JEE Mains · Physics · STD 12 - Electric potential and capacitance
- JEE Mains 2024
- Hard
- MCQ
A capacitor is made of a tlat plate of area \(A\) and a second plate having a stair-like structure as shown in figure. If the area of each stair is \(\frac{A}{3}\) and the height is \(\mathrm{d}\), the capacitance of the arrangement is _______.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(\frac{11 \varepsilon_0 \mathrm{~A}}{18 \mathrm{~d}}\)
Step-by-step Solution
Detailed explanation
All capacitor are in parallel combination.
Also effective area is common area only
\(\Rightarrow C_{e q}=C_1+C_2+C_3\)
\(\Rightarrow C_{e q}=\frac{A \varepsilon_0}{3 d}+\frac{A \varepsilon_0}{3(2 d)}+\frac{A \varepsilon_0}{3(3 d)}\)
\(\Rightarrow C_{e q}=\frac{A \varepsilon_0}{3}\left(\frac{11}{6 d}\right)\)
\(\Rightarrow C_{e q}=\frac{11 A \varepsilon_0}{18 d}\)
More questions from Physics
- The electric field of light wave is given as \(\vec E\, = \,{10^{ - 3}}\,\cos \,\,\left( {\frac{{2\pi x}}{{5 \times {{10}^{ - 7}}}} - 2\pi \times 6 \times {{10}^{14}}t} \right)\hat x\frac{N}{C}\). This light falls on a metal plate of work function \(2\,eV.\) The stopping potential of the photoelectrons is ................ \(V\)JEE Mains 2019 Hard
- The height of any point \(P\) above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point \(P\) will be : (Given \(g=\) acceleration due to gravity at the surface of earth)JEE Mains 2022 Medium
- A particle of charge \(1.6 \mu \mathrm{C}\) and mass \(16 \mu \mathrm{~g}\) is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is ________ S. \((\pi=3.14)\)JEE Mains 2025 Easy
- A \(2 \,{kg}\) steel rod of length \(0.6\, {m}\) is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity, Ignoring the friction due to clamping at its lower end, the speed of the free end of rod when it passes through its lowest position is \(\ldots \ldots \ldots \ldots \,{ms}^{-1}\). (Take \(g = 10\, {ms}^{-2}\) )JEE Mains 2021 Hard
- A diverging lens with magnitude of focal length \(25\ cm\) is placed at a distance of \(15\ cm\) from a converging lens of magnitude of focal length \(20\ cm\). A beam of parallel light falls on the diverging lens. The final image formed isJEE Mains 2017 Medium
- Two separate wires \(A\) and \(B\) are stretched by \(2 \,mm\) and \(4\, mm\) respectively, when they are subjected to a force of \(2\, N\). Assume that both the wires are made up of same material and the radius of wire \(B\) is 4 times that of the radius of wire \(A\). The length of the wires \(A\) and \(B\) are in the ratio of \(a : b\). Then \(a / b\) can be expressed as \(1 / x\) where \(x\) isJEE Mains 2021 Hard
More PYQs from JEE Mains
- A point like object is placed at a distance of \(1\, m\) in front of a convex lens of focal length \(0.5\, m .\) A plane mirror is placed at a distance of \(2\,m\) behind the lens. The position and nature of the final image formed by the system isJEE Mains 2020 Medium
- Resistance are connected in a meter bridge circuit as shown in the figure. The balancing length \(l_{1}\) is \(40\,cm\). Now an unknown resistance \(x\) is connected in series with \(P\) and new balancing length is found to be \(80\,cm\) measured from the same end. Then the value of \(x\) will be \(.......\Omega\)
JEE Mains 2022 Hard - A resistor develops \(300 \,J\) of thermal energy in \(15 \,s\), when a current of \(2\, A\) is passed through it. If the current increases to \(3 \,A\), the energy developed in \(10\,\,s\) is........\(J.\)JEE Mains 2022 Medium