Capacitors in DC Circuits & RC

Under steady state condition the potential difference across the capacitor in the circuit is ______ V.

The stored charge in the capacitor in steady state of the following circuit is $\rule{2.5em}{0.4pt}\ \mu\text{C}$.

A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of $1\ \mu\text{F}$ when the space between the plates is filled with an insulating material of resistivity $1\times 10^{13}\ \Omega\text{ m}$ and resistance $17.7\times 10^{14}\ \Omega$. Relative permittivity of the insulating material is $\alpha\times 10^{7}$. The value of $\alpha$ is ______.

(Take permittivity of free space $=8.85\times 10^{-12}\text{ F/m}$)

The voltage between the plates of a parallel plate capacitor of capacity $1\ \mu\text{F}$ is changing at the rate of $4\text{ V/s}$. the displacement current in the capacitor is

A parallel plate capacitor with plate area A and plate separation $d$ is charged by constant current $I$. A plane surface of area $\frac{A}{2}$, parallel to the plates is drawn simultaneously between the plates. The displacement current through this area is

At steady state the charge on the capacitor, as shown in the circuit below, is _________ $\mu$C.

Identify the valid statements relevant to the given circuit at the instant when the key is closed.

A. There will be no current through resistor $R$.

B. There will be maximum current in the connecting wires.

C. Potential difference between the capacitor plates A and B is minimum.

D. Charge on the capacitor plates is minimum.

Choose the correct answer from the options given below:

A $4\ \mu\text{F}$ capacitor is charged to 10 V. The battery is then disconnected and a pure 10 mH coil is connected across the capacitor so that LC oscillations are set up. The maximum current in the coil is

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A. If the rate of change of potential difference between the plates is $7\times 10^{8}\text{ V/s}$ then the integer value of the distance between the parallel plates is $($ Take, $\epsilon_0=9\times 10^{-12}\frac{\text{F}}{\text{m}},\ \pi=\frac{22}{7})$ ____________ $\mu\text{m}$.

In the given circuit diagram, in the steady state the current through the battery and the charge on the capacitor respectively are

The steady state current in the circuit shown below is:

A galvanometer $(G)$ of $2\ \Omega$ resistance is connected in the given circuit. The ratio of charge stored in $C_1$ and $C_2$ is:

In an electrical circuit drawn below the amount of charge stored in the capacitor is _______ $\mu$ C.

A $16\ \Omega$ wire is bent to form a square loop. A $9\text{ V}$ battery with internal resistance $1\ \Omega$ is connected across one of its sides. If a $4\ \mu\text{F}$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\frac{x}{2}\ \mu\text{J}$, where $x=$ _________

The charge accumulated on the capacitor connected in the following circuit is _______ $\mu\text{C}$ (Given $C=150\ \mu\text{F})$

A circuit having a self inductance of 1 henry carries a current of 1 A. To prevent the sparking when the circuit is broken, a capacitor which can withstand 500 V is connected across the switch. What is the minimum value of the capacitance of the capacitor?

The electric field between the two parallel plates of a capacitor of $1.5\ \mu\text{F}$ capacitance drops to one third of its initial value in $6.6\ \mu\text{s}$ when the plates are connected by a thin wire. The resistance of this wire is ________ $\Omega$. (Given, $\log_e 3=1.1$)

To produce an instantaneous displacement current of $2\text{ mA}$ in the space between the parallel plates of a capacitor of capacitance $4\ \mu\text{F}$, the rate of change of applied variable potential difference $\left(\frac{dV}{dt}\right)$ must be :-

In the network shown below, the charge accumulated in the capacitor in steady state will be:

In this figure the resistance of the coil of galvanometer G is $2\ \Omega$. The emf of the cell is $4\text{ V}$. The ratio of potential difference across $C_1$ and $C_2$ is:

In the circuit shown, the energy stored in the capacitor is $n\ \mu\text{J}$. The value of $n$ is __________

In the given circuit, $C_1=2\ \mu\text{F}, C_2=0.2\ \mu\text{F}, C_3=2\ \mu\text{F}, C_4=4\ \mu\text{F}, C_5=2\ \mu\text{F}, C_6=2\ \mu\text{F}$, The charge stored on capacitor $C_4$ is ____________ $\mu\text{C}$.

