Question:
An air-filled capacitor of capacitance \( C \) is filled with dielectric (\( k = 3 \)) of width \( \frac{d}{3} \), where \( d \) is the separation between plates. The new capacitance is
An air-filled capacitor of capacitance \( C \) is filled with dielectric (\( k = 3 \)) of width \( \frac{d}{3} \), where \( d \) is the separation between plates. The new capacitance is
Show Hint
When a dielectric is inserted between the plates of a capacitor, the capacitance increases according to the dielectric constant and the geometry of the plates.
Updated On: Jan 31, 2026
- \( \frac{9}{5}C \)
- \( \frac{5}{4}C \)
- \( \frac{4}{3}C \)
- \( \frac{9}{7}C \)
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Use the formula for capacitance.
The capacitance of a parallel plate capacitor is given by: \[ C = \frac{\varepsilon_0 A}{d} \] Where: \( \varepsilon_0 \) = permittivity of free space, \( A \) = area of the plates, and \( d \) = separation between the plates.
Step 2: Calculate the new capacitance.
The new capacitance when filled with dielectric is: \[ C_{\text{new}} = \frac{\varepsilon_0 A}{d + 6d} = \frac{9\varepsilon_0 A}{7d} \] Thus, the new capacitance is \( \frac{9}{7}C \), which corresponds to option (4).
Step 3: Conclusion.
The new capacitance is \( \frac{9}{7}C \).
The capacitance of a parallel plate capacitor is given by: \[ C = \frac{\varepsilon_0 A}{d} \] Where: \( \varepsilon_0 \) = permittivity of free space, \( A \) = area of the plates, and \( d \) = separation between the plates.
Step 2: Calculate the new capacitance.
The new capacitance when filled with dielectric is: \[ C_{\text{new}} = \frac{\varepsilon_0 A}{d + 6d} = \frac{9\varepsilon_0 A}{7d} \] Thus, the new capacitance is \( \frac{9}{7}C \), which corresponds to option (4).
Step 3: Conclusion.
The new capacitance is \( \frac{9}{7}C \).
Was this answer helpful?
0
0
Top Questions on Electrostatics
- Two point charges of \(1\,\text{nC}\) and \(2\,\text{nC}\) are placed at two corners of an equilateral triangle of side \(3\) cm. The work done in bringing a charge of \(3\,\text{nC}\) from infinity to the third corner of the triangle is ________ \(\mu\text{J}\). \[ \left(\frac{1}{4\pi\varepsilon_0}=9\times10^9\,\text{N m}^2\text{C}^{-2}\right) \]
- JEE Main - 2026
- Physics
- Electrostatics
Match List-I with List-II.
Choose the correct answer from the options given below :}- JEE Main - 2026
- Physics
- Electrostatics
There are three co-centric conducting spherical shells $A$, $B$ and $C$ of radii $a$, $b$ and $c$ respectively $(c>b>a)$ and they are charged with charges $q_1$, $q_2$ and $q_3$ respectively. The potentials of the spheres $A$, $B$ and $C$ respectively are:
- JEE Main - 2026
- Physics
- Electrostatics
Two resistors $2\,\Omega$ and $3\,\Omega$ are connected in the gaps of a bridge as shown in the figure. The null point is obtained with the contact of jockey at some point on wire $XY$. When an unknown resistor is connected in parallel with $3\,\Omega$ resistor, the null point is shifted by $22.5\,\text{cm}$ towards $Y$. The resistance of unknown resistor is ___ $\Omega$.
- JEE Main - 2026
- Physics
- Electrostatics
- The electrostatic potential in a charged spherical region of radius $r$ varies as $V = ar^{3} + b$, where $a$ and $b$ are constants. The total charge in the sphere of unit radius is $a \times \pi \varepsilon_{0}$. The value of $a$ is ___.
(Permittivity of vacuum is $\varepsilon_{0}$)
- JEE Main - 2026
- Physics
- Electrostatics
View More Questions
Questions Asked in JEE Main exam
Consider an A.P. $a_1,a_2,\ldots,a_n$; $a_1>0$. If $a_2-a_1=-\dfrac{3}{4}$, $a_n=\dfrac{1}{4}a_1$, and \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then $\sum_{i=1}^{17} a_i$ is equal to
- JEE Main - 2026
- Arithmetic Progression
- A thin convex lens of focal length \( 5 \) cm and a thin concave lens of focal length \( 4 \) cm are combined together (without any gap), and this combination has magnification \( m_1 \) when an object is placed \( 10 \) cm before the convex lens.
Keeping the positions of the convex lens and the object undisturbed, a gap of \( 1 \) cm is introduced between the lenses by moving the concave lens away. This leads to a change in magnification of the total lens system to \( m_2 \).
The value of \( \dfrac{m_1}{m_2} \) is
- Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E. The energy stored in B, when spring constants \(k_A, k_B\) of A and B, respectively satisfy the relation \(4k_A = 3k_B\), is :
- JEE Main - 2026
- Alternating current
- Correct statements regarding Arrhenius equation among the following are:
Factor \(e^{-E_a/RT}\) corresponds to fraction of molecules having kinetic energy less than \(E_a\).
At a given temperature, lower the \(E_a\), faster is the reaction.
Increase in temperature by about \(10^\circ\text{C}\) doubles the rate of reaction.
Plot of \(\log k\) vs \(\dfrac{1}{T}\) gives a straight line with slope \(= -\dfrac{E_a}{R}\).
Choose the correct answer from the options given below:- JEE Main - 2026
- Chemical Kinetics
- If the image of the point \( P(1, 2, a) \) in the line \[ \frac{x - 6}{3} = \frac{y - 7}{2} = \frac{7 - z}{2} \] is \( Q(5, b, c) \), then \( a^2 + b^2 + c^2 \) is equal to
- JEE Main - 2026
- Distance of a Point From a Line
View More Questions