Capacitance

In the circuit shown below, the key is pressed at time $t=0$. Which of the following statement(s) is(are) true?

Which one of the following statements is correct?

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the 4 μF and 9 μF capacitors), at a point distant 30 m from it, would equal :

Three capacitors each of 4 μF are to be connected in such a way that the effective capacitance is 6 μF. This can be done by connecting them :

Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be 1 μF is :

A parallel plate capacitor having plates of area $S$ and plate separation $d$, has capacitance $C_1$ in air. When two dielectrics of different relative permittivities ($\varepsilon_1=2$ and $\varepsilon_2=4$) are introduced between the two plates as shown in the figure, the capacitance becomes $C_2$. The ratio $\dfrac{C_2}{C_1}$ is

In the given circuit, charge $Q_2$ on the 2μF capacitor changes as C is varied from 1μF to 3μF. $Q_2$ as a function of 'C' is given properly by : (figures are drawn schematically and are not to scale)

If the capacitance of a nanocapacitor is measured in terms of a unit '$u$' made by combining the electronic charge 'e', Bohr radius '$a_0$', Planck's constant 'h' and speed of light 'c' then :

In the circuits (a) and (b) switches $S_1$ and $S_2$ are closed at t = 0 and are kept closed for a long time. The variation of currents in the two circuits for t ≥ 0 are roughly shown by (figures are schematic and not drawn to scale) :

In figure is shown a system of four capacitors connected across a 10 V battery. Charge that will flow from switch S when it is closed is :

For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor C', when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor C', must have been connected in :

At time $t=0$, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current $I(t)=I_0\cos(\omega t)$, with $I_0=1$ A and $\omega=500\ \mathrm{rad\,s^{-1}}$ starts flowing in it with the initial direction shown in the figure. At $t=\dfrac{7\pi}{6\omega}$, the key is switched from B to D. Now onwards only A and D are connected. A total charge $Q$ flows from the battery to charge the capacitor fully. If $C=20\ \mu$F, $R=10\ \Omega$ and the battery is ideal with emf of 50 V, identify the correct statement(s).

A parallel plate capacitor has a dielectric slab of dielectric constant $K$ between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is $C$ while that of the portion with dielectric in between is $C_1$. When the capacitor is charged, the plate area covered by the dielectric gets charge $Q_1$ and the rest of the area gets charge $Q_2$. The electric field in the dielectric is $E_1$ and that in the other portion is $E_2$. Choose the correct option/options, ignoring edge effects.

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is $3\times10^4$ V/m, the charge density of the positive plate will be close to :

Three capacitances, each of 3 μF, are provided. These cannot be combined to provide the resultant capacitance of :

A parallel plate capacitor is made of two plates of length $l$, width $w$ and separated by distance $d$. A dielectric slab (dielectric constant K) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force $F=-\dfrac{\partial U}{\partial x}$ where U is the energy of the capacitor when dielectric is inside the capacitor up to distance $x$ (See figure). If the charge on the capacitor is Q then the force on the dielectric when it is near the edge is :

The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation :
$$K(x)=K_o+\lambda x\quad(\lambda=\text{ a constant})$$
The capacitance C, of this capacitor, would be related to its 'vacuum' capacitance $C_o$ as per the relation :

The circuit shown here has two batteries of 8.0 V and 16.0 V and three resistors 3 Ω, 9 Ω and 9 Ω and a capacitor 5.0 μF.

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

The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from $\epsilon_1$ at one plate to $\epsilon_2$ at the other. The capacitance of capacitor is :

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $C$. The switch $S_1$ is pressed first to fully charge the capacitor $C_1$ and then released. The switch $S_2$ is then pressed to charge the capacitor $C_2$. After some time, $S_2$ is released and then $S_3$ is pressed. After some time,