Capacitors

JEE Main level, numerical answer, medium

15 of 180

Question 15 of 180

The displacement current of 4.425μA4.425\mu A is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 106Vs−1{10}^{6}V{s}^{-1}. The area of each plate of the capacitor is 40cm240{cm}^{2}. The distance between each plate of the capacitor is x×10−3mx\times {10}^{-3}m. The value of xx is ,
(Permittivity of free space, ϵ0=8.85×10−12C2N−1m−2{\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}) _______

Show answer and solution

Answer: 8

Displacement current is given by id={i}_{d}=ϵ0dϕEdt\dfrac{{\epsilon }_{0}d{\phi }_{E}}{dt}
Or id=ϵ0ddt(EA){i}_{d}=\dfrac{{\epsilon }_{0}d}{dt}\left(EA\right), where E=qAϵ0E=\dfrac{q}{A{\epsilon }_{0}}
Or id=ϵ0ddt(qAAϵ0)=dqdt=ddt(CV){i}_{d}={\epsilon }_{0}\dfrac{d}{dt}\left(\dfrac{qA}{A{\epsilon }_{0}}\right)=\dfrac{dq}{dt}=\dfrac{d}{dt}\left(CV\right)
Or id=CdVdt=ϵ0AddVdt{i}_{d}=C\dfrac{dV}{dt}=\dfrac{{\epsilon }_{0}A}{d}\dfrac{dV}{dt}
Putting the values, we have
4.425×10−6=8.85×10−12×40×10−4×106d4.425\times {10}^{-6}=\dfrac{8.85\times {10}^{-12}\times 40\times {10}^{-4}\times {10}^{6}}{d}
d=2×10−6×10−4×106×40d=2\times {10}^{-6}\times {10}^{-4}\times {10}^{6}\times 40
d=80×10−4=8×10−3md=80\times {10}^{-4}=8\times {10}^{-3}m
Hence, value of x=8x=8.

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 (Capacitance), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.