Discharging of Capacitors

Q. A series $LCR$ circuit driven by $300\text{V}$ at a frequency of $50\text{Hz}$ contains a resistance $R=3k\Omega$, an inductor of inductive reactance $X_L=250\pi \Omega$ and an unknown capacitor. The value of capacitance, to maximize the average power, should be:$\text{Take}({\pi }^2\approx 10)$

1. $25\mu F$
2. $40\mu F$
3. $4\mu F$
4. $400\mu F$

Q. A parallel plate capacitor is connected to a battery and a dielectric plate is inserted into the capacitor. Which quantity will increase?

1. Potential difference across the capacitor
2. Electric field
3. Stored energy
4. EMF of battery

Q. Two capacitors $2\mu \text{F}$ and $6\mu \text{F}$ in series are connected in parallel to a third capacitor of $4\mu \text{F}$. This arrangement is then connected to a battery of emf $2\text{V}$. Find the total energy of system of capacitors?

1. $22\mu \text{J}$
2. $11\mu \text{J}$
3. $5.5\mu \text{J}$
4. $44\mu \text{J}$

Q. A radioactive sample has an average life of $30\text{ms}$ and is decaying. A capacitor of capacitance $200\mu \text{F}$ is first charged and later connected with resistor ${}^{\prime }{R}^{\prime }$. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of ${}^{\prime }{R}^{\prime }$ should be _____$\Omega$.

Q. In an LC oscillator circuit, $L=10\text{mH},C=40\mu \text{F}$. At $t=0$, the capacitor is fully charged with $q_0=4\mu \text{C}$. Find the current in the circuit, when the capacitor and inductor share energies equally.

1. $0.2\text{mA}$
2. $4.5\text{mA}$
3. $0.3\text{mA}$
4. $2.2\text{mA}$

Q. In the circuit shown there is steady state with the switch closed. The switch is opened at $t=0$. Choose the correct option(s). (Given : $\epsilon =24\text{V},C_1=3\text{F}$ and $C_2=2\text{F})$

1. The voltage across $C_1$ before the switch is open is $12\text{V}$.
2. The voltage across $C_1$ after the switch is open for a long time is $12\text{V}$.
3. The voltage across $C_2$ after the switch is open for a long time is $24\text{V}$.
4. The voltage across $C_2$ before the switch is open is $8\text{V}$.

Q. Capacitor in the circuit is in steady state along with the current flowing in the branches. The value of each resisatnce is shown in figure. Calculate the energy stored in the capacitor of capacitance $4\mu \text{F}$.

1. $6\times {10}^{-4}\text{J}$
2. $8\times {10}^{-4}\text{J}$
3. $9\times {10}^{-4}\text{J}$
4. $12\times {10}^{-4}\text{J}$

Q.

The square root of the product of inductance and capacitance has the dimension of

1. length

2. mass

3. time

4. No dimension

Q.

Figure shows a system of three concentric metal shells A, B and C with radii, a, 2a and 3a respectively. Shell B is earthed and shell C is given a charge Q. Now, if shell C is connected to shell A, then the final charge on the shell B, is equal to

1. $-\frac{4Q}{13}$

2. $-\frac{8Q}{11}$

3. $-\frac{3Q}{7}$

4. $-\frac{5Q}{3}$

Q.

In a closed circuit, the electric current at any instant of time $t$ (in $sec$) is given by an equation $I=(4–0.08t)$$t=50s$. How many electrons flow through the circuit in $50s$?

Q. The capacitor in the circuit shown below is initially charged. After closing the switch, choose the correct option(s)

1. Energy of the capacitor becomes half of its initial value in time. $RC\frac{\left(ln2\right)}{2}$
2. Charge on the capacitor becomes half of its initial value in RC(ln2).
3. Current in the circuit becomes half of its initial value in time RC(ln2).
4. Current in the circuit becomes half of its initial in time $RC\frac{ln2}{2}$

Q. Two parallel plate capacitors $\text{A}$ and $\text{B}$ with capacitance $1\mu \text{F}$ and $5\mu \text{F}$ are charged separately to the same potential of $100\text{V}$. Now, the positive plate of $\text{A}$ is connected to the negative plate of $\text{B}$. Find the total loss of electrical energy in the given system.

1. $33.4\text{mJ}$
2. $8.35\text{mJ}$
3. $44.67\text{mJ}$
4. $16.7\text{mJ}$

Q. A $4\mu \text{F}$ and a $9\mu \text{F}$ capacitors are connected in series combination across a $26\text{V}$ battery. What is the voltage (in $\text{V}$) of the battery required to charge the capacitors in parallel combination to the same total energy?

