JEE Mains · Physics · STD 12 - Electric potential and capacitance
- JEE Mains 2019
- Hard
- Numerical
A parallel plate capacitor is of area \(6\, cm^2\) and a separation \(3\, mm\). The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants \(K_1 = 10, K_2 = 12\) and \(K_3 = 14\). The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(12\)
Step-by-step Solution
Detailed explanation
\(\mathrm{C}_{\mathrm{net}}=\mathrm{C}_{1}+\mathrm{C}_{2}+\mathrm{C}_{3}\)
\(\frac{\mathrm{k} \mathrm{AE}_{\mathrm{o}}}{\mathrm{d}}=\mathrm{k}_{1}\left(\frac{\mathrm{A}}{3}\right) \frac{\mathrm{E}_{\mathrm{o}}}{\mathrm{d}}+\mathrm{k}_{2}\left(\frac{\mathrm{A}}{3}\right) \frac{\mathrm{E}_{\mathrm{o}}}{\mathrm{d}}+\mathrm{k}_{3}\left(\frac{\mathrm{A}}{3}\right) \frac{\mathrm{E}_{\mathrm{o}}}{\mathrm{d}}\)
\(\mathrm{k}=\frac{\mathrm{k}_{1}+\mathrm{k}_{2}+\mathrm{k}_{3}}{3}=12\)
More questions from Physics
- In meter bridge experiment for measuring unknown resistance ' \(S\) ', the null point is obtained at a distance \(30 cm\) from the left side as shown at point \(D\). If \(R\) is \(5.6 k \Omega\), then the value of unknown resistance ' \(S\) ' will be \(\Omega .\)
JEE Mains 2022 Medium - A wire of length 25 m and cross-sectional area \(5 \mathrm{~mm}^2\) having resistivity of \(2 \times 10^{-6} \Omega \mathrm{~m}\) is bent into a complete circle. The resistance between diametrically opposite points will be:JEE Mains 2025 Medium
- Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for \(V =5 \sin (100 t )\). The values of L and \(R\) are shown in the figure. The capacitance of the capacitor \(( C )\) used is ___________ \(\mu F\).
JEE Mains 2026 Hard - A fly wheel is accelerated uniformly from rest and rotates through \(5 \,rad\) in the first second. The angle rotated by the fly wheel in the next second, will be.........\(rad\)JEE Mains 2022 Easy
- Two equal positive point charges are separated by a distance \(2 a\). The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge \(q_0\) becomes maximum is \(\frac{a}{\sqrt{x}}\). The value of \(x\) is \(................\)JEE Mains 2023 Hard
- A person travelling on a straight line moves with a uniform velocity \(\mathrm{v}_1\) for a distance x and with a uniform velocity \(\mathrm{v}_2\) for the next \(\frac{3}{2} \mathrm{x}\) distance. The average velocity in this motion is \(\frac{50}{7} \mathrm{~m} / \mathrm{s}\). If \(\mathrm{v}_1\) is \(5 \mathrm{~m} / \mathrm{s}\) then \(\mathrm{v}_2=\) _________ \(\mathrm{m} / \mathrm{s}\).JEE Mains 2025 Easy