RC circuits

Consider a circuit consisting of a capacitor (20 μF), resistor (100 Ω) and two identical diodes as shown in figure. The resistance of diode under forward biasing condition is 10 Ω. The time constant of the circuit is $\alpha\times10^{-3}$ s. The value of $\alpha$ is ________.

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 ________ μC.

In a circuit shown in the figure, the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition, a current of 1 A flows through the $1\,\Omega$ resistor. The key is closed at time $t = t_0$. Which of the following statement(s) is(are) correct?

[Given: $e^{-1} = 0.36$]

A capacitor is discharging through a resistor R. Consider in time $t_1$, the energy stored in the capacitor reduces to half of its initial value and in time $t_2$, the charge stored reduces to one eighth of its initial value. The ratio $t_1/t_2$ will be

As show in the figure, in steady state, the charge stored in the capacitor is ______ $\times10^{-6}$ C.

A long straight wire carries a current, $I = 2$ ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at distances 1 cm and 4 cm from the wire. At time $t = 0$, the rod starts moving on the rails with a speed $v = 3.0$ m/s (see the figure).

A resistor $R = 1.4\ \Omega$ and a capacitor $C_o = 5.0\ \mu$F are connected in series between the rails. At time $t = 0$, $C_o$ is uncharged. Which of the following statement(s) is(are) correct? [$\mu_0 = 4\pi \times 10^{-7}$ SI units. Take $\ln 2 = 0.7$]

In the circuit shown, initially there is no charge on capacitors and keys $S_1$ and $S_2$ are open. The values of the capacitors are $C_1 = 10\ \mu$F, $C_2 = 30\ \mu$F and $C_3 = C_4 = 80\ \mu$F.

Which of the statement(s) is/are correct?

In Process 1, the energy stored in the capacitor $E_C$ and heat dissipated across resistance $E_D$ are related by:

In Process 2, total energy dissipated across the resistance $E_D$ is:

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

An infinite line charge of uniform electric charge density $\lambda$ lies along the axis of an electrically conducting infinite cylindrical shell of radius $R$. At time $t=0$, the space inside the cylinder is filled with a material of permittivity $\varepsilon$ and electrical conductivity $\sigma$. The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density $j(t)$ at any point in the material?

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

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) :

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).

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 ?

A series R-C combination is connected to an AC voltage of angular frequency $\omega=500$ radian/s. If the impedance of the R-C circuit is $R\sqrt{1.25}$, the time constant (in millisecond) of the circuit is

At time $t=0$, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V?

[Take: $\ln5=1.6$, $\ln3=1.1$]

You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current $I$ (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage $V_1$ and $V_2$ (indicated in circuits) are related as shown in Column I. Match the two.

A parallel plate capacitor C with plates of unit area and separation $d$ is filled with a liquid of dielectric constant $K=2$. The level of liquid is $\frac d3$ initially. Suppose the liquid level decreases at a constant speed $V$, the time constant as a function of time $t$ is