A parallel plate capacitor with air between the plates is charged to a potential difference of $500V$ and then insulated. A plastic plate is inserted between the plates filling the whole gap. The potential difference between the plates now becomes $75V$. The dielectric constant of plastic is :

A

$10/3$

B

$5$

C

$20/3$

D

$10$

Medium

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Solution

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Correct option is

C

$20/3$

If $C$ be the air filled capacitance , dielectric filled capacitance becomes $C_{′}=KC$ where K is the dielectric constant. Initial charge , $q_{i}=CV_{i}=500C$ and final charge $q_{f}=C_{′}V_{f}=75KC$ As the system is isolated so charge will be constant. Thus, $q_{i}=q_{f}$ $⇒500C=75KC⇒K=75500 =20/3$