Question:
A 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)
A 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)
Show Hint
With the battery disconnected the charge stays constant, so the stored energy falls from \(\frac{Q^2}{2C}\) to \(\frac{Q^2}{2kC}\); the loss appears as mechanical energy of the plate.
Updated On: Nov 4, 2026
Show Solution
Verified By Collegedunia
Correct Answer: 864
Solution and Explanation
Initial energy: \(U_i=\frac{1}{2}CV^2=\frac{1}{2}(14)(12)^2=1008\ \mathrm{pJ}\).
The battery is disconnected, so the charge \(Q=CV\) stays constant.
With the dielectric (k = 7) fully inside, the capacitance becomes \(kC\), so \(U_f=\frac{Q^2}{2kC}=\frac{U_i}{k}=\frac{1008}{7}=144\ \mathrm{pJ}\).
The plate is pulled in by the field and, with no friction, oscillates with constant mechanical energy equal to the energy lost by the field: \(E=U_i-U_f=1008-144=864\ \mathrm{pJ}\).
Answer: 864
The battery is disconnected, so the charge \(Q=CV\) stays constant.
With the dielectric (k = 7) fully inside, the capacitance becomes \(kC\), so \(U_f=\frac{Q^2}{2kC}=\frac{U_i}{k}=\frac{1008}{7}=144\ \mathrm{pJ}\).
The plate is pulled in by the field and, with no friction, oscillates with constant mechanical energy equal to the energy lost by the field: \(E=U_i-U_f=1008-144=864\ \mathrm{pJ}\).
Answer: 864
Was this answer helpful?
0
0
Top JEE Main Physics Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
- A particle starts with an initial velocity of 10.0 m/s along x-direction and accelerates uniformly at the rate of 2.0 m/s$^2$. The time taken by the particle to reach the velocity of 60.0 m/s is
View More Questions
Top JEE Main Capacitors and Capacitance Questions
- Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2V. 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
- A parallel plate capacitor has a capacitance C = 200 pF. It is connected to 230 V ac supply with an angular frequency 300 rad/s. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :
A capacitor of capacitance 100 μF is charged to a potential of 12 V and connected to a 6.4 mH inductor to produce oscillations. The maximum current in the circuit would be:
- A parallel plate capacitor of capacitance \( 12.5 \, \text{pF} \) is charged by a battery connected between its plates to a potential difference of \( 12.0 \, \text{V} \). The battery is now disconnected and a dielectric slab (\( \varepsilon_r = 6 \)) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is ______ \( \times 10^{-12} \, \text{J} \).
- A capacitor of $10 \, \mu\text{F}$ capacitance whose plates are separated by $10 \, \text{mm}$ through air and each plate has area $4 \, \text{cm}^2$ is now filled equally with two dielectric media of $K_1 = 2$, $K_2 = 3$ respectively as shown in the figure. If new force between the plates is $8 \, \text{N}$, the supply voltage is ____ $\text{V}$.
View More Questions
Top JEE Main Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
View More Questions