Charging of Capacitors

Q. A capacitor of capacitance $ \text C=900 \text{ pF}$ is charges fully by $100 \text{ V}$ battery B as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance $\text{C}=900 \text{ pF}$ as shown in figure (b). The electrostatic energy stored by the system (b) is

Q. Two point charges Q and -2Q are placed at some distance apart. If the electric field at the location of Q is E, then the electric field at the location of -2Q will be

1. - E
2. - 2E
3. $\frac{-E}{2}$
4. $\frac{-3E}{2}$

Q.

Why does capacitor block DC and allow AC ?

Q. A battery consists of a variable number $n$ of identical cells (having internal resistance $r$ each) which are connected in series. The terminal of the battery are short circuited and the current $I$ is measured. Which of the graph shows the correct relationship between $I$ and $n?$

1. 
2. 
3. 
4. 

Q. Choose the correct answer from the alternatives given.
The conduction current is the same as displacement current when the source is

1. $\text{AC}$ only
2. $\text{DC}$ only
3. both $\text{AC}$ and $\text{DC}$ (Transition phase)
4. neither $\text{AC}$ nor for $\text{DC}$

Q.

How energy is stored in the capacitor and inductor?

Q. A parallel plate capacitor of capacitance $20\mu F$ is being charged by a voltage source whose potential is changing at the rate of $3V{s}^{-1}$. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively :

1. $60\mu A,0$
2. $0,0$
3. $0,60\mu A$
4. $60\mu A,60\mu A$

Q. A $1\mu \text{F}$ capacitor is connected in the circuit shown below. The emf of the cell is $3\text{V}$ and internal resistance is $0.5\Omega$. The resistors $R_1$ and $R_2$ have values $4\Omega$ and $1\Omega$ respectively. The charge on the capacitor in steady state must be

1. $1\mu \text{C}$
2. $2\mu \text{C}$
3. $1.33\mu \text{C}$
4. zero

Q.

A parallel plate capacitor has a plate of length $‘l’$, width $‘w’$ and separation of plates is $‘d’$. It is connected to a battery of emf $V$. A dielectric slab of the same thickness $‘d’$ and of dielectric constant $k=4$ is being inserted between the plates of the capacitor. At what length of the slab inside plates, will the energy stored in the capacitor be two times the initial energy stored?

1. $2l/3$

2. $l/2$

3. $l/4$

4. $l/3$

Q.

A body has a charge of $-2\mu C$. If it has $2.5\times {10}^{13}$ protons, then how many electrons the body has?

Q.

Express dielectric constant of a medium in terms of capacitance. What is its SI unit?

Q. In the circuit shown, capacitor is initially uncharged the switch is turned on at $t=0$. Then,

1. At $t=0$, current supplied by battery is $4\text{mA}$
2. At $t=0$, current in $R_3$ is $2\text{mA}$
3. In the steady state, current supplied by battery is $3\text{mA}$
4. In the steady state, current in $R_3$ is zero

Q. A car battery is charged by a $12\text{V}$ supply, and energy stored in it is $7.20\times {10}^5\text{J}$. The charge passed through the battery is

Q.

A parallel-plate capacitor has plate area 40 $c{m}^2$, and separation between the plates 0.10 mm is connected to a battery of emf 2.0 V through a 16 $\Omega$ resistor. Find the electric field in the capacitor 10 ns after the connections are made.

Q. A capacitor of capacitance $50pF$ is charged by $100V$ source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ________ $nJ.$

Q. A capacitor is connected to a $10\text{V}$ battery. When the medium is air, the charge on plates is $40\mu \text{C}$ . When the medium between plates is oil, the charge on plates becomes $100\mu \text{C}$ . The dielectric constant of oil is

1. $2.5$
2. $4$
3. $6.25$
4. $10$

Q. A capacitor of capacitance \(10 \mu F\) is charged up to a potential difference of 2V and then the cell is removed. Now it is connected to a cell of emf 4 V and is charged fully. In both cases the polarities of the two cells are in same directions. Total heat produced in the complete charging process is

Q. Time constant of charging of capacitor shown in figure is

1. $\frac{RC}{2}$
2. 0
3. 2 RC
4. infinite

Q.

What is the working principle of capacitors?

