Kirchhoff's Laws with Capacitors

In the circuit shown in figure the switch $S$ is initially open and both the capacitors are initially uncharged. If the ratio of current through $2\Omega$ resistor, just after the switch $\mathrm{S}$ is closed and a long time after the switch $\mathrm{S}$ is closed is $\frac{x}{2}$, find the value of $x$.

Three uncharged capacitors of capacities $C_1,C_2$ and $C_3$ are connected as shown in the figure. $A,B$ and $C$ are at potentials $V_1, V_2$ and $V_3$ respectively. The potential at $O$ is

Three uncharged capacitors of capacitance $C_1,C_2$ and ${\mathrm{C}}_3$ are connected as shown in the figure to one another at point $O$. Points $A, B$ and $D$ are at potentials $V_A,$ $V_B$ and $V_D$ respectively. Then the potential at $O$ will be,: 

The charge on the capacitor $\mathrm{C}$ in steady state is ${\mathrm{q}}_1$ in the given diagram. Now, key is closed and steady state charge on $\mathrm{C}$ is ${\mathrm{q}}_2$ .The ratio of charges ${\mathrm{q}}_1 \mathrm{and} {\mathrm{q}}_2$ will be -

In steady state, charge on $\mathrm{3 }\mathrm{\mu }\mathrm{F}$ capacitor is

In the adjacent circuit $V_A–V_B$ will be:
  

In the circuit of following figure, the final voltage drop across the capacitor $\mathrm{C}$ in steady state is

Two condensers $C_1$ and $C_2$ in a circuit are joined as shown in figure. The potential of point $A$ is $V_1$ and that of $\mathrm{B}$ is $V_2$ . The potential of point $D$ will be

In the circuit shown in the figure, a potential difference of $60\mathrm{ }\mathrm{V}$ is applied between $\mathrm{a}$ and $\mathrm{b}$. The potential difference between the points $\mathrm{c}$ and $\mathrm{d}$ is

The figure shows two capacitors $C_1$ and $C_2$ connected with $10\mathrm{ }\mathrm{V}$ battery and terminals $A$ and $B$ are earthed. The graph shows the variation of potential as one moves from left to right. Then the ratio of $\frac{{\mathit{C}}_{\mathit{1}}}{{\mathit{C}}_{\mathit{2}}}$ is

The correct combination is : (symbols have their usual meanings)

In the following circuit composed of the identical capacitor, across which terminals would you connect a battery in order for all capacitors to charge up

A voltmeter of $900 \mathrm{\Omega }$ resistance measures the potential difference across $100 \mathrm{\Omega }$ resistance, in the following circuit. The percentage of the error made in reading the potential difference is

A network of six identical capacitors, each of value $C$, is made, as shown in the figure.

The equivalent capacitance between the points $A$ and $B$ is

Which statement(s) is/are true?

$\left(i\right)$ Kirchhoff's law is equally applicable to both AC and DC.

$\left(ii\right)$ Semiconductors have a positive temperature coefficient of resistance.

$\left(iii\right)$ Meter bridge has a greater sensitivity when the resistances of all the four arms of the bridge are of the same order.

$\left(iv\right)$ The emf of a cell depends upon the size and area of electrodes.

One end each of a resistance $r$, capacitor $C$ and resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries, $P, Q, R$ having, respectively, emf's $E, E \mathrm{and} 2E$. The negative terminals of the batteries are then connected together. In this circuit, with steady current the potential drop across the capacitor is,

In the given circuit, with steady current, the potential difference across the capacitor must be