A parallel plate capacitor has capacitance C . If it is equally filled with parallel layers of mater

English

Gujarati

Hindi

2. Electric Potential and Capacitance

medium

A parallel plate capacitor has capacitance $C$. If it is equally filled with parallel layers of materials of dielectric constants $K_1$ and $K_2$ its capacity becomes $C_1$. The ratio of $C_1$ to $C$ is

A

${K_1} + {K_2}$

B

$\frac{{{K_1}{K_2}}}{{{K_1} - {K_2}}}$

C

$\frac{{{K_1} + {K_2}}}{{{K_1}{K_2}}}$

D

$\frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}$

Solution

(d)${C_A} = \frac{{{K_1}{\varepsilon _0}A}}{{d/2}},\,{C_B} = \frac{{{K_2}{\varepsilon _0}A}}{{d/2}}$
${C_{eq}} = \frac{{{C_1}}}{{{C_2}}} = \frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}$
$ = \frac{{{C_A}{C_B}}}{{{C_A} + {C_B}}} = \left( {\frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}} \right)\,\frac{{{\varepsilon _0}A}}{d}$ $\left( {\,\,c = \frac{{{\varepsilon _0}A}}{d}} \right)$

Standard 12

Physics

Share

Similar Questions

A parallel plate capacitor with air between the plate has a capacitance of $15 pF$. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant $3.5.$ Then the capacitance becomes $\frac{ x }{4}\,pF$.The value of $x$ is $…………$

medium

(JEE MAIN-2023)

A parallel plate capacitor has plates with area $A$ and separation $d$ . A battery charges the plates to a potential difference $V_0$ . The battery is then disconnected and a dielectric slab of thickness $d$ is introduced. The ratio of energy stored in the capacitor before and after the slab is introduced, is

medium

Figure given below shows two identical parallel plate capacitors connected to a battery with switch $S$ closed. The switch is now opened and the free space between the plate of capacitors is filled with a dielectric of dielectric constant $3$. What will be the ratio of total electrostatic energy stored in both capacitors before and after the introduction of the dielectric

hard

(IIT-1983)

Polar molecules are the molecules:

easy

(NEET-2021)

Two identical parallel plate capacitors are connected in series to a battery of $100\,V$. A dielectric slab of dielectric constant $4.0$ is inserted between the plates of second capacitor. The potential difference across the capacitors will now be respectively

medium