A parallel plate capacitor of area $A$, plate separation $d$ and capacitance $C$ is filled with three different dielectric materials having dielectric constant $K_1,K_2$ and $K_3$ as shown. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $K$ is given by: ($A =$ Area of plates)
A parallel plate capacitor of area $A$, plate separation $d$ and capacitance $C$ is filled with three different dielectric materials having dielectric constant $K_1,K_2$ and $K_3$ as shown. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $K$ is given by: ($A =$ Area of plates)
- A
$\frac{1}{K} = \frac{1}{{{K_1}}} + \frac{1}{{{K_2}}} + \frac{1}{{2{K_3}}}$
- B
$\frac{1}{K} = \frac{1}{{{K_1} + {K_2}}} + \frac{1}{{2{K_3}}}$
- C
$K = \frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}} + 2{K_3}$
- D
$K = K_1 + K_2 + 2K_3$
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