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 const

Question

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____.

TestHub · Accepted Answer

Capacitance of the parallel plate capacitor when air is present between the plates, $C = \frac{ε_{0} A}{d} = 15 pF$

Capacitance of the parallel plate capacitor when dielectric is filled in between the plates,

$C^{'} = \frac{k ε_{0} A}{d^{'}} = \frac{3.5 ε_{0} A}{2 d} = \frac{3.5}{2} \times 15 pF = \frac{105}{4} pF$

Therefore, $x = 105$ .

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