Half portion of a spherical capacitor is filled with a dielectric of dielectric constant $\mathrm{k}=2$ and conductivity $\sigma$. The charge given to spherical capacitor is ${\mathrm{Q}}_0$. Due to the conductivity of dielectric charge leaks and the time constant for the discharge circuit is $\mathrm{x}$ time of $\frac{{\epsilon }_0}{\sigma }$. Find the value of $\mathrm{x}$.

An $RC$ circuit as shown in the figure is driven by a $AC$ source generating a square wave. The output wave pattern monitored by $CRO$ would look close to :

For the given input voltage waveform ${\mathrm{V}}_{\text{in }}\left(\mathrm{t}\right),$ the output voltage waveform ${\mathrm{V}}_0\left(\mathrm{t}\right),$ across the capacitor is correctly depicted by :

A capacitor of capacitance $C=1 \mu \mathrm{F}$ is suddenly connected to a battery of $100 \mathrm{V}$ through a resistance $R=100 \mathrm{\Omega }.$ The time taken for the capacitor to be charged to get $50 \mathrm{V}$ is:

(Take $\ln 2=0.69$)

The circuit shown in the figure consists of a charged capacitor of capacity $3 \mu \mathrm{F}$ and a charge of $30 \mu \mathrm{C}.$ At time $t=0,$ when the key is closed, the value of current flowing through the $5 \mathrm{M}\Omega$ resistor is $x \mathrm{\mu A}.$ The value of $x$ to the nearest integer is

Consider the circuit shown in the figure below:



All the resistors are identical. The charge stored in the capacitor, once it is fully charged, is

A blackbox $\left(BB\right)$ which may contain a combination of electrical circuit elements (resistor, capacitor or inductor) is connected with other external circuit elements as shown below in the figure $\left(a\right)$ . After the switch $\left(S\right)$ is closed at time $t=0$ , the current $\left(I\right)$ as a function of time $\left(t\right)$ is shown in the figure $\left(b\right)$ .



From this we can infer that the black-box contains

What is the charge on the capacitor in the circuit shown below?

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

The circuit shown has been connected for a long time. The voltage across the capacitor is,