Between the plates of a parallel plate capaci | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) When the capacitor is disconnected from the battery, the charge $Q$ on the plates remains constant.The capacitance $C$ of a parallel plate capacit

Vedclass · Accepted Answer

Vedclass · Answer

(B) When the capacitor is disconnected from the battery, the charge $Q$ on the plates remains constant.The capacitance $C$ of a parallel plate capacitor with a dielectric is given by $C = \frac{K \epsilon_0 A}{d}$.As the dielectric plate of length $L$ is drawn out by a distance $x$, the capacitor can be considered as two capacitors in parallel: one with dielectric (length $L-x$) and one with air (length $x$).The equivalent capacitance $C(x)$ decreases as $x$ increases.Since $V = \frac{Q}{C}$, and $Q$ is constant, the potential difference $V$ increases as $C$ decreases.Specifically, $C(x) = \frac{\epsilon_0 w}{d} (L-x)K + \frac{\epsilon_0 w}{d} x = \frac{\epsilon_0 w}{d} [K(L-x) + x]$.As $x$ increases from $0$ to $L$, $C(x)$ decreases linearly, which means $V(x) = \frac{Q}{C(x)}$ will increase non-linearly (specifically, it follows a hyperbolic curve $V \propto \frac{1}{a-bx}$).Once the dielectric is completely removed $(x=L)$, the capacitance becomes constant $(C_{air} = \frac{\epsilon_0 A}{d})$, and thus the potential difference $V$ becomes constant.Graph $B$ correctly shows $V$ increasing non-linearly and then becoming constant.

Similar Questions

The force between two point charges placed in a material medium of dielectric constant $K$ is $F$. If the material is removed,then the force between them becomes . . . . . . .

In the given circuit,two identical capacitors $C_1$ and $C_2$ are connected to a battery. The space between the plates of $C_1$ is filled with air,while the space between the plates of $C_2$ is filled with a dielectric material of dielectric constant $K$. Then,

$A$ parallel plate capacitor is connected to the terminals of a battery. The distance between the plates is $6\,mm$. If a glass plate (dielectric constant $K = 9$) of thickness $4.5\,mm$ is introduced between them,then the capacity will become how many times the original capacity?

Vedclass Test Series

Exam Paper Generator

Online Exam Module