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A parallel plate capacitor of area A, pl...

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 in the following 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

A

`1/k=1/k_1+1/k_2+1/(2k_3)`

B

`1/k=1/(k_1+k_2)+1/(2k_3)`

C

`k=(k_1k_2)/(k_1+k_2)+2k_3`

D

`k=(k_1 k_3)/(k_1+k_3)+(k_2 k_3)/(k_2+k_1)`

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The correct Answer is:
B
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Knowledge Check

  • 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 dielectic constant k is given by

    A
    (a) `1/K=1/K_1+1/K_2+1/(2K_3)`
    B
    (b) `1/K=(1)/(K_1+K_2)+1/(2K_3)`
    C
    (c) `K=(K_1K_2)/(K_1+K_2)+2K_3`
    D
    (d) `K=K_1+K_2+2K_3`

  • 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 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

    A
    `(2)/(k)= (3)/(k_(1) + k_(2) + k_(3)) + (1)/(k_(4))`
    B
    `(1)/(k)= (1)/(k_(1)) + (1)/(k_(2)) + (1)/(k_(1))= (3)/(2k_(4))`
    C
    `k= k_(1) + k_(2) + k_() + 3k_(4)`
    D
    `k=(2)/(3) (k_(1) + k_(2) + k_(3)) + 2k_(4)`

  • A parallel -plate capacitor of area A , plate separation d and capacitance C is filled with four dielectric materials having dielectric constant k_(1), k_(2), k_(3) and k_(4) as shown in the figure below. If a single dielectric materical is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by

    A
    `(2)/(k) = (3)/(k_(1) + k_(2) + k_(3)) + (1)/(k_(4))`
    B
    `(1)/(k) = (1)/(k_(1) + (1)/(k_(2)) + (1)/(k_(3)) + (3)/(2k_(4))`
    C
    `k = k_(1) + k_(2) + k_(3) + 3k_(4)`
    D
    `k = (2)/(3) (k_(1) + k_(2) + k_(3)) + 2k_(4)`
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