Question

The capacitance of a parallel plate condenser is $C_{1}$(fig. a). A dielectric of dielectric constant ‘K’ is inserted as shown in figure ‘b’ and ‘c’. If $C_{2}$ and $C_{3}$ are the capacitances in figures ‘b’ and ‘c’ then :

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Correct option is A)

$C_{1}=d.ε_{0}A $

b) In $C_{2}dkε_{0}A2 anddε_{o}A2 $ are in series

$⇒C_{2}1 =kεA2d +2ε_{0}Ad =2ε_{0}Ad (k1 +1)$

$⇒C_{2}=dε_{0}A (1+k2k )$ we know k>1

$∴1+k2k >1.$

$∴C_{2}>C_{1}.$

c) in $C_{3}2dkε_{0}A anddkε_{o}A $ are in parallel

$∴C_{3}=dε_{0}A (2k +1)$

$∴C_{3}>C_{1}.$

b) In $C_{2}dkε_{0}A2 anddε_{o}A2 $ are in series

$⇒C_{2}1 =kεA2d +2ε_{0}Ad =2ε_{0}Ad (k1 +1)$

$⇒C_{2}=dε_{0}A (1+k2k )$ we know k>1

$∴1+k2k >1.$

$∴C_{2}>C_{1}.$

c) in $C_{3}2dkε_{0}A anddkε_{o}A $ are in parallel

$∴C_{3}=dε_{0}A (2k +1)$

$∴C_{3}>C_{1}.$

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