Q.

A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric constants k1,  k2  and k3 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[Take k1=2 , k2=4 , k3=6 ]

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answer is 3.90.

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Detailed Solution

C1=k1∈0A2d2=k1∈0Ad C2=k2∈0A2d2=k2∈0Ad and C3=k3∈0A2d2=k3∈0Ad  Ceff = C1C3C1+C3 + C2C3C2+C3 ⇒Ceff = ∈0Adk1k3k1+k3+k2k3k2+k3 Hence, keff = k1k3k1+k3+k2k3k2+k3=128+2410=3.9
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