Problem 3.184

Find a potential difference $\varphi_{A}-\varphi_{B}$ between the plates of a capacitor $C$ in the circuit shown in Fig. 3.47 if the sources have emf's $\mathscr{E}_ {1}=4.0 \mathrm{~V}$ and $\mathscr{E}_ {2}=1.0 \mathrm{~V}$ and the resistances are equal to $R_{1}=10 \Omega, R_{2}=20 \Omega,$ and $R_{3}=30$ \Omega. The internal resistances of the sources are negligible.