What is a parallel plate capacitor? Obtain the formula for the capacitance of such a parallel plate capacitor and state the factors on which the value of capacitance depends.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance $d$.
$A$ non-conducting medium (dielectric) is typically kept between the two plates.
Let the charges on plate $1$ and plate $2$ be $+Q$ and $-Q$ respectively,$A$ be the area of each plate,and $d$ be the separation between them.
Since $d$ is much smaller than the linear dimensions of the plates $(d^2 << A)$,we can use the result for the electric field $E = \frac{\sigma}{2\epsilon_0}$ produced by an infinite plane sheet of uniform surface charge density $\sigma = \frac{Q}{A}$.
In the region between the plates,the electric fields due to both plates point in the same direction (from positive to negative plate):
$E = E_1 + E_2 = \frac{\sigma}{2\epsilon_0} + \frac{\sigma}{2\epsilon_0} = \frac{\sigma}{\epsilon_0} = \frac{Q}{A\epsilon_0}$.
The potential difference $V$ between the plates is given by $V = E \cdot d = \frac{Qd}{A\epsilon_0}$.
The capacitance $C$ is defined as $C = \frac{Q}{V} = \frac{Q}{(Qd / A\epsilon_0)} = \frac{\epsilon_0 A}{d}$.
The capacitance depends on:
$1$. The area of the plates $(A)$.
$2$. The distance between the plates $(d)$.
$3$. The permittivity of the medium between the plates ($\epsilon_0$ or $\epsilon = k\epsilon_0$).

Explore More

Similar Questions

$A$ capacitor is connected to a battery. What happens to the force of attraction between the plates when the separation between them is halved?

Charges of $2Q$ and $-Q$ are placed on two plates of a parallel plate capacitor. If the capacitance of the capacitor is $C$,the potential difference between the plates is:

Assertion : The total charge stored in a capacitor is zero.
Reason : The field just outside the capacitor is $\frac{\sigma }{{{\varepsilon _0}}}$. ( $\sigma $ is the charge density).

Five identical capacitor plates,each of area $A$,are arranged such that adjacent plates are at a distance $d$ apart. The plates are connected to a source of $emf$ $V$ as shown in the figure. Then the charges on plates $1$ and $4$ are,respectively:

Difficult
View Solution

The graph shows the variation of voltage $(V)$ across the plates of two parallel plate capacitors $A$ and $B$ versus the charge $(Q)$ stored in them. Then

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo