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Saturday, 31 October

JEE Main 2021 · PhysicsMultiple choiceDiagram basedMediumMulti-step

JEE Main 26 August 2021, Shift 2, Physics Q18

Question 18 of 90 in this shift, Physics question 18 of 30, Section A.

A parallel-plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K1\mathrm{K_1} and K2\mathrm{K_2} of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by :

The figure, in words

Parallel plates drawn horizontally: top plate marked with + signs and labelled +Q, bottom plate marked with - signs and labelled -Q. Between them, two hatched slabs stacked vertically, K1 on top and K2 below, occupying part of the plate width; the separation between the plates is marked d with a double arrow on the right.
  1. (1)ε0Ad(12+2(K1+K2)K1K2)\frac{\varepsilon_0 A}{d}\left(\frac{1}{2}+\frac{2(K_1+K_2)}{K_1K_2}\right)
  2. (2)ε0Ad(12+K1K22(K1+K2))\frac{\varepsilon_0 A}{d}\left(\frac{1}{2}+\frac{K_1K_2}{2(K_1+K_2)}\right)
  3. (3)ε0Ad(12+K1+K2K1K2)\frac{\varepsilon_0 A}{d}\left(\frac{1}{2}+\frac{K_1+K_2}{K_1K_2}\right)
  4. (4)ε0Ad(12+K1K2K1+K2)\frac{\varepsilon_0 A}{d}\left(\frac{1}{2}+\frac{K_1K_2}{K_1+K_2}\right)Official answer

Official answer

Option 4

NTA final key.

Chapter
Electrostatic Potential and Capacitance
Topic
Dielectrics
Idea tested
Partial and Multiple Slabs

Same idea in other shifts

Asked 10× in all
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  4. 8 Apr 2024, Shift 2 · Q40A capacitor has air as dielectric medium and two conducting plates of area 12 cm212\ \mathrm{cm}^2 and they are 0.60.6 cm apart. When a slab of…MediumSingle correct
  5. 6 Apr 2023, Shift 1 · Q56A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric material of dielectric constant K=4K=4. The…MediumNumerical valueHas a figure
  6. 27 Jul 2022, Shift 2 · Q56A parallel plate capacitor with width 4 cm, length 8 cm and separation between the plates of 4 mm is connected to a battery of 20 V. A…MediumNumerical value
  7. 28 Jul 2022, Shift 2 · Q9A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness 34\frac{3}{4}…EasySingle correct
  8. 30 Jun 2022, Shift 1 · Q40Co\mathrm{C_o} is the capacitance of a parallel plate capacitor with air as a medium between the plates (as shown in Fig. 1). If half…EasySingle correctHas a figure

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.