Embibe Experts Solutions for Chapter: Capacitance, Exercise 2: Exercise-2

A parallel plate capacitor of plate area $A$ and plate separation $d$ is charged to potential difference $V$ and then the battery is disconnected. A slab of dielectric constant $K$ is then inserted between the plates of the capacitor so as to fill the space between the plates. If $Q,E$ and $W$ denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted) and the work done on the system, in question, in the process of inserting the slab, then

Two capacitors of equal capacitance $\left(C_1=C_2\right)$ are shown in the figure. Initially, while the switch $S$ is open, one of the capacitors is uncharged and the other carries charge $Q_0$. The energy stored in the charged capacitor is $U_0$. Sometimes after the switch is closed, the capacitors $C_1$ and $C_2$ carry charges $Q_1$ and $Q_2$, respectively; the voltage across the capacitors are $V_1$ and $V_2$; and the energies stored in the capacitors are $U_1$ and $U_2$. Which of the following statements is incorrect ?

Two thin conducting shells of radii $R$ and $3R$ are shown in the figure. The outer shell carries a charge $+Q$ and the inner shell is neutral. The inner shell is earthed with the help of a switch $S$.

In the figure a capacitor of capacitance $2\mathrm{\mu F}$ is connected to a cell of emf $20$ volt. The plates of the capacitor are drawn apart slowly to double the distance between them, The work done by the external agent on the plates is :

Two insulating plates are both uniformly charged in such a way that the potential difference between them is ${\mathrm{V}}_2-{\mathrm{V}}_1=20 \mathrm{V}$. (i.e., plate $2$ is at a higher potential). The plates are separated by $d=0.1 \mathrm{m}$, and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $1$. What is its speed when it hits plate $2$? $\left(e=1.6\times {10}^{-19}\mathrm{C}, m_e=9.11\times {10}^{-31} \mathrm{kg}\right)$

The distance between plates of a parallel plate capacitor is $5d$. The positively charged plate is at $x=0$ and negatively charged plates is at $x=5d$. Two slabs one of conductor and the other of a dielectric$\left(K\right)$ of same thickness $d$ are inserted between the plates as shown in figure. Potential $\left(V\right)$ versus distance $x$ graph will be

In the given circuit, all the capacitors are initially uncharged. After closing the switch $S_1$ for a long time suddenly $S_2$ is also closed and kept closed for a long time. Total heat produced after closing $S_2$ will be :

A conducting body $1$ has some initial charge $Q$, and its capacitance is $C$. There are two other conducting bodies, $2$ and $3$, having capacitance : $C_2=2\mathrm{C}$ and $C_3\to \infty$. Bodies $2$ and $3$ are initially uncharged. Body $2$ is touched with body $1$. Then, body $2$ is removed from body $1$ and touched with body $3$, and then removed. This process is repeated for $N$ times. Then, the charge on body $1$ at the end must be :