A parallel plate capacitor is of area 6c m ^ 2 and a separation 3mm...

A parallel plate capacitor is of area

6c{m}^{2}

and a separation

3mm .

The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constant

{K}_{1} = 10, {K}_{2} = 12

and

{K}_{3} = 14 .

The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be:

A parallel plate capacitor is of area 6c m ^ 2 and a separation 3mm . The gap is filled with three dielectric materials

A parallel plate capacitor is of area 6c m ^ 2 and a separation 3mm . The gap is filled with three dielectric materials

Options

A $4$
B $36$
C $14$
D $12$

Correct answer

D. $12$

Step-by-step solution

C = \dfrac{{\in}_{0}A}{d}

{C}_{1} = \dfrac{{K}_{1}{\in}_{0}A}{3d} = \dfrac{{K}_{1}C}{3}

{C}_{2} = \dfrac{{K}_{2}C}{3}

{C}_{3} = \dfrac{{K}_{3}C}{3}

{C}_{eq} = {K}_{eq} C = \dfrac{C}{3} ( {K}_{1} + {K}_{2} + {K}_{3} )

{K}_{eq} = \dfrac{{K}_{1} + {K}_{2} + {K}_{3}}{3} = \dfrac{36}{3} = 12

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