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  4. A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K = (5/3) is inserted between the plates, the magnitude of the induced charge will be :

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Q. A parallel plate capacitor of capacitance $90\, pF$ is connected to a battery of emf $20\, V$. If a dielectric material of dielectric constant $ K = \frac{5}{3} $ is inserted between the plates, the magnitude of the induced charge will be :

JEE MainJEE Main 2018Electrostatic Potential and Capacitance

Solution:

$C'=K C_{0}$
$Q=K C_{0} V$
$Q_{\text {induced }}=Q\left(1-\frac{1}{K}\right)$
$=\frac{5}{3} \times 90 \times 10^{-12} \times 20\left(1-\frac{3}{5}\right)$
$=1.2\, nC$