Problem 3.197

In a circuit shown in Fig. 3.54 resistances $R_{1}$ and $R_{2}$ are known, as well as emf's $\mathscr{E}_ {1}$ and $\mathscr{E}_{2} .$ The internal resistances of the sources are negligible. At what value of the resistance $R$ will the thermal power generated in it be the highest? What is it equal to?

\begin{array}{c} \text { 3.197. } R=R_{1} R_{2} /\left(R_{1}+R_{2}\right) \\ Q_{\max }=\left(\mathscr{E}_{1} R_{2}+\mathscr{E}_{2} R_{1}\right)^{2} / 4 R_{1} R_{2}\left(R_{1}+R_{2}\right) . \end{array}

Electric Current