question_answer

Two long cylindrical metal tubes stand on insulating floor. A dielectric oil is filled between plates. Two tubes are maintained with potential difference \[V.\text{ }A\]small hole is opened at bottom then

A) Reading of ammeter decreases

B) Capacitance of system increases

C) Current in circuit is dependent on area of hole

D) Current in circuit is inversely proportional to dielectric constant

Correct Answer: C

Solution :

\[q=CV\]

=\[\left[ \frac{{{\varepsilon }_{0}}\left( l-x \right)}{\ell n\left( \frac{b}{a} \right)}+{{n}_{2}}\frac{{{\varepsilon }_{0}}xk}{\ell n\left( \frac{b}{a} \right)} \right]V\]

Now \[i=\frac{dq}{dt}\]

\[=\frac{{{\varepsilon }_{0}}}{\ell n\left( \frac{b}{a} \right)}(k-1){{\left( \frac{dx}{dt} \right)}^{V}}\]

As\[\frac{dx}{dt}\] depends on the area of the hole, so \[i\]in the circle depends on area of the hole.