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Q.

A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k1, k2,k3 and k4 as shown in the figure below. 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

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a

k=k1+k2+k3+3k4

b

k=23k1+k2+k3+2k4

c

2k=3k1+k2+k3+1k4

d

k=2K43k1k1+k4+k2k2+k4+k3k3+k4

answer is C.

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Detailed Solution

c1=2k1ε0A3d, c2=2k2ε0A3d, c3=2k3ε0A3d,if c=ε0Ad C1=2k1c3, C2=2k2c3, C3=2k3c3Since c1,c2 ,c3 are parallel ; cp = c1 + c2 + c3=2c3k1+k2+k3 ; c4=2k4ε0Ad=2k4cSince cp and c4 are series 1cs=1cp+1c41kc=32ck1+k2+k3+12k4c 2k=3k1+k2+k3+1k4
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