New Capacitance in Dielectric

Q.

Consider the combination of $2$ capacitors $C_1$ and $C_2$, with $C_2>C_1$, when connected in parallel, the equivalent capacitance is $\frac{15}{4}$ times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, $\frac{C_2}{C1}$

1. Imaginary

2. $\frac{15}{11}$

3. $\frac{29}{15}$

4. $\frac{15}{4}$

Q.

Find the minimum number of capacitors of 2 $\mu f$ each required. To obtain a capacitance of 5 $\mu f$.

Q. Two parallel-plate capacitors of capacitance $C$ and $2C$ are connected in parallel and charged to a potential difference $V$. The battery is then disconnected and the region between the plates of capacitor $C$ is filled completely with a material of dielectric constant $K$. The common potential difference across the combination becomes

1. $\frac{2V}{K+2}$
2. $\frac{2V}{K+2}$
3. $\frac{3V}{K+3}$
4. $\frac{3V}{K+2}$

Q. The greater the dielectric susceptibility, the greater is the ability of a material to polarize in response to the field, and thereby reduce the total electric field inside the material.

1. False
2. True

Q. A parallel-plate capacitor of area $A$, plate separation 𝑑, and capacitance $C$ is filled with four dielectric material having dielectric constants $k_1,k_2,k_3$ and $k_4$ as shown in the figure. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $k$ is given by

1. $k=k_1+k_2+k_3+3k_4$
2. $K=\frac{2}{3}(k_1+k_2+k_3)+2k_4$
3. $\frac{2}{k}=\frac{3}{k_1+k_2+k_3}+\frac{1}{k_4}$
4. $\frac{1}{k_4}=\frac{1}{k_1}+\frac{1}{k_2}+\frac{1}{k_3}+\frac{3}{2k_4}$

Q. A parallel-plate capacitor of area $A$, plate separation 𝑑, and capacitance $C$ is filled with four dielectric material having dielectric constants $k_1,k_2,k_3$ and $k_4$ as shown in the figure. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $k$ is given by

1. $k=k_1+k_2+k_3+3k_4$
2. $K=\frac{2}{3}(k_1+k_2+k_3)+2k_4$
3. $\frac{2}{k}=\frac{3}{k_1+k_2+k_3}+\frac{1}{k_4}$
4. $\frac{1}{k_4}=\frac{1}{k_1}+\frac{1}{k_2}+\frac{1}{k_3}+\frac{3}{2k_4}$

Q. A parallel- plate capacitor is placed in such a way that its plates are horizontal and lower plate is dipped into a liquid of dielectric constant $k$ and density $\rho$. Charge on plates of capacitor is $Q$ and $-Q$. [$+Q$ is charge on upper plate]

1. Level of liquid in the space between plates rises.
2. Level of liquid in the space between plates falls.
3. Net charge on the lower plate is $\frac{-Q}{k}$.
4. Charge induced on the upper surface of liquid is $-Q(1-k)$

Q.

A parallel plate capacitor is charged by connecting its plates to the terminals of a battery. The battery is then disconnected and a glass plate is interposed between the plates of the capacitor, then

1. The capacity increases while the potential difference decreases

2. The capacity increases while the potential difference increases

3. The capacity decreases while the potential difference increases

4. capacity decreases while the potential difference decreases

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.

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. Two identical parallel-plate capacitors are connected in series and then joined across a battery of 100 V. A slab of dielectric constant K = 3 is inserted between the plates of the first capacitor. Then, the potential difference across the capacitors will respectively be

1. 25 V, 75 V
2. 75 V, 25 V
3. 20 V, 80 V
4. 50 V, 50 V

Q. The capacities of the three capacitors are in ratio 1 : 2 : 3. Their equivalent capacity when connected in parallel is $\frac{60}{11}\mu F$ more than when they are connected in series. The individual capacities of capacitors in $\mu F$ are?

1. 4, 6, 7
2. 1, 2, 3
3. 2, 3, 4
4. 1, 3, 6

Q. A parallel plate condenser of capacity 5 $\mu$ F is kept connected to a battery of emf 10 V. If the space between the plates is filled with a medium of dielectric constant 12, then the additional charge taken from the battery is?

1. $400\mu c$
2. $450\mu c$
3. $500\mu c$
4. $550\mu c$

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. Find the capacitance of the system

1. $\frac{ϵA}{d}$
2. $\frac{ϵA}{d-t}$
3. $\frac{ϵA}{d-t+t/k}$
4. $\frac{kϵA}{t}$

Q. In the circuit shown, charge on the $5\mu \text{F}$ capacitor is

1. $18.00\mu \text{C}$
2. $10.90\mu \text{C}$
3. $5.45\mu \text{C}$
4. $16.36\mu \text{C}$

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.

I have an insulator with dielectric constant k. If I place it in a region in vacuum with a field E, what is the induced field inside the dielectric?

1. $-\frac{E}{k}$

2. $E(1-\frac{1}{k})$

3. $E(1+\frac{1}{k})$

4. $E(1-k)$

Q.

I have an insulator with dielectric constant k. If I place it in a region in vacuum with a field E, what is the induced field inside the dielectric?

1. $-\frac{E}{k}$

2. $E(1-\frac{1}{k})$

3. $E(1+\frac{1}{k})$

4. $E(1-k)$

Q. A parallel plate condenser of capacity 5 $\mu$ F is kept connected to a battery of emf 10 V. If the space between the plates is filled with a medium of dielectric constant 12, then the additional charge taken from the battery is?

1. $400\mu c$
2. $450\mu c$
3. $500\mu c$
4. $550\mu c$

Q. A parallel- plate capacitor is placed in such a way that its plates are horizontal and lower plate is dipped into a liquid of dielectric constant $k$ and density $\rho$. Charge on plates of capacitor is $Q$ and $-Q$. [$+Q$ is charge on upper plate]

1. Level of liquid in the space between plates rises.
2. Level of liquid in the space between plates falls.
3. Net charge on the lower plate is $\frac{-Q}{k}$.
4. Charge induced on the upper surface of liquid is $-Q(1-k)$