A parallel plate capacitor of capacitance $2\; F$ is charged to a potential $V$. The energy stored in the capacitor is $E_1$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $E _2$. The ratio $E _2 / E _1$ is
JEE MAIN 2023, Medium
Download our app for free and get started
Initially
$Q _1= CV =(2) V$
$E _1=1 / 2 CV ^2=1 / 2(2) V ^2= V ^2$
Finally
Charge on each capacitor, $Q _2=\frac{ Q _1}{2}=\frac{2 V }{2}= V$
$E _2=2\left(\frac{1}{2} \frac{ Q _2^2}{ C }\right)=\frac{ V ^2}{2} \quad \therefore \frac{ E _2}{ E _1}=\frac{1}{2}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A uniform electric field pointing in positive $x$-direction exists in a region. Let $A$ be the origin, $B$ be the point on the $x$-axis at $x = + 1$ $cm$ and $C$ be the point on the $y$-axis at $y = + 1\,cm$. Then the potentials at the points $A$, $B$ and $C$ satisfyView Solution
- 2In the figure shown the electric potential energy of the system is: ( $q$ is at the centre of the conducting neutral spherical shell of inner radius $a$ and outer radius $b$ )View Solution
- 3Two identical capacitors, have the same capacitance $C$. One of them is charged to potential $V_1$ and the other to $V_2$. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system isView Solution
- 4In the circuit shown in figure battery is $10 \ V$ and $C = 6\,\mu F$ . The charge stored in capacitor of capacity $C$ is......$\mu C$View Solution
- 5The insulated spheres of radii ${R_1}$ and ${R_2}$ having charges ${Q_1}$and ${Q_2}$ respectively are connected to each other. There isView Solution
- 6In a hollow spherical shell potential $(V)$ changes with respect to distance $(r)$ from centreView Solution
- 7View SolutionTwo equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be
- 8Consider a sphere of radius $R$ with uniform charge density and total charge $Q$. The electrostatic potential distribution inside the sphere is given by $\theta_{(r)}=\frac{Q}{4 \pi \varepsilon_{0} R}\left(a+b(r / R)^{C}\right)$. Note that the zero of potential is at infinity. The values of $(a, b, c)$ areView Solution
- 9A conducting sphere $A$ of radius $a$, with charge $Q$, is placed concentrically inside a conducting shell $B$ of radius $b$. $B$ is earthed. $C$ is the common centre of the $A$ and $B$.View Solution
- 10$2\,\mu F$ capacitance has potential difference across its two terminals $200\;volts$. It is disconnected with battery and then another uncharged capacitance is connected in parallel to it, then $P.D.$ becomes $20\;volts$. Then the capacity of another capacitance will be.......$\mu F$View Solution