Q. The given figure represents the phasor diagram of a series $LCR$ circuit connected to an $AC$ source. At instant $t$ when the source voltage is given by $V=V_0\cos \omega t$, the current in the circuit in terms of peak current $I_0$ will be
Given:
$V_{OR}=\sqrt{3}\text{V}$ = Voltage Across Resistor
$V_{OL}=3\text{V}$ = Voltage Across Inductor
$V_{OC}=2\text{V}$ = Voltage Across capacitor

1. $I=I_0\cos (\omega t+\frac{\pi }{6})$
2. $I=I_0\cos (\omega t-\frac{\pi }{6})$
3. $I=I_0\cos (\omega t+\frac{\pi }{3})$
4. $I=I_0\cos (\omega t-\frac{\pi }{3})$

Q. In the circuit shown, the cell is ideal, with EMF $=15\text{V}$. Each resistance is of $3\Omega$. The potential difference across the capacitor in the steady state is -

1. Zero
2. $9\text{V}$
3. $12\text{V}$
4. $15\text{V}$

Q. Two capacitors of $2\mu F$ and $3\mu F$ are charged to $150V$ and $120V$ respectively. The plates of capacitor are connected as shown in the figure. An uncharged capacitor of capacity $1.5\mu F$ is connected to the free end of the wires as shown. Then:

1. Charge on $1.5\mu F$ capacitor is $180\mu C$
2. Charge on $2\mu F$ capacitor is $120\mu C$
3. Positive charge flows through $A$ from right to left
4. Positive charge flows through $A$ from left to right

Q. Find out the potential difference between the points $x$ and $y$ in the figure.

1. $7\text{V}$
   
2. $10\text{V}$
   
3. $17\text{V}$
   
4. $12\text{V}$
   

Q. $\text{Assertion:}$- Average Power loss in series $\text{LC}$ circuit is always zero.
$\text{Reason:}$- Average value of voltage and current in A.C. is zero.

1. Both $\text{Assertion}$ & $\text{Reason}$ are true & the $\text{Reason}$ is a correct explanation of the $\text{Assertion}$.
2. Both $\text{Assertion}$ & $\text{Reason}$ are true, but $\text{Reason}$ is a correct explanation of the $\text{Assertion}$.
3. $\text{Assertion}$ is true, but the $\text{Reason}$ is false.
4. Both $\text{Assertion}$ & $\text{Reason}$ are false.

Q. For the circuit shown in the figure, find the current passing through $10\Omega$ resistor.

1. $\frac{5}{18}\text{A}$
2. $\frac{5}{12}\text{A}$
3. $\frac{5}{6}\text{A}$
4. $\frac{5}{3}\text{A}$

Q. An $\text{AC}$ source producing emf $E=E_0(\sin 2\omega t+\sin 3\omega t)$ is connected in series with a capacitor and a resistor. The current found in the circuit is $i=i_1\sin (2\omega t+{\varphi }_1)+i_2\sin (3\omega t+{\varphi }_2)$. Then

1. $i_1=i_2$
2. $i_1<i_2$
3. $i_1>i_2$
4. $i_1$ may be less than, equal to or greater than $i_2$.

Q.

If the above capacitor is connected across a 6.0 V battery, find (a) the charge supplied by the battery, (b) the induced charge on the dielectric and (c) the net charge appearing on one of the coated surfaces.

Q. In the given circuit the steady state current is?

1. Zero
2. $0.6\text{A}$
3. $0.9\text{A}$
4. $1.5\text{A}$

Q. Effective capacitance of parallel combination of two capacitors $C_1$ and $C_2$ is $10\mu \text{F}$. When these capacitors are individually connected to a voltage source of $1\text{V}$, the energy stored in the capacitor $C_2$ is $4$ times that of $C_1$. If these capacitors are connected in series, their effective capacitance will be:

1. $4.2\mu \text{F}$
2. $3.2\mu \text{F}$
3. $1.6\mu \text{F}$
4. $8.4\mu \text{F}$

Q. A parallel plate capacitor of capacitance $20\mu F$ is being charged by a voltage source whose potential is changing at the rate of $3V{s}^{-1}$. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively :

1. $60\mu A,0$
2. $0,0$
3. $0,60\mu A$
4. $60\mu A,60\mu A$