An air-filled parallel plate capacitor has a capacitance C_ 0 . The separation between the plates is d . A dielectric slab of thickness (d)/(2) and dielectric constant K is introduced between the plates. If the new

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Correct answer: C. 2

The capacitance of an air-filled parallel plate capacitor is

C_{0} = \dfrac{\epsilon_{0}A}{d}

.

When a dielectric slab of thickness

t

and dielectric constant

K

is inserted, the new capacitance is given by:

C = \dfrac{\epsilon_{0}A}{d - t + \dfrac{t}{K}}

Given

t = \dfrac{d}{2}

and

C = \dfrac{4}{3}C_{0}

:

\dfrac{4}{3}C_{0} = \dfrac{\epsilon_{0}A}{d - \dfrac{d}{2} + \dfrac{d}{2K}}

\dfrac{4}{3}C_{0} = \dfrac{\epsilon_{0}A}{\dfrac{d}{2} + \dfrac{d}{2K}}

\dfrac{4}{3}C_{0} = \dfrac{C_{0}}{\dfrac{1}{2} + \dfrac{1}{2K}}

\dfrac{1}{2} + \dfrac{1}{2K} = \dfrac{3}{4}

\dfrac{1}{2K} = \dfrac{3}{4} - \dfrac{1}{2} = \dfrac{1}{4}

2K = 4 \Rightarrow K = 2

Answer:

2

An air-filled parallel plate capacitor has a capacitance C_ 0 . The...

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