For the given circuit, in the steady state, $|V_B-V_D|=$ ________ V.

As shown in the figure, in steady state, the charge stored in the capacitor is ____________ $\times 10^{-6}$ C.

A capacitor is discharging through a resistor R. Consider in time t1, the energy stored in the capacitor reduces to half of its initial value and in time t2, the charge stored reduces to one eighth of its initial value. The ratio t1/t2 will be

Calculate the amount of charge on capacitor of 4$\mu$F. The internal resistance of battery is 1$\Omega$:

A capacitor of 50 $\mu$F is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is ______________$\mu$C.

A capacitor is connected to a 20 V battery through a resistance of 10$\Omega$. It is found that the potential difference across the capacitor rises to 2 V in 1 $\mu$s. The capacitance of the capacitor is __________ $\mu$F. Given: $\ln\left(\frac{10}{9}\right)=0.105$

The material filled between the plates of a parallel plate capacitor has resistivity 200 $\Omega$m. The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is: (given the value of relative permittivity of material is 50)

A capacitor of capacitance C = 1 $\mu$F is suddenly connected to a battery of 100 volt through a resistance R = 100 $\Omega$. The time taken for the capacitor to be charged to get 50 V is: [Take ln 2 = 0.69]

The circuit shown in the figure consists of a charged capacitor of capacity 3 $\mu$F and a charge of 30 $\mu$C. At time t = 0, when the key is closed, the value of current flowing through the 5 M$\Omega$ resistor is 'x' $\mu$-A. The value of 'x' to the nearest integer is ___________.

An ideal cell of emf 10 V is connected in circuit shown in figure. Each resistance is 2 $\Omega$. The potential difference (in V) across the capacitor when it is fully charged is ______.

For the given input voltage waveform Vin(t), the output voltage waveform V0(t), across the capacitor is correctly depicted by:

The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure:

What is the value of current at t = 4 s?

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. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively:

Determine the charge on the capacitor in the following circuit:

In the following circuit, the switch S is closed at t = 0. The charge on the capacitor C1 as a function of time will be given by $\left(C_{eq}=\frac{C_1C_2}{C_1+C_2}\right)$

In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be:

In the given circuit, charges $Q_2$ on the $2\ \mu\text{F}$ capacitor changes as $C$ is varied from $1\ \mu\text{F}$ to $3\ \mu\text{F}.\ Q_2$ as a function of $'C'$ is given properly by:

$\text{(figures are drawn schematically and are not to scale)}$

The circuit shown here has two batteries of 8.0 V and 16.0 V and three resistors 3 $\Omega$, 9 $\Omega$ and 9 $\Omega$ and a capacitor 5.0 $\mu$F.

How much is the current I in the circuit in steady state?

To establish an instantaneous current of 2 A through a 1$\mu$F capacitor; the potential difference across the capacitor plates should be changed at the rate of:

The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant $\tau$ of this circuit lies between

A resistor $'R'$ and $2\ \mu\text{F}$ capacitor in series is connected through a switch to $200\text{ V}$ direct supply. Across the capacitor is a neon bulb that lights up at $120\text{ V}.$ Calculate the value of $R$ to make the bulb light up $5\text{ s}$ after the switch has been closed. $(\log_{10}2.5=0.4)$

Let $C$ be the capacitance of a capacitor discharging through a resistor $R.$ Suppose $t_1$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_2$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $t_1/t_2$ will be

When the key $K$ is pressed at time $t=0$, then which of the following statement about the current $I$ in the resistor $AB$ of the given circuit is true?

The time constant of $C\text{-}R$ circuit is