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If the area of each plate is A and then ...

If the area of each plate is A and then successive separations are `d, 2d` and `3d`, then find the equivalent capacitance across A and B.
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Text Solution

Verified by Experts

The correct Answer is:
`(epsilon_(0)A)/(4d)`
.
Plates can be rearranged as shown in
plates `1` and `2` and plates `3` and `4` form two capacitors, which are in series between `A` and `B` plates `2` and `3` do not form any capacitor as they at the same potential.
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`C_(eq)=(C_(1)C_(2))/(C_(1)+C_(2))=((epsilon_(0)A/d)xx((epsi_(0)A)/3d))/((epsi_(0)A)/(d)+(epsi_(0)A)/(3d))=(epsi_(0))/(4d)`
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Knowledge Check

  • Find the equivalent capacitance across A & B

    A
    `(28)/(3)muF`
    B
    `(15)/(2) muF`
    C
    `15 muF`
    D
    None

  • Four plates of the same area of cross-section are joined as shown in the figure. The distance each plate is d . The equivalent capacity across A and B will be

    A
    `(2epsilon_(0)A)/(d)`
    B
    `(3epsilon_(0)A)/(d)`
    C
    `(3epsilon_(0)A)/(2d)`
    D
    `(epsilon_(0)A)/(d)`

  • Six plates each of area A arranged as shown· in figure. The separation between adjoining plates is d . Find the equivalent capacitance between points A and B :

    A
    `(epsilon_(0)A)/d`
    B
    `(7epsilon_(0)A)/d`
    C
    `(6epsilon_(0)A)/d`
    D
    `(5epsilon_(0)A)/d`

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