Embibe Experts Solutions for Chapter: Capacitance, Exercise 3: Exercise - 3

Two capacitors $C_1$ and $C_2$ are charged to $120 \mathrm{V}$ and $200 \mathrm{V}$, respectively. It is found that by connecting them together the potential on each one can be made zero. Then

A parallel plate capacitor is made of two circular plates separated by a distance of $5 \mathrm{mm}$ and with a dielectric of a dielectric constant $2.2$ between them. When the electric field in the dielectric is $3\times {10}^4 \mathrm{V} {\mathrm{m}}^{-1}$, the charge density of the positive plate will be close to

In the given circuit, the charge $Q_2$ on the $2 \mathrm{\mu F}$ capacitor changes as $C$ is varied from $1 \mathrm{\mu F}$ to $3 \mathrm{\mu F}$. $Q_2$ as a function of $C$ is given properly by (figures are drawn schematically and are not to scale)

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 $4 \mathrm{\mu F}$ and $9 \mathrm{\mu F}$ capacitors), at a point distance $30 \mathrm{m}$ from it, would equal

A capacitance of $2 \mathrm{\mu F}$ is required in an electrical circuit across a potential difference of $1.0 \mathrm{kV}$. Many $1 \mathrm{\mu F}$ capacitors are available which can withstand a potential difference of not more than $300 \mathrm{V}$. The minimum number of capacitors required to achieve this is

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

A parallel plate capacitor of capacitance $90 \mathrm{pF}$ is connected to a battery of emf $20 \mathrm{V}$. If a dielectric material of dielectric constant $K=\frac{5}{3}$ is inserted between the plates, the magnitude of the induced charge will be:

In an $LCR$ circuit as shown below both switches are open initially. Now the switch $S_1$ is closed, $S_{2 }$kept open. ($q$ is the charge on the capacitor and $\tau =RC$ is capacitive time constant). Which of the following statement is correct?