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QJEEM23Ph3f1c: JEE Main 2023 Physics - Class 12 JEEM23Ph3f1c Solution: A parallel plate capacitor with air between the plate has a…

A parallel plate capacitor with air between the plate has a capacitance of 15pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes x4\frac{x}{4} pF. The value of xx is ____________.

Step-by-Step Verified Solution

Initially

ε0Ad=15×10−12 F\frac{\varepsilon_{0} A}{d}=15 \times 10^{-12} \mathrm{~F}

Finally

amp;3.5ε0A2d=x4×10−12 Famp;∴3.52×15=x4amp;⇒x=3.5×15×42=105\begin{aligned}& \frac{3.5 \varepsilon_{0} A}{2 d}=\frac{x}{4} \times 10^{-12} \mathrm{~F} \\\\& \therefore \frac{3.5}{2} \times 15=\frac{x}{4} \\\\& \Rightarrow x=\frac{3.5 \times 15 \times 4}{2}=105\end{aligned}

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