Q. In the given circuit, the potential difference between $\text{A}$ and $\text{B}$ in the steady state is

1. $25\text{V}$
2. $50\text{V}$
3. $75\text{V}$
4. $35\text{V}$

Q. A capacitor of $2\mu F$ is charged as shown in the diagram. When the switch $S$ is turned to position 2, the percentage of its stored energy dissipated is :

1. $0\%$
2. $20\%$
3. $75\%$
4. $80\%$

Q. As shown in the figure below, if a capacitor $C$ is charged by connecting it with resistance $R$ then, the energy stored in the capacitor is

1. $\frac{1}{2}C{V}^2$
2. More than $\frac{1}{2}C{V}^2$
3. Less than $\frac{1}{2}C{V}^2$
4. Zero

Q. Two parallel plate capacitors $\text{A}$ and $\text{B}$ having capacitances $3\mu \text{F}$ and $15\mu \text{F}$ are charged seperately upto $10\text{V}$ and $20\text{V}$ respectively. Now positive plate of $\text{A}$ is connected to the negative plate of $\text{B}$ and vice-versa. Find how much heat produced in the circuit?

1. $2025\mu \text{J}$
2. $150\mu \text{J}$
3. $3000\mu \text{J}$
4. $1125\mu \text{J}$

Q. A capacitor of capacitance $12\mu \text{F}$ is joined to an $\text{AC}$ source of frequency $200\text{Hz}$. The $rms$ current in the circuit is $2\text{A}$. The average energy stored in the capacitor is

1. $0.01\text{J}$
2. $0.02\text{J}$
3. $0.2\text{J}$
4. $0.1\text{J}$

Q. For the circuit shown in the figure, find the instantaneous current through the capacitor.

1. $V_0\omega C\sin \omega t$
2. $V_0\omega C\cos \omega t$
3. $V_0\omega C$
4. None

Q.

In a series LCR circuit $V_{L=}{V}_C\ne V_R$.What is the value of power factor?

Q.

How many time constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit ?

Q.

In a series RC circuit with an AC source, R = 300 $\Omega ,C=25\mu F$, ${ϵ}_0=50Vandv=\frac{50}{\pi }$ Hz. Find the peak current and the average power dissipated in the circuit.

Q.

How many time constants will elapse before the charge on a capacitor falls to 0.1$\%$ of its maximum value in a discharging RC circuit ?

Q. Two parallel plate capacitors $\text{A}$ and $\text{B}$ have capacitors $1\mu \text{F}$ and $5\mu \text{F}$ are charged separately to same potential of $100\text{V}$. Now the positive plate of $\text{A}$ is connected to the negative plate of $\text{B}$ and the negative plate of $\text{A}$ to the positive plate of $\text{A}$ then the loss of energy in this process is

1. $1.37\times {10}^{-2}\text{J}$
2. $1.67\times {10}^{-2}\text{J}$
3. $2.25\times {10}^{-2}\text{J}$
4. $2.75\times {10}^{-2}\text{J}$

Q. A parallel plate capacitor of $1\mu F$ capacity is discharging through a resistor. If its energy reduces to half in one $\text{second}$. The value of resistance will be

1. $\frac{2}{ln\left(2\right)}M\Omega$
2. $\frac{4}{ln\left(2\right)}M\Omega$
3. $\frac{10}{ln\left(2\right)}M\Omega$
4. $\frac{16}{ln\left(2\right)}M\Omega$

Q. A capacitor having an initial charge 0.1 C, is discharging in a simple RC circuit with the time constant 3 seconds. How much charge will remain after 6 sec?

1. $0.1e^{2}C$
2. $\frac{0.1}{e^2}C$
3. $\frac{0.01}{e^2}C$
4. $0.01e^{2}C$

Q. A capacitor of capacitance, $C=25\mu \text{F}$ is fully charged and then connected with an inductor of inductance, $L=10\text{mH}$. The ratio of magnitude of maximum charge on the capacitor to the maximum current through the circuit, is -

Assume ideal conditions.

1. $1:2000$
2. $2000:1$
3. $1:1000$
4. $1000:1$

Q. A capacitor of capacitance ${}^{\prime }{C}^{\prime }$ is being charged by connecting it across a dc source along with an ammeter. Will the ammeter show a momentary deflection during the process of charging? If so, how would you explain this momentary deflection and the resulting continuity of current in the circuit? Write the expression for the current inside the capacitor.

Q. Two identical parallel plate capacitors, of capacitance \(C\) each, have plates of area \(A\), separated by a distance \(d\). The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants \(K_{1}, \)\(K_{2}\) and \(K_{3}\). The first capacitor is filled as shown in Figure \(I\), and the second one is filled as shown in Figure \(II\). If these two modified capacitors are charged by the same potential \(V\), the ratio of the energy stored in the two, would be:
\((E_{1}\) refers to capacitor \((I)\) and \(E_{2}\) to capacitor \((II))\):


(I) (II)

Q. Two capacitors of $400\mu \text{F}$ and $600\mu \text{F}$ are connected in parallel to a battery of $100\text{V}.$ Find the ratio of charge stored in $400\mu \text{F}$ to charge stored in $600\mu \text{F}$.

1. $2:3$
2. $1:3$
3. $1:2$
4. $3:2$