JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance
A parallel - plate capacitor with plate area \(A\) has separation \(d\) between the plates. Two dielectric slabs of dielectric constant \({K}_{1}\) and \({K}_{2}\) of same area \(\frac A2\) and thickness \(\frac d2\) are inserted in the space between the plates. The capacitance of the capacitor will be given by :
- A \(\frac{\varepsilon_{0} {A}}{{d}}\left(\frac{1}{2}+\frac{{K}_{1} {K}_{2}}{{K}_{1}+{K}_{2}}\right)\)
- B \(\frac{\varepsilon_{0} {A}}{{d}}\left(\frac{1}{2}+\frac{{K}_{1} {K}_{2}}{2\left({K}_{1}+{K}_{2}\right)}\right)\)
- C \(\frac{\varepsilon_{0} {A}}{{d}}\left(\frac{1}{2}+\frac{{K}_{1}+{K}_{2}}{{K}_{1} {K}_{2}}\right)\)
- D \(\frac{\varepsilon_{0} {A}}{{d}}\left(\frac{1}{2}+\frac{2\left({K}_{1}+{K}_{2}\right)}{{K}_{1} {K}_{2}}\right)\)
Answer & Solution
Correct Answer
(A) \(\frac{\varepsilon_{0} {A}}{{d}}\left(\frac{1}{2}+\frac{{K}_{1} {K}_{2}}{{K}_{1}+{K}_{2}}\right)\)
Step-by-step Solution
Detailed explanation
\(C_{eq}=\frac{\frac{A}{2} \varepsilon_{0}}{d}+\frac{A \varepsilon_{0}}{d} \frac{K_{1} K_{2}}{K_{1}+K_{2}}\) \(=\frac{A \varepsilon_{0}}{d}\left(\frac{1}{2}+\frac{K_{1} K_{2}}{K_{1}+K_{2}}\right)\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A slender uniform rod of mass \(M\) and length \(l\) is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle \(\theta\) with the vertical is
JEE Mains 2017 Hard - A Laser light of wavelength \(660\,nm\) is used to weld Retina detachment. If a Laser pulse of width \(60\, ms\) and power \(0.5\, kW\) is used the approximate number of photons in the pulse are : [Take Planck's constant \(h\, = 6.62\times10^{- 34}\, Js\)]JEE Mains 2017 Medium
- A block of mass \(m\) slides down the plane inclined at angle \(30^{\circ}\) with an acceleration \(\frac{ g }{4}\). The value of coefficient of kinetic friction will be :JEE Mains 2023 Medium
- Two wires A and B are made of same material having ratio of lengths \(\frac{L_A}{L_B}=\frac{1}{3}\) and their diameters ratio \(\frac{d_A}{d_B}=2\). If both the wires are stretched using same force, what would be the ratio of their respective elongations?JEE Mains 2025 Easy
- A string is wrapped around the rim of a wheel of moment of inertia \(0.40 \mathrm{kgm}^2\) and radius \(10 \mathrm{~cm}\). The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of \(40 \mathrm{~N}\). The angular velocity of the wheel after \(10\) \(\mathrm{s}\) is \(\mathrm{x} \mathrm{rad} / \mathrm{s}\), where \(\mathrm{x}\) is _______.JEE Mains 2024 Hard
- At \(300\,K\), the rms speed of oxygen molecules is \(\sqrt{\frac{\alpha+5}{\alpha}}\) times to that of its average speed in the gas. Then, the value of \(\alpha\) will be (used \(\pi=\frac{22}{7}\) )JEE Mains 2023 Medium
More PYQs from JEE Mains
- If the projection of the vector \(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\) on the sum of the two vectors \(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-5 \hat{\mathrm{k}}\) and \(-\lambda \hat{i}+2 \hat{j}+3 \hat{k}\) is \(1,\) then \(\lambda\) is equal to ..... .JEE Mains 2021 Medium
- For a series \(LCR\) circuit with \({R}=100\,\ \Omega, {L}=0.5\, {mH}\) and \({C}=0.1\, {pF}\) connected across \(220 \,{V}-50\, {Hz}\) \(AC\) supply, the phase angle between current and supplied voltage and the nature of the circuit is :JEE Mains 2021 Medium
- Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is \(\sqrt{2}\) times the speed of sound, then the value of \(n\) will beJEE Mains 2022 Hard
- A ray of light coming from the point \((2,2 \sqrt{3})\) is incident at an angle \(30^{\circ}\) on the line \(x=1\) at the point \(A\). The ray gets reflected on the line \(x =1\) and meets \(x\) -axis at the point \(B\). Then, the line \(AB\) passes through the pointJEE Mains 2020 Hard
- A uniform rod \(A B\) of mass \(2 \mathrm{~kg}\) and Length \(30 \mathrm{~cm}\) at rest on a smooth horizontal surface. An impulse of force \(0.2\ \mathrm{Ns}\) is applied to end \(B.\) The time taken by the rod to turn through at right angles will be \(\frac{\pi}{\mathrm{x}}\ \mathrm{s}\), where X = _______.JEE Mains 2024 Hard
- In Vander Waals equation \(\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT\); \(P\) is pressure, \(V\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The ratio of constants \(\frac{a}{b}\) is dimensionally equal to .................JEE Mains 2022 Medium