A parallel-plate capacitor of area , plate separation and capacitance is filled with four dielectric materials having dielectric constants , and as shown in the figure. If a single dielectric material is to be used to have the same capacitance C in thi

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Solution

Q.
A parallel-plate capacitor of area $A$ , plate separation $d$ and capacitance $C$ is filled with four dielectric materials having dielectric constants $k_{1}, k_{2}, k_{3}$ , and $k_{4}$ as shown in the figure. 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 [2016]

1
$k = k_{1} + k_{2} + k_{3} + 3 k_{4}$

2
$k = \frac{2}{3} (k_{1} + k_{2} + k_{3}) + 2 k_{4}$

3
$\frac{2}{k} = \frac{3}{k_{1} + k_{2} + k_{3}} + \frac{1}{k_{4}}$

4
$\frac{1}{k} = \frac{1}{k_{1}} + \frac{1}{k_{2}} + \frac{1}{k_{3}} + \frac{3}{2 k_{4}}$

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