Two identical capacitors have same capacitance $C$. One of them is charged to the potential $\mathrm{V}$ and other to the potential $2 \mathrm{~V}$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :
JEE MAIN 2024, Diffcult
Download our app for free and get started
$\mathrm{V}_{\mathrm{C}}-\frac{\mathrm{q}_{\text {net }}}{\mathrm{C}_{\text {net }}}=\frac{\mathrm{CV}+2 \mathrm{CV}}{2 \mathrm{C}}$
$\mathrm{V}_{\mathrm{C}}=\frac{3 \mathrm{~V}}{2}$
Loss of energy
$=\frac{1}{2} \mathrm{CV}^2+\frac{1}{2} \mathrm{C}(2 \mathrm{~V})^2-\frac{1}{2} 2 \mathrm{C}\left(\frac{3 \mathrm{~V}}{2}\right)^2$
$=\left(\frac{\mathrm{CV}^2}{4}\right)$
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 charge is spread non-uniformly on the surface of a hollow sphere of radius $R$, such that the charge density is given by $\sigma=\sigma_0(1-\sin \theta)$, where $\theta$ is the usual polar angle. The potential at the centre of the sphere isView Solution
- 2Force acting upon a charged particle kept between the plates of a charged condenser is $F$. If one plate of the condenser is removed, then the force acting on the same particle will becomeView Solution
- 3Five capacitors of $10\,\mu F$ capacity each are connected to a $d.c.$ potential of $100\;volts$ as shown in the adjoining figure. The equivalent capacitance between the points $A$ and $B$ will be equal to..........$\mu F$View Solution
- 4Two identical capacitors are joined in parallel, charged to potential $V$, separated and then, connected in series, $i.e.$, the positive plate of one is connected to the negative plate of the other. ThenView Solution
- 5A 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
- 6The plates of parallel plate capacitor are charged upto $100\;V$. A $2\,mm$ thick plate is inserted between the plates. Then to maintain the same potential difference, the distance between the plates is increased by $1.6\;mm$. The dielectric constant of the plate isView Solution
- 7A $4\ \mu F$ capacitor, a resistance of $2.5 \,MW$$\Omega$ is in series with $12\, V$ battery. Find the time after which the potential difference across the capacitor is $3$ times the potential difference across the resistor.......$s$ [Given $ln(2)= 0.693$]View Solution
- 8A conducting sphere of radius $R$ is given a charge $Q$. The electric potential and the electric field at the centre of the sphere respectively areView Solution
- 9Charge $q_{2}$ is at the centre of a circular path with radius $r$. Work done in carrying charge $q_{1}$, once around this equipotential path, would beView Solution
- 10A parallel plate capacitor whose capacitance $C$ is $14\, pF$ is charged by a battery to a potential difference $V =12\, V$ between its plates. The charging battery is now disconnected and a porcelin plate with $k =7$ is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of $..........pJ$. (Assume no friction)View Solution