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

\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}

Electric Capacitance, Energy of an Electric Field