Problem 3.177

In the circuit shown in Fig. 3.41 the sources have emf's $\mathscr{E}_ {1}=1.0 \mathrm{~V}$ and $\mathscr{C}_ {2}=2.5 \mathrm{~V}$ and the resistances have the values $R_{1}=10 \Omega$ and $R_{2}=20 \Omega .$ The internal resistances of the sources are negligible. Find a potential difference $\varphi_{A}-\varphi_{B}$ between the plates $A$ and $B$ of the capacitor $C$.