Question

Dielectric sheet placed between the plates of parallel plate capacitor. Now capacitor is charged and battery is disconnected. Now $t=0$ sheet is taken out very slowly then which of the following is correct for the variation of capacitance with time

Answer 1

Let the distance between plates be $d$ and length of sheet be $a$.

Now, at same instant let sheet has been taken out by the distance of x

This system can be considered as a combination of two capacitors connected in parallel: one capacitance without dielectric with plate length x and other capacitor with dielectric with plate length $(a-x)$

equivalent capacitance will be

$C=\frac{\left(bx\right){ϵ}_0}{d}+\frac{k{ϵ}_0(a-x)b}{d}$

(b = plate width)

$=\frac{ab{ϵ}_{0}k}{d}-\frac{{ϵ}_{0}b(k-1)}{d}x$

Now, let the dielectric is being pulled out at constant slow speed of $v$

then at time $t$

$x=vt$

$C=\frac{ab{ϵ}_{0}k}{d}-\frac{{ϵ}_{0}b(k-1)}{d}vt$

this equation is of the form of a straight line with -ve slope

$\therefore$ Graph of C - t curve will have negative slope with +ve y - axis intercept.
Hence, correct option is (c)