Capacitors

JEE Main level, single correct, medium

71 of 180

Question 71 of 180

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25%25 \% more charge from the battery. The dielectric constant of mica is ____\_\_\_\_.

Show answer and solution

Answer: (C) 2.0

Initial capacitor has plate separation 5 mm with capacitance C1=ϵ0A/5C_1 = \epsilon_0 A / 5.
After inserting 2 mm mica sheet, the gap remaining is 3 mm of air. The effective separation becomes: deff=3+2/kd_{eff} = 3 + 2/k where kk is the dielectric constant of mica.
New capacitance: C2=ϵ0A3+2/kC_2 = \frac{\epsilon_0 A}{3 + 2/k}
Since battery remains connected, voltage is constant. The charge is: Q=CVQ = CV
Ratio of charges: Q2Q1=C2C1=ϵ0A/(3+2/k)ϵ0A/5=53+2/k\frac{Q_2}{Q_1} = \frac{C_2}{C_1} = \frac{\epsilon_0 A/(3 + 2/k)}{\epsilon_0 A/5} = \frac{5}{3 + 2/k}
Given that charge increases by 25%: Q2=1.25Q1Q_2 = 1.25 Q_1
53+2/k=1.25\frac{5}{3 + 2/k} = 1.25
5=1.25(3+2/k)5 = 1.25(3 + 2/k)
5=3.75+2.5/k5 = 3.75 + 2.5/k
1.25=2.5/k1.25 = 2.5/k
k=2k = 2

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Capacitors, dielectrics and RC circuits simulationDrag the sliders and watch the numbers in this question change.

More Physics practice

JEE Main Physics practice question on Capacitors (Capacitors with Dielectric), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.