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  4. Separation between the plates of a parallel plate capacitor is 5 mm . This capacitor, having air as the dielectric medium between the plates, is charged to a potential difference 25 V using a battery. The battery is then disconnected and a dielectric slab of thickness 3 mm and dielectric constant K=10 is placed between the plates as shown. Potential difference between the plates after the dielectric slab has been introduced is - <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-9kaimrj7mf74.png />

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Q. Separation between the plates of a parallel plate capacitor is $5 \, mm$ . This capacitor, having air as the dielectric medium between the plates, is charged to a potential difference $25 \, V$ using a battery. The battery is then disconnected and a dielectric slab of thickness $3 \, mm$ and dielectric constant $K=10$ is placed between the plates as shown. Potential difference between the plates after the dielectric slab has been introduced is -

Question

NTA AbhyasNTA Abhyas 2020Electrostatic Potential and Capacitance

Solution:

As the charge remain constant, hence
$Q=CV=C_{1}V_{1}$
$Q=\frac{\epsilon _{0} A}{d}V=\frac{\epsilon _{0} A}{d - t + \frac{t}{K}}V_{1}$

$\frac{\varepsilon_0 A}{0.005}(25)=\frac{\varepsilon_0 A}{0.002+\frac{0.003}{10}}(V)$
$V =11.5 \, \text{V}$