NEET 2016 Physics - Class 12 NEET-2016-Ph-1182 Solution: A parallel-plate capacitor of area a plate separation d and…

QNEET-2016-Ph-1182: NEET 2016 Physics - Class 12 NEET-2016-Ph-1182 Solution: A parallel-plate capacitor of area a plate separation d and…

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

k = k_1 + k_2 + k_3 + 3k_4

k = \frac{2}{3}(k_1+k_2+k_3)+2k_4

\frac{2}{k} = \frac{3}{k_1+k_2+k_3}+\frac{1}{k_4}

\frac{1}{k} = \frac{1}{k_1}+\frac{1}{k_2}+\frac{1}{k_3}+\frac{3}{2k_4}

Multiple Choice Options

A k = k 1 + k 2 + k 3 + 3k 4
B k = ${2 \over 3}$ 3 2 _ (k 1 + k 2 + k 3 ) + 2k 4
C ${2 \over k}$ k 2 _ = ${3 \over {{k_1} + {k_2} + {k_3}}} + {1 \over {{k_4}}}$ k 1 _ + k 2 _ + k 3 _ 3 _ + k 4 _ 1 _
D ${1 \over k}$ k 1 _ = ${1 \over {{k_1}}} + {1 \over {{k_2}}} + {1 \over {{k_3}}} + {3 \over {2{k_4}}}$ k 1 _ 1 _ + k 2 _ 1 _ + k 3 _ 1 _ + 2 k 4 _ 3 _

Step-by-Step Verified Solution

Here, C 1 = 2 _ 0 k 1 A 3 d , C 2 = 2 _ 0 k 2 A 3 d C 3 = 2 _ 0 k 3 A 3 d , C 4 = 2 _ 0 k 4 A d Given system of C 1 , C 2 , C 3 and C 4 can be simplified as _ 1 C A B = 1 C 1 + C 2 + C 3 + 1 C 4 Suppose, C A B = k _ 0 A d C A B = 1 k ( _ 0 A d ) = 1 2 3 _ 0 A d ( k 1 + k 2 + k 3 ) + 1 2 _ 0 A d k 4 _ 1 k = 1 2 ( k 1 + k 2 + k 3 ) + 1 2 k 4 _ 2 k = 3 k 1 + k 2 + k 3 + 1 k 4

QNEET-2016-Ph-1182: NEET 2016 Physics - Class 12 NEET-2016-Ph-1182 Solution: A parallel-plate capacitor of area a plate separation d and…

Multiple Choice Options

Step-by-Step Verified Solution

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