Half of the space between a parallel plate capacitor is filled with a medium of dielectric constant K parallel to the plates. If initially the capacity was C. Then the new capacity will be:

\frac{2 K C}{(1 + K)}

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\frac{C (K + 1)}{2}

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C K (1 + K)

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K C

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Solution

The correct option is A $\frac{2 K C}{(1 + K)}$
REF. Image.
$C^{1} = ϵ_{0} A [\frac{ϵ_{r_{1}} ϵ_{r_{2}}}{d_{1} ϵ_{r_{1}} + d_{2} ϵ_{r_{2}}}]$
$d_{1} = d_{2} = d / 2$
$ϵ_{r_{1}} = k$
$ϵ_{r_{2}} = 1$
$c = \frac{ϵ_{0} A}{d}$
$c^{1} = \frac{ϵ_{0} A}{d} [\frac{2 k}{k + 1}]$
$c^{1} = \frac{2 c k}{k + 1}$

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Half of the space between a parallel plate capacitor is filled with a medium of dielectric constant K parallel to the plates. If initially the capacity was C. Then the new capacity will be:

The correct option is A 2KC(1+K)REF. Image.C1=ϵ0A[ϵr1ϵr2d1ϵr1+d2ϵr2]d1=d2=d/2ϵr1=kϵr2=1c=ϵ0Adc1=ϵ0Ad[2kk+1]c1=2ckk+1