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JEE Main 202227 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
27 June
Shift
Evening Shift
Subject
Physics
Chapter
Capacitance

JEE Main 2022 · 27 June · Evening Shift · Physics · Capacitance

A parallel plate capacitor is made up of stair like structure with...

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length bb, as shown in the figure. The capacitance of the arrangement is x15ε0Ab\dfrac{x}{15}\dfrac{{ε}_{0}A}{b}, The value of xx is _____ .

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected

Correct answer

0

Step-by-step solution

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected

Here the system can be considered as three capacitors in parallel.

So, net capacitance is

C=ε0A5b+ε0A3b+ε0AbC = \dfrac{{ε}_{0}A}{5b} + \dfrac{{ε}_{0}A}{3b} + \dfrac{{ε}_{0}A}{b}

C=ε0Ab[15+13+11]C = \dfrac{{ε}_{0}A}{b}\left[\dfrac{1}{5} + \dfrac{1}{3} + \dfrac{1}{1}\right]

C=23ε0A15bC = \dfrac{23{ε}_{0}A}{15b}

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