Effect of Dielectric Charging and Discharging of Capacitor
Capacitance

165954 Two materials having the dielectric constants $K_{1}$ and $K_{2}$ are filled between two parallel plates of a capacitor, which is shown in figure. The capacity of the capacitor is :

1 $\frac{\mathrm{A} \varepsilon_{0}\left(\mathrm{~K}_{1} \times \mathrm{K}_{2}\right)}{\mathrm{d}\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right)} \mathrm{A}$
2 $\frac{A \varepsilon_{0}\left(K_{1}-K_{2}\right)}{d}$
3 $\frac{\mathrm{A} \varepsilon_{0} \mathrm{~K}_{1} \mathrm{~K}_{2}}{\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)}$
4 $\frac{A \varepsilon_{0}\left(K_{1}+K_{2}\right)}{d}$
Capacitance

165955 In a parallel plate with air capacitor of capacitance $8 \mu \mathrm{F}$, if the lower half of the air space is filled with a material of dielectric constant 3, its capacitance changes to:

1 $3 \mu \mathrm{F}$
2 $12 \mu \mathrm{F}$
3 $16 \mu \mathrm{F}$
4 $24 \mu \mathrm{F}$
Capacitance

165956 A parallel plate capacitor is formed by two plates each of areas $30 \pi \mathrm{cm}^{2}$ separated by $1 \mathrm{~mm}$. A material of dielectric strength $3.6 \times 10^{7}$ $\mathrm{Vm}^{-1}$ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is $7 \times 10^{-6} \mathrm{C}$, the value of dielectric constant of the material is:
$\left[\text { Use } \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} \mathrm{C}^{-2}\right]$

1 1.66
2 1.75
3 2.25
4 2.33
Capacitance

165957 Two positive point charges of $10 \mu \mathrm{C}$ and $12 \mu \mathrm{C}$ are placed $10 \mathrm{~cm}$ apart in air. The work done to bring them $6 \mathrm{~cm}$ closer is

1 $8.1 \mathrm{~J}$
2 $3.2 \mathrm{~J}$
3 $9 \mathrm{~J}$
4 $13.5 \mathrm{~J}$
Capacitance

165958 A capacitor of capacitance $20 \mu \mathrm{F}$ is charged by a battery of potential $24.3 \mathrm{~V}$. The capacitor is then disconnected from the battery and is connected to another uncharged capacitor of capacitance $10 \mu \mathrm{F}$. After some time, the second capacitor is disconnected, discharged fully and is again connected to the first capacitor. If the process is repeated several times, the charge on the first capacitor at the end of the fifth process is $\mu \mathrm{C}$.

1 256
2 128
3 64
4 32
Capacitance

165954 Two materials having the dielectric constants $K_{1}$ and $K_{2}$ are filled between two parallel plates of a capacitor, which is shown in figure. The capacity of the capacitor is :

1 $\frac{\mathrm{A} \varepsilon_{0}\left(\mathrm{~K}_{1} \times \mathrm{K}_{2}\right)}{\mathrm{d}\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right)} \mathrm{A}$
2 $\frac{A \varepsilon_{0}\left(K_{1}-K_{2}\right)}{d}$
3 $\frac{\mathrm{A} \varepsilon_{0} \mathrm{~K}_{1} \mathrm{~K}_{2}}{\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)}$
4 $\frac{A \varepsilon_{0}\left(K_{1}+K_{2}\right)}{d}$
Capacitance

165955 In a parallel plate with air capacitor of capacitance $8 \mu \mathrm{F}$, if the lower half of the air space is filled with a material of dielectric constant 3, its capacitance changes to:

1 $3 \mu \mathrm{F}$
2 $12 \mu \mathrm{F}$
3 $16 \mu \mathrm{F}$
4 $24 \mu \mathrm{F}$
Capacitance

165956 A parallel plate capacitor is formed by two plates each of areas $30 \pi \mathrm{cm}^{2}$ separated by $1 \mathrm{~mm}$. A material of dielectric strength $3.6 \times 10^{7}$ $\mathrm{Vm}^{-1}$ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is $7 \times 10^{-6} \mathrm{C}$, the value of dielectric constant of the material is:
$\left[\text { Use } \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} \mathrm{C}^{-2}\right]$

