A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric constants $${{k}_{1}},{{k}_{2}}$$ 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 [IIT-JEE Screening 2000]

Question

A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric constants $${{k}_{1}},{{k}_{2}}$$ 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                                               [IIT-JEE Screening 2000]

TuteeHUB · Accepted Answer

$$k=\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}+2{{k}_{3}}$$

TuteeHUB · Answer

$$\frac{1}{k}=\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}+\frac{1}{2{{k}_{3}}}$$

TuteeHUB · Answer

$$\frac{1}{k}=\frac{1}{{{k}_{1}}+{{k}_{2}}}+\frac{1}{2{{k}_{3}}}$$

TuteeHUB · Answer

$$k={{k}_{1}}+{{k}_{2}}+2{{k}_{3}}$$

1.	A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric constants \[{{k}_{1}},{{k}_{2}}\] 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 [IIT-JEE Screening 2000]
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.	\[k={{k}_{1}}+{{k}_{2}}+2{{k}_{3}}\]
Answer» C. \[k=\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}+2{{k}_{3}}\]

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