91影视

$\begin{array}{r}{C}_1=8.4渭F\\ C_2=8.4渭F\\ C_3=4.2渭F\\ V_{ab}=36\mathrm{V}\end{array}$

The total charge flow through the system is given by

$Q_t=C_t{V}_{ab}$ (1)

The total capacitance is given by

$\frac{1}{C_t}=鈭�\frac{1}{C_i}=\frac{1}{8.4}+\frac{1}{8.4}+\frac{1}{4.2}=\frac{10}{21}=2.1渭F$

Substituting in (1) yields

$Q=36脳2.1脳{10}^{鈭�6}=75.6脳{10}^{鈭�6}\mathrm{C}$

$Q_3=75.6脳{10}^{鈭�6}\mathrm{C}$

The total charge stored in capacitors is given by

$U=\frac{1}{2}{C}_t{V}^2=0.5脳2.1脳{10}^{鈭�6}脳{36}^2=1.36脳{10}^{鈭�3}\mathrm{J}$

The charge in the system will be redistributed on each capacitor but the total charge is the same.

$Q_1+Q_2+Q_3=3脳75.6=226.8渭\mathrm{C}$

$V_1=V_2=V_3=\frac{Q_1}{C_1}=\frac{Q_2}{C_2}=\frac{Q_3}{C_3}$ (2)

Substituting in (1) yields

$\begin{array}{r}\frac{Q_1}{8.4}=\frac{Q_2}{8.4}=\frac{Q_3}{4.2}\\ Q_1=Q_2=2Q_3\end{array}$

And for $c_3$

$Q_3=Q_1/2=45.4渭C$

$V=\frac{Q_1}{C_1}=\frac{0.72脳{10}^{鈭�6}}{8.4脳{10}^{鈭�8}}=10.8\mathrm{V}$

The new energy stored in the system is given by

$U=\frac{1}{2}{C}_P{V}^2$ (4)

The capacitance is given by

$C_t=C_1+C_2+C_3=8.4+8.4+4.2=21.0渭F$

$U_P=0.5脳21脳{10}^{鈭�6}脳(10.8{)}^2=1.22脳{10}^{鈭�3}\mathrm{J}$