1 1.66
2 1.75
3 2.25
4 2.33
Capacitance

165957 Two positive point charges of $10 \mu \mathrm{C}$ and $12 \mu \mathrm{C}$ are placed $10 \mathrm{~cm}$ apart in air. The work done to bring them $6 \mathrm{~cm}$ closer is

1 $8.1 \mathrm{~J}$
2 $3.2 \mathrm{~J}$
3 $9 \mathrm{~J}$
4 $13.5 \mathrm{~J}$
Capacitance

165958 A capacitor of capacitance $20 \mu \mathrm{F}$ is charged by a battery of potential $24.3 \mathrm{~V}$. The capacitor is then disconnected from the battery and is connected to another uncharged capacitor of capacitance $10 \mu \mathrm{F}$. After some time, the second capacitor is disconnected, discharged fully and is again connected to the first capacitor. If the process is repeated several times, the charge on the first capacitor at the end of the fifth process is $\mu \mathrm{C}$.

1 256
2 128
3 64
4 32
Capacitance

165954 Two materials having the dielectric constants $K_{1}$ and $K_{2}$ are filled between two parallel plates of a capacitor, which is shown in figure. The capacity of the capacitor is :

1 $\frac{\mathrm{A} \varepsilon_{0}\left(\mathrm{~K}_{1} \times \mathrm{K}_{2}\right)}{\mathrm{d}\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right)} \mathrm{A}$
2 $\frac{A \varepsilon_{0}\left(K_{1}-K_{2}\right)}{d}$
3 $\frac{\mathrm{A} \varepsilon_{0} \mathrm{~K}_{1} \mathrm{~K}_{2}}{\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)}$
4 $\frac{A \varepsilon_{0}\left(K_{1}+K_{2}\right)}{d}$
Capacitance

165955 In a parallel plate with air capacitor of capacitance $8 \mu \mathrm{F}$, if the lower half of the air space is filled with a material of dielectric constant 3, its capacitance changes to:

1 $3 \mu \mathrm{F}$
2 $12 \mu \mathrm{F}$
3 $16 \mu \mathrm{F}$
4 $24 \mu \mathrm{F}$
Capacitance

165956 A parallel plate capacitor is formed by two plates each of areas $30 \pi \mathrm{cm}^{2}$ separated by $1 \mathrm{~mm}$. A material of dielectric strength $3.6 \times 10^{7}$ $\mathrm{Vm}^{-1}$ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is $7 \times 10^{-6} \mathrm{C}$, the value of dielectric constant of the material is:
$\left[\text { Use } \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} \mathrm{C}^{-2}\right]$

1 1.66
2 1.75
3 2.25
4 2.33
Capacitance

165957 Two positive point charges of $10 \mu \mathrm{C}$ and $12 \mu \mathrm{C}$ are placed $10 \mathrm{~cm}$ apart in air. The work done to bring them $6 \mathrm{~cm}$ closer is

1 $8.1 \mathrm{~J}$
2 $3.2 \mathrm{~J}$
3 $9 \mathrm{~J}$
4 $13.5 \mathrm{~J}$
Capacitance

165958 A capacitor of capacitance $20 \mu \mathrm{F}$ is charged by a battery of potential $24.3 \mathrm{~V}$. The capacitor is then disconnected from the battery and is connected to another uncharged capacitor of capacitance $10 \mu \mathrm{F}$. After some time, the second capacitor is disconnected, discharged fully and is again connected to the first capacitor. If the process is repeated several times, the charge on the first capacitor at the end of the fifth process is $\mu \mathrm{C}$.

1 256
2 128
3 64
4 32
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Capacitance

165954 Two materials having the dielectric constants $K_{1}$ and $K_{2}$ are filled between two parallel plates of a capacitor, which is shown in figure. The capacity of the capacitor is :

1 $\frac{\mathrm{A} \varepsilon_{0}\left(\mathrm{~K}_{1} \times \mathrm{K}_{2}\right)}{\mathrm{d}\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right)} \mathrm{A}$
2 $\frac{A \varepsilon_{0}\left(K_{1}-K_{2}\right)}{d}$
3 $\frac{\mathrm{A} \varepsilon_{0} \mathrm{~K}_{1} \mathrm{~K}_{2}}{\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)}$
4 $\frac{A \varepsilon_{0}\left(K_{1}+K_{2}\right)}{d}$
Capacitance

