New Capacitance in Dielectric

Q. The radius of a thin wire is 0.16 mm. Thearea of cross-section taking significantfiguremillimetres isintoconsideration0Zinsquare

Q. Three different dielectrics are filled in a parallel plate capacitor as shown. What should be the value of dielectric constant of a material , which when fully filled between the plates produces same capacitance ? (Asssume terminals are connected between $AC$ and $BD$).

1. $6$
2. $9$
3. $4$
4. $5$

Q.

The capacity of a parallel plate condenser is . When a glass plate is

placed between the plates of the conductor, its potential becomes 1/8thof

the original value. The value of dielectric constant will be

1. 1.6

2. 5

3. 8

4. 40

Q. Three different dielectrics are filled in a parallel plate capacitor as shown. What should be the value of dielectric constant of a material , which when fully filled between the plates produces same capacitance ? (Asssume terminals are connected between $AC$ and $BD$).

1. $5$
2. $6$
3. $9$
4. $4$

Q. A parallel plate air condenser has a capacity ‘C’. When the plate separation is halved and a dielectric of constant k is inserted, new capacitance is found to be 12C. The value of dielectric constant ‘k’ is?

1. 12
2. 24
3. 6
4. 3

Q. The dimension of Eo E^2/2 (Eo is permittivity of free space; E: electric field) is?

Q. A capacitor is formed by two square metal plates of edge $1\text{m}$, separated by a distance $1\text{mm}$. Dielectrics of dielectric constant $K_1$ and $K_2$ are filled in the gap as shown in figure. The new capacitance is


$[$ Take $\ln 2=0.7]$

1. $15\text{nF}$
2. $25\text{nF}$
3. $10\text{nF}$
4. $20\text{nF}$

Q. I have an insulator with dielectric constant k. If I place it in a region in vacuum with a field E. Then the net field inside the dielectric will be?

1. $Ek$
2. $\frac{E}{k}$
3. $\frac{E}{k^2}$
4. $E{k}^2$

Q. Two parallel-plate capacitors, each of capacitance $40\mu F$, are connected in series. The space between the plates of one capacitor is filled with a dielectric of dielectric constant $K=3$, then the equivalent capacitance of the combination is

1. $30\mu F$
2. $120\mu F$
3. $40\mu F$
4. $160\mu F$

Q. The plates of a parallel plate capacitor are charged up to $100\text{V}$. Now, after removing the battery, a $2\text{mm}$ thick plate is inserted between the plates . Then, to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\text{mm}$. The dielectric constant of the plate is

1. $2.5$
2. $4$
3. $5$
4. $1.25$

Q. The plates of a parallel plate capacitor are charged up to $100\text{V}$. Now, after removing the battery, a $2\text{mm}$ thick plate is inserted between the plates . Then, to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\text{mm}$. The dielectric constant of the plate is

1. $5$
2. $1.25$
3. $4$
4. $2.5$

Q. A parallel plate condenser has a capacitance 50μF in air and 110μF when immersed in an oil. The dielectric constant of the oil is?

1. 0.45

2. 0.55

3. 1.10

4. 2.20

Q. A dielectric slab of dielectric constant $k=5$ is placed between plates of parallel plate capacitor, thickness of slab is $30$% of plate spacing & its area is same as that of the plates, new capacitance is $C^{\prime }$ & old capacitance was $C$. The ratio $\frac{C^{\prime }}{C}$ is approximately equal to

1. $\frac{5}{4}$
2. $\frac{3}{5}$
3. $\frac{7}{5}$
4. $\frac{4}{3}$

Q. When a capacitor of capacitance C is filled with a dielectric (i.e. thickness of the dielectric is equal to the spacing between the plates) of dielectric constant k, what is the new capacitance?

1. $Ck$
2. $\frac{C}{k}$
3. $C{k}^2$
4. $\frac{C}{k^2}$

Q. The figure shows a parallel plate capacitor with charge $Q_1$ and plate area A. Capacitor is filled with two dielectrics $k_1$ and $k_2$ as shown.

1. Ratio of energy density in first dielectric to second dielectric is $\frac{5}{3}$
2. Ratio of energy stored in the two dielectrics is 1 : 1
3. Surface charge at interface of the two dielectrics is $\frac{2Q}{15}$
4. Surface charge at interface of the two dielectrics is 0.

Q. A capacitor is formed by two square metal plates of edge $1\text{m}$, separated by a distance $1\text{mm}$. Dielectrics of dielectric constant $K_1$ and $K_2$ are filled in the gap as shown in figure. The new capacitance is


$[$ Take $\ln 2=0.7]$

1. $25\text{nF}$
2. $10\text{nF}$
3. $20\text{nF}$
4. $15\text{nF}$

Q. When a dielectric material is introduced between the plates of a charges condenser, then electric field between the plates
[Pb PMT 2004]

1. Remain constant
2. Decreases
3. Increases
4. First increases then decreases

Q. Figure shows a parallel plate capacitor having square plates of edge length $a$ and separation $d$. The gap between the plates is filled with a dielectric of dielectric constant $K$ which varies parallel to an edge as, $K=K_o+\alpha x$
Where, $K$ and $\alpha$ are constants and $x$ is the distance from the left end. Calculate the capacitance of system.

1. $\frac{{ϵ}_{o}a{K}_o\alpha }{2d}$
2. $\frac{{ϵ}_o{a}^2{K}_o}{d}$
3. $\frac{{ϵ}_o{a}^2(K_o+a\alpha )}{2}$
4. $\frac{{ϵ}_o{a}^2}{d}(K_o+\frac{a\alpha }{2})$

Q. A hemispherical earth plate is buried into the earth. Find the potential difference between the feet of a man standing on ground as shown in figure. Current through earth plate is I. Conductivity of earth is [$\delta ={10}^{-3}\pi ,I=1A$](up to two decimal places)