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Electric Current

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.

Reveal Answer
3.184.φA−φB=[E2R3(R1+R2)−E1R1(R2+R3)]/(R1R2++R2R3+R3R1=−1.0 V\begin{array}{l} 3.184 . \varphi_{A}-\varphi_{B}=\left[\mathscr{E}_{2} R_{3}\left(R_{1}+R_{2}\right)-\mathscr{E}_{1} R_{1}\left(R_{2}+R_{3}\right)\right] /\left(R_{1} R_{2}+\right. \\ +R_{2} R_{3}+R_{3} R_{1}=-1.0 \mathrm{~V} \end{array}
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