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  4. A parallel plate capacitor with air between the plate has a capacitance of 15 pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes (x/4) pF. The value of x is

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Q. A parallel plate capacitor with air between the plate has a capacitance of $15\, pF$. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant $3.5$. Then the capacitance becomes $\frac{x}{4} pF$. The value of $x$ is _______

JEE MainJEE Main 2023Electrostatic Potential and Capacitance

Solution:

$ C _0=\frac{\in_0 A }{ d }=15 pF $
$ C =\frac{ K \in_0 A }{2 d }=\frac{3.5}{2} \times 15 pF =\frac{105}{4} pF $