Two capacitors of capacitances $1 \mathrm{\mu F}$ and $2 \mathrm{\mu F}$ are charged to potential differences $20 \mathrm{V}$ and $15 \mathrm{V}$ as shown in the figure. If terminals $\mathrm{B}$ and $\mathrm{C}$ are connected together and terminals $\mathrm{A}$ and $\mathrm{D}$ are connected with the positive and negative ends of the battery with emf $E=30 \mathrm{V}$, respectively, then find the final charges on both the capacitors.

Two capacitors $C_1$, and $C_2$ are connected with two batteries of emf ${\epsilon }_1$and ${\epsilon }_2$. The circuit components are connected with a switch $S$ as shown in figure. Initially the switch is open and the capacitors are charged. Find the heat produced when switch $S$ is closed.

The figure shows a capacitive circuit with a switch $S_{\mathrm{W}}$.

(a) What is the potential difference between $a$ and $b$ when the switch is open?

(b) What charge flows through the switch when it is closed?

In figure, plate $A$ has $100 \mu \mathrm{C}$ charge, while plate $B$ has $60 \mu \mathrm{C}$ charge.

When both switches are open, then

$q_1=$______

$q_2=$______

$q_3=$ ______

$q_4=$______

In the arrangement shown in the figure, plate $B$ is given a charge equal to $60 \mu \mathrm{C}.$ The ratio $\frac{d_1}{d_2}$ is $2$. Then

$q_1=$_______

$q_2=$_______

$q_3=$_______

$q_4=$_______

$q_5=$_______

$q_6=$_______

Two large parallel metal plates, each having area $A$, are oriented horizontally and separated by a distance $3d$. A grounded conducting wire joins them, and initially each plate carries no charge. Now a third identical plate carrying charge $Q$ is inserted between the two plates, parallel to them and located a distance $d$ from the upper plate, as shown in the figure. What induced charge appears on each of the two original plates?

Four parallel large plates separated by equal distance $d$ are arranged as shown in the figure. The area of the plates is $S$. Find the potential difference between plates $B$ and $C$, if plate $B$ is given a charge $Q$.