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Electric Capacitance, Energy of an Electric Field

Problem 3.117

A circuit has a section \(A B\) shown in Fig. \(3.21 .\) The emf of the source equals \(\mathscr{E}=10 \mathrm{~V},\) the capacitor capacitances are equal to \(C_{1}=1.0 \mu \mathrm{F}\) and \(C_{2}=2.0 \mu \mathrm{F},\) and the potential difference \(\varphi_{A}\) \(-\varphi_{B}=5.0 \mathrm{~V}\). Find the voltage across each capacitor.

Reveal Answer
 3.117. V1=q/C1=10 V,V2=q/C2=5 V, where q==(φA−φB+E)C1C2/(C1+C2)\begin{aligned} &\text { 3.117. } V_{1}=q / C_{1}=10 \quad \mathrm{~V}, \quad V_{2}=q / C_{2}=5 \quad \mathrm{~V}, \quad \text { where } q=\\ &=\left(\varphi_{A}-\varphi_{B}+\mathscr{E}\right) C_{1} C_{2} /\left(C_{1}+C_{2}\right) \end{aligned}
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