A parallel plate capacitor with air between the plates has a capacitance of $9\,pF$. The separation between its plates is $'d'$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1=3$ and thickness $\frac {d}{3}$ while the other one has dielectric constant $K_2 = 6$ and thickness $\frac {2d}{3}$ . Capacitance of the capacitor is now........$pF$
Medium
Download our app for free and get started
$\frac{\varepsilon_{\mathrm{o}} \mathrm{A}}{\mathrm{d}}=9 \mathrm{\,PF}$
$\mathrm{C}^{\prime}=\frac{\frac{\varepsilon_{\mathrm{o}} \times 3 \mathrm{A}}{\mathrm{d} / 3} \times \frac{\varepsilon_{\mathrm{o}} \times 6 \mathrm{A}}{2 \mathrm{d} / 3}}{\frac{\varepsilon_{\mathrm{o}} \times 3 \mathrm{A}}{\mathrm{d} / 3}+\frac{\varepsilon_{\mathrm{o}} \times 6 \mathrm{A}}{2 \mathrm{d} / 3}}=\frac{\frac{9 \varepsilon_{\mathrm{o}} \mathrm{A}}{\mathrm{d}} \times \frac{9 \varepsilon_{\mathrm{o}} \mathrm{A}}{2 \mathrm{d}}}{\frac{18 \varepsilon_{\mathrm{o}} \mathrm{A}}{2 \mathrm{d}}}=\frac{9}{2} \frac{\varepsilon_{\mathrm{o}} \mathrm{A}}{\mathrm{d}}$
$C^{\prime}=\left(\frac{9}{2} \times 9\right) \,p F=40.5 \,p F$
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
- 1Choose the correct statement for the given capacitor arrangement. (All the $6$ capacitor are of same capacitance)View Solution
- 2A $30\,\mu F$ 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
- 3View SolutionAssertion : Two equipotential surfaces cannot cut each other.
Reason : Two equipotential surfaces are parallel to each other.
- 4Two parallel plate capacitors $C_1$ and $C_2$ each having capacitance of $10 \mu F$ are individually charged by a $100\,V$ $D.C.$ source. Capacitor $C _1$ is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor $C _2$ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor $C_1$ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be $.........V.$ (Assuming Dielectric constant $=10$ )View Solution
- 5View SolutionTwo identical conductors of copper and aluminium are placed in an identical electric fields. The magnitude of induced charge in the aluminium will be
- 6In the figure shown below, the charge on the left plate of the $10\, \mu F$ capacitor is $-30\,\mu C.$ The charge on the right place of the $6\,\mu F$ capacitor is.....$\mu C$View Solution
- 7Three capacitors of capacitances $25 \mu \mathrm{F}, 30 \mu \mathrm{F}$ and $45 \mu \mathrm{F}$ are connected in parallel to a supply of $100$View Solution
$V$. Energy stored in the above combination is $\mathrm{E}$. When these capacitors are connected in series to the same supply, the stored energy is $\frac{9}{\mathrm{x}} \mathrm{E}$. The value of $x$ is___________.
- 8At time $\mathrm{t}=0$, a battery of $10 \mathrm{~V}$ is connected across points $\mathrm{A}$ and $\mathrm{B}$ in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them becomes $4$ volt?View Solution
[take $\ln 5=1.6, \ln 3=1.1]$
- 9An infinite number of charges each numerically equal to q and of the same sign are placed along the $x-$ axis at $x = 1,2,4,8.... \,metres$. Then the electric potential at $x = 0$ due to this set of charges isView Solution
- 10A cylindrical capacitor has two co-axial cylinders of length $20 \,cm$ and radii $2 r$ and $r$. Inner cylinder is given a charge $10 \,\mu C$ and outer cylinder a charge of $-10 \,\mu C$. The potential difference between the two cylinders will beView Solution