A parallel plate capacitor is to be designed | vedclass

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

Question

(C) Given:Voltage rating,$V = 1\; kV = 1000\; V$Dielectric constant,$\varepsilon_{r} = 3$Dielectric strength,$E_{max} = 10^{7}\; V/m$Safety limit for

Vedclass · Accepted Answer

$19$

Vedclass · Answer

(C) Given:Voltage rating,$V = 1\; kV = 1000\; V$Dielectric constant,$\varepsilon_{r} = 3$Dielectric strength,$E_{max} = 10^{7}\; V/m$Safety limit for electric field,$E = 10\% 	ext{ of } 10^{7} = 10^{6}\; V/m$Capacitance,$C = 50\; pF = 50 	imes 10^{-12}\; F$The distance $d$ between the plates is given by $d = V/E = 1000 / 10^{6} = 10^{-3}\; m$.Using the formula for capacitance $C = \frac{\varepsilon_{0} \varepsilon_{r} A}{d}$,we can find the area $A$:$A = \frac{C \cdot d}{\varepsilon_{0} \cdot \varepsilon_{r}}$Substituting the values:$A = \frac{50 	imes 10^{-12} 	imes 10^{-3}}{8.854 	imes 10^{-12} 	imes 3}$$A = \frac{50 	imes 10^{-15}}{26.562 	imes 10^{-12}} \approx 1.882 	imes 10^{-3}\; m^2$Converting to $cm^2$ $(1\; m^2 = 10^{4}\; cm^2)$:$A \approx 1.882 	imes 10^{-3} 	imes 10^{4} = 18.82\; cm^2 \approx 19\; cm^2$.

Similar Questions

Two parallel plate capacitors with different plate separations but the same capacitance are connected in series to a battery. Both capacitors are filled with air. The quantity that is $NOT$ the same for both the capacitors when they are fully charged is:

$A$ parallel plate capacitor is charged by a battery and then the battery is disconnected. If the distance between the plates is increased using an insulated handle,then:

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).

Seven identical plates each of area $A$ and successive separation $d$ are arranged as shown in the figure. The effective capacitance of the system between $P$ and $Q$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module