In one design of capacitor thin sheets ot metal of area $80\ mm \times 80\ mm$ sandwich between them a piece of paper whose thickness is $40\ μm$. The relative permittivity of the paper is $4.0$ and its dielectric strength is $20\ MVm^{-1}$. Calculate the maximum charge that can be put on the capacitor
[permittivity of free space $ = 9 \times 10^{-12}\ Fm^{-1}$]
Medium
Download our app for free and get started
$\mathrm{E}_{\max }=20 \times 10^{6}-\frac{\mathrm{V}}{\mathrm{d}}$
$\mathrm{V}=20 \times 10^{6} \times 40 \times 10^{-6}=800$
$Q_{\max }=C V=\frac{K \epsilon_{0} A}{d} V$
$ = \frac{{4 \times 5 \times {{10}^{ - 12}} \times 6400 \times {{10}^{ - 6}}}}{{40 \times {{10}^{ - 6}}}} \times 800$
$=4608 \times 10^{-9} \mathrm{\,C}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1The total charge on the system of capacitance $C _{1}=1\,\mu F , C _{2}=2\,\mu F , C _{3}=4\,\mu F$ and $C _{4}=3\,\mu F$ connected in parallel is $......\mu C$ (Assume a battery of $20\,V$ is connected to the combination)View Solution
- 2A capacitor of capacity ${C_1}$ is charged to the potential of ${V_o}$. On disconnecting with the battery, it is connected with a capacitor of capacity ${C_2}$ as shown in the adjoining figure. The ratio of energies before and after the connection of switch $S$ will beView Solution
- 3A capacitor of capacitance $C_1 = 1\ \mu F$ can with stand maximum voltage $V_1= 6\ kV$ (kilo-volt) and another capacitor of capacitance $ C_2 = 3\ \mu F$ can withstand maximum voltage $V_2 = 4\ kV$. When the two capacitors are connected in series, the combined system can withstand a maximum voltage of......$kV$View Solution
- 4A parallel plate air capacitor has capacity $C,$ distance of separation between plates is $d$ and potential difference $V$ is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor isView Solution
- 5Potential at a point $x$-distance from the centre inside the conducting sphere of radius $R$ and charged with charge $Q$ isView Solution
- 6A $2\,\mu F$ Capacitor is charged as shown in the figure. The percentage of its store energy dissipated after the switch $S$ is turned to position $2$, is.....$\%$View Solution
- 7A $40$ $\mu F$ capacitor in a defibrillator is charged to $3000\,V$. The energy stored in the capacitor is sent through the patient during a pulse of duration $2\,ms$. The power delivered to the patient is......$kW$View Solution
- 8What is the effective capacitance between $A$ and $B$ in the following figure........$\mu \,F$View Solution
- 9Find the equivalent capacitance between $A$ and $B$.......$\mu f$View Solution
- 10The dielectric strength of air at $NTP$ is $3 \times {10^6}\,V/m$ then the maximum charge that can be given to a spherical conductor of radius $3\, m$ isView Solution