E}_2 = 4.0 \text{ V}\), and \(\mathcal{E}_3 = 4.0 \text{ V}\), and the resistances are \(R_1 = 2.0 \text{ }\Omega\), \(R_2 = 3.0 \text{ }\Omega\), and \(R_3 = 6.0 \text{ }\Omega\). What is the net rate at which chemical energy is transformed into electrical energy within the entire system?