165955 In a parallel plate with air capacitor of capacitance $8 \mu \mathrm{F}$, if the lower half of the air space is filled with a material of dielectric constant 3, its capacitance changes to:

1 $3 \mu \mathrm{F}$
2 $12 \mu \mathrm{F}$
3 $16 \mu \mathrm{F}$
4 $24 \mu \mathrm{F}$
Capacitance

165956 A parallel plate capacitor is formed by two plates each of areas $30 \pi \mathrm{cm}^{2}$ separated by $1 \mathrm{~mm}$. A material of dielectric strength $3.6 \times 10^{7}$ $\mathrm{Vm}^{-1}$ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is $7 \times 10^{-6} \mathrm{C}$, the value of dielectric constant of the material is:
$\left[\text { Use } \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} \mathrm{C}^{-2}\right]$

1 1.66
2 1.75
3 2.25
4 2.33
Capacitance

165957 Two positive point charges of $10 \mu \mathrm{C}$ and $12 \mu \mathrm{C}$ are placed $10 \mathrm{~cm}$ apart in air. The work done to bring them $6 \mathrm{~cm}$ closer is

1 $8.1 \mathrm{~J}$
2 $3.2 \mathrm{~J}$
3 $9 \mathrm{~J}$
4 $13.5 \mathrm{~J}$
Capacitance

165958 A capacitor of capacitance $20 \mu \mathrm{F}$ is charged by a battery of potential $24.3 \mathrm{~V}$. The capacitor is then disconnected from the battery and is connected to another uncharged capacitor of capacitance $10 \mu \mathrm{F}$. After some time, the second capacitor is disconnected, discharged fully and is again connected to the first capacitor. If the process is repeated several times, the charge on the first capacitor at the end of the fifth process is $\mu \mathrm{C}$.

1 256
2 128
3 64
4 32
Capacitance

165954 Two materials having the dielectric constants $K_{1}$ and $K_{2}$ are filled between two parallel plates of a capacitor, which is shown in figure. The capacity of the capacitor is :

1 $\frac{\mathrm{A} \varepsilon_{0}\left(\mathrm{~K}_{1} \times \mathrm{K}_{2}\right)}{\mathrm{d}\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right)} \mathrm{A}$
2 $\frac{A \varepsilon_{0}\left(K_{1}-K_{2}\right)}{d}$
3 $\frac{\mathrm{A} \varepsilon_{0} \mathrm{~K}_{1} \mathrm{~K}_{2}}{\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)}$
4 $\frac{A \varepsilon_{0}\left(K_{1}+K_{2}\right)}{d}$
Capacitance

165955 In a parallel plate with air capacitor of capacitance $8 \mu \mathrm{F}$, if the lower half of the air space is filled with a material of dielectric constant 3, its capacitance changes to:

1 $3 \mu \mathrm{F}$
2 $12 \mu \mathrm{F}$
3 $16 \mu \mathrm{F}$
4 $24 \mu \mathrm{F}$
Capacitance

165956 A parallel plate capacitor is formed by two plates each of areas $30 \pi \mathrm{cm}^{2}$ separated by $1 \mathrm{~mm}$. A material of dielectric strength $3.6 \times 10^{7}$ $\mathrm{Vm}^{-1}$ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is $7 \times 10^{-6} \mathrm{C}$, the value of dielectric constant of the material is:
$\left[\text { Use } \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} \mathrm{C}^{-2}\right]$

1 1.66
2 1.75
3 2.25
4 2.33
Capacitance

165957 Two positive point charges of $10 \mu \mathrm{C}$ and $12 \mu \mathrm{C}$ are placed $10 \mathrm{~cm}$ apart in air. The work done to bring them $6 \mathrm{~cm}$ closer is

1 $8.1 \mathrm{~J}$
2 $3.2 \mathrm{~J}$
3 $9 \mathrm{~J}$
4 $13.5 \mathrm{~J}$
Capacitance

165958 A capacitor of capacitance $20 \mu \mathrm{F}$ is charged by a battery of potential $24.3 \mathrm{~V}$. The capacitor is then disconnected from the battery and is connected to another uncharged capacitor of capacitance $10 \mu \mathrm{F}$. After some time, the second capacitor is disconnected, discharged fully and is again connected to the first capacitor. If the process is repeated several times, the charge on the first capacitor at the end of the fifth process is $\mu \mathrm{C}$.

1 256
2 128
3 64
4 32