Four capacitors are connected as given in figure, find $V_a-V_b.$

The equivalent capacitance between points $A$ and $B$ is

Initial charges on both the capacitors are $CV.$ Find change in potential energy of both if a battery is connected as shown. Also find the work done by battery.

A thin metallic strip is introduced between the plates of a parallel plate capacitor, touching the plates. How will capacitance change?

A thin metallic sheet is introduced as shown in figure. The sheet is moved perpendicularly to the plates $X$ & $Y$ of the capacitor. The capacitance of capacitor

Consider two capacitors: $C_1=10\mu \mathrm{F}$ and $C_2=40\mu \mathrm{F}.$ What is the equivalent capacitance if the two are connected

(a) In parallel?
(b) In series?
(c) If the two are connected in series to a $9.0$ volt battery what are the charges $Q_1$ and $Q_2$ stored on the two capacitors?

A parallel plate air capacitor has capacitance $C.$ Half of space between the plates is filled with di-electric of di-electric constant $K$ as shown in figure. The new capacitance is $C\text{'}.$ Then