In a parallel plate capacitor with air between the plates, the distance ' $\mathrm{d}$ ' between the plates…
In a parallel plate capacitor with air between the plates, the distance ' $\mathrm{d}$ ' between the plates is changed and the space is filled with dielectric constant 8 . The capacity of the capacitor is increased 16 times, the distance between the plates is
$2 \mathrm{~d}$
$4 \mathrm{~d}$
$\frac{\mathrm{d}}{2}$
$\frac{\mathrm{d}}{4}$
Solution
$\mathrm{C}_1=\frac{\mathrm{A} \varepsilon_0}{\mathrm{~d}}$ ...(i)
$\mathrm{C}_2=\frac{8 \mathrm{~A} \varepsilon_0}{\mathrm{~d}^{\prime}} \Rightarrow 16 \mathrm{C}_1=\frac{8 \mathrm{~A} \varepsilon_0}{\mathrm{~d}^{\prime}}$
...(iii)
where $\mathrm{d}^{\prime}$ the unknown separation.
Dividing (i) by (ii)
$\frac{C_1}{16 C_1}=\frac{A \varepsilon_0}{d} \times \frac{d^{\prime}}{A \varepsilon_0}$
$\frac{8 \mathrm{~d}}{16}=\mathrm{d}^{\prime}$
$\therefore \quad \mathrm{d}^{\prime}=\frac{\mathrm{d}}{2}$