Question

What are the charge on and the potential difference across each capacitor in FIGURE $P26.56$?

Short answer

The charge on each capacitor is $60\mu C$, and the potential difference is respectively$V_1=5V,V_2=15V,V_3=10V$.

Step-by-step solution

Given information

We have given that the FIGURE $P26.56$.

We need to find the charge on and the potential difference across each capacitor in FIGURE $P26.56$.

Simplify 

If the capacitors are connected in series the charge on every capacitor is the same, and it is equal to the charge of a single equivalent capacitor. The expression for the equivalent capacitance $C$of this series is given by

$\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$.

This yields

$\frac{1}{C}=\frac{C_2{C}_3}{C_1{C}_2{C}_3}+\frac{C_1{C}_3}{C_1{C}_2{C}_3}+\frac{C_1{C}_2}{C_1{C}_2{C}_3}$,

or

$C=\frac{C_1{C}_2{C}_3}{C_1{C}_2+C_2{C}_3+C_1{C}_3}=2\mu F$.

Therefore the charge on each capacitor is

$q=CV=60\mu C$.

Then the potential difference on each capacitor is given as

$$\begin{gathered} V_1=\frac{q}{C_1}=5V, \\ {V}_2=\frac{q}{C_2}=15V, \\ {V}_3=\frac{q}{C_3}=10V. \end{gathered}$$