If an electron enters into a space between the plates of a parallel plate capacitor at an angle $\alpha$ with the plates and leaves at an angle $\beta$ to the plates,the ratio of its kinetic energy while entering the capacitor to that while leaving will be

$A$ body of mass $1 \,g$ and carrying a charge $10^{-8} \,C$ passes through two points $P$ and $Q$. $P$ and $Q$ are at electric potentials $600 \,V$ and $0 \,V$, respectively. The velocity of the body at $Q$ is $20 \,cm/s$. Its velocity in $m/s$ at $P$ is:

While working on a physics project at a school physics lab,you require a $4 \,\mu F$ capacitor in a circuit across a potential difference of $1 \,kV$. Unfortunately,$4 \,\mu F$ capacitors are out of stock in your lab,but $2 \,\mu F$ capacitors which can withstand a potential difference of $400 \,V$ are available in plenty. If you decide to use the $2 \,\mu F$ capacitors in place of the $4 \,\mu F$ capacitor,what is the minimum number of capacitors required?

For the circuit shown,which of the following statements is true?

$A$ parallel plate capacitor of capacitance $C$ is connected to a battery and charged to a potential difference $V$. Another capacitor of capacitance $3C$ is similarly charged to a potential difference $3V$. The charging battery is then disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

Four identical thin, square metal sheets, $S_1, S_2, S_3$, and $S_4$, each of side $a$ are kept parallel to each other with equal distance $d( < < a)$ between them, as shown in the figure. Let $C_0 = \varepsilon_0 a^2 / d$, where $\varepsilon_0$ is the permittivity of free space.
Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option.

$List-I$	$List-II$
$(P)$ The capacitance between $S_1$ and $S_4$, with $S_2$ and $S_3$ not connected, is	$(1)$ $3 C_0$
$(Q)$ The capacitance between $S_1$ and $S_4$, with $S_2$ shorted to $S_3$, is	$(2)$ $C_0 / 2$
$(R)$ The capacitance between $S_1$ and $S_3$, with $S_2$ shorted to $S_4$, is	$(3)$ $C_0 / 3$
$(S)$ The capacitance between $S_1$ and $S_2$, with $S_3$ shorted to $S_1$, and $S_2$ shorted to $S_4$, is	$(4)$ $2 C_0 / 3$
	$(5)$ $2 C_0$