A capacitor is made of a tlat plate of area $A$ and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\frac{A}{3}$ and the height is $\mathrm{d}$, the capacitance of the arrangement is:
JEE MAIN 2024, Diffcult
Download our app for free and get started
All capacitor are in parallel combination.
Also effective area is common area only
$\Rightarrow C_{e q}=C_1+C_2+C_3$
$\Rightarrow C_{e q}=\frac{A \varepsilon_0}{3 d}+\frac{A \varepsilon_0}{3(2 d)}+\frac{A \varepsilon_0}{3(3 d)}$
$\Rightarrow C_{e q}=\frac{A \varepsilon_0}{3}\left(\frac{11}{6 d}\right)$
$\Rightarrow C_{e q}=\frac{11 A \varepsilon_0}{18 d}$
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 charge across the capacitor in two different $RC$ circuits $1$ and $2$ are plotted as shown in figure. Identify the correct statement$(s)$ related to the $R_1, R_2, C_1 $ and $C_2$ of the two $RC$ circuits.View Solution
- 2If $E$ is the electric field intensity of an electrostatic field, then the electrostatic energy density is proportional toView Solution
- 3A proton of mass $m$ and charge $e$ is projected from a very large distance towards an $\alpha$-particle with velocity $v$. Initially $\alpha$-particle is at rest, but it is free to move. If gravity is neglected, then the minimum separation along the straight line of their motion will beView Solution
- 4To form a composite $16\,\mu F,\;1000\,V$ capacitor from a supply of identical capacitors marked $8\,\mu F,\;250\,V$, we require a minimum number of capacitorsView Solution
- 5A $30\,\mu F$ capacitor is charged by a constant current of $30\, mA$. If the capacitor is initially uncharged, how long does it take for the potential difference to reach $400\, V$.....$s$View Solution
- 6A capacitor is connected to a battery of voltage $V$. Now a di electric slab of dielectric constant $k$ is completely inserted between the plates, then the final charge on the capacitor will beView Solution
(If initial charge is $q_{0}$ )
- 7A sphere of radius $1\,cm$ has potential of $8000\,V$, then energy density near its surface will beView Solution
- 8An electric dipole of moment $\overrightarrow p $ placed in a uniform electric field $\overrightarrow E $ has minimum potential energy when the angle between $\overrightarrow p $ and $\overrightarrow E $ isView Solution
- 9A dipole consisting of two charge $\pm q$ separated by a distance $2 a$ is placed with its centre $D$ away from the center of a grounded sphere of radius $R ( D > > a )$. When the dipole moment vector is perpendicular to the line joining the two centres (those of the dipole and sphere) the charge induced on the sphere isView Solution
- 10A capacitor is discharging through a resistor $R$. Consider in time $t _{1}$, the energy stored in the capacitor reduces to half of its initial value and in time $t_{2}$, the charge stored reduces to one eighth of its initial value. The ratio $t_{1} / t_{2}$ will be ................View Solution