Partially Filled Dielectrics

Q.

What causes damping?

Q. A capacitor cannot be used as a battery because

1. It cannot store a large amount of charge
2. It produces too much heat
3. It gets discharged very rapidly
4. It is very costly as compared to a battery

Q. Three capacitors, each of capacitance $4\mu \text{F}$ are connected to a battery of voltage $10\text{V}$. When key $K$ is closed, the charge which will flow through the battery is

1. $40\mu \text{C}$
2. $40/3\mu \text{C}$
3. $80\mu \text{C}$
4. $20\mu \text{C}$

Q. Capacitance of a parallel plate capacitor becomes $\frac{4}{3}$ times its original value if a dielectric slab of thickness $t=\frac{d}{2}$ is inserted between the plates [$d$ is the separation between the plates]. The dielectric constant of the slab is

1. $4$
2. $8$
3. $2$
4. $6$

Q. A parallel plate air capacitor is made using two square plates each of side $0.2\text{m}$, spaced $1\text{cm}$ apart. It is connected to a $50\text{V}$ battery. What is the charge on each plate?

1. $1.77\times {10}^{-3}\mu \text{C}$
2. $1.77\times {10}^{-3}\text{C}$
3. $3.54\times {10}^{-3}\text{C}$
4. $3.54\times {10}^{-3}\mu \text{C}$

Q. Determine the current flowing $\left(\text{in A}\right)$ through an element at time $t=2\text{sec}$, if the charge flow is given by $q=(2t^2+3)\text{C}$.

1. $8$
2. $1$
3. $2$
4. $4$

Q. A parallel plate capacitor is made of two square plates of side ${}^{\prime }{a}^{\prime }$, separated by a distance $d(d<<a)$. The lower triangular portion is filled with a dielectric of dielectric constant $K$. The capacitance of this capacitor is :

1. $\frac{1}{2}K\frac{{ϵ}_0{a}^2}{d}$
2. $K\frac{{ϵ}_0{a}^2}{d}\ln K$
3. $K\frac{{ϵ}_0{a}^2}{d(K-1)}\ln K$
4. $K\frac{{ϵ}_0{a}^2}{2d(K+1)}$

Q. In the circuit shown in Fig, capacitors $A$ and $B$ have identical geometry, but a material of dielectric constant 3 is present between the plates of $B$. The potential difference across $A$ and $B$ are respectively

1. $2.5\text{V},7.5\text{V}$
2. $2\text{V},8\text{V}$
3. $7.5\text{V},2.5\text{V}$
4. $8\text{V},2\text{V}$

Q. A parallel-plate capacitor has a dielectric slab in it. The slab just fills the space inside the capacitor. The capacitor is charged by a battery and then the battery is disconnected. Now, the slab is pulled out slowly at $t=0$. If at time $t$, the capacitance of the capacitor is $C$ and potential difference between the plates of the capacitor is $V$, then which of the following graphs is/are correct.

1. 
2. 
3. 
4.