Capacitor

A container of height 2 m , length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates ( $\mathrm{M}_1$ and $\mathrm{M}_2$ ) which extend far beyond the vertical walls in all directions. The c...

Four identical thin, square metal sheets, $S_1, S_2, S_3$ and $S_4$, each of side $a$ are kept parallel to each other with equal distance $d(\ll a)$ between them, as shown in the figure. Let \({C_0} = {{{\varepsilon _0}{a^2}} \over d}\), wh...

A container has a base of $50 \mathrm{~cm} \times 5 \mathrm{~cm}$ and height $50 \mathrm{~cm}$, as shown in the figure. It has two parallel electrically conducting walls each of area $50 \mathrm{~cm} \times 50 \mathrm{~cm}$. The remaining w...

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 $1 \mathrm{~A}