Question

What are the charge on and the potential difference across each capacitor in FIGURE $P26.58$?

Short answer

The charge on each capacitor is$q_1=45\mu C,q_2=q_3=21.6\mu C$respectively, and the potential difference across each capacitor is$U_1=9v,U_2=5.4v,U_3=3.6v$respectively.

Step-by-step solution

Given information

We need to find the charge on and the potential difference across each capacitor.

Simplify

The potential difference on the first capacitor is $∆V_1=9V$. And the charge will be

$q_1=C_1∆V=5·{10}^{-6}·9=45\mu C$

As for the two other capacitors, their common capacitance will be

$C_{23}=\frac{C_2{C}_3}{C_2+C_3}=\frac{24·{10}^{-12}}{10·{10}^{-6}}=2.4\mu C$

From that, the charge on both capacitors will be

$q_2=q_3=C_{23}∆V_3\Rightarrow ∆V_3=\frac{C_2}{C_3}∆V_3$

So, now

$U_3=\frac{2}{3}{U}_2$

and

$U_2+U_3=9$

Therefore, the solution will be

$$\begin{gathered} U_2=5.4V \\ {U}_3=3.6V \end{gathered}$$