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 \(C\).