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JEE Main20236 Apr 2023Morning ShiftPhysicsCapacitanceActual

A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric material of dielectric constant K = 4 . The thickness of the dielectric material is x , where x < d . Let C 1 and C 2 be the capacitance of the system for x = 1 3 d and x = 2 d 3 , respectively. If C 1 = 2 μF , the value of C 2 is _____ μF .

Correct answer

0

Step-by-step solution

The formula to calculate the capacitance of a parallel plate capacitor having thickness d and with a dielectric of thickness x between the plates is given by C = ε 0 A d - x + x K       . . . ( 1 ) Substitute the values of the parameters for first case into equation (1) to obtain the capacitance. C 1 = ε 0 A 2 d 3 + d 3 4 = 4 ε 0 A 3 d       . . . ( 2 ) Similarly, substitute the parameters into equation (1) for the second case to obtain the capacitance C 2 = ε 0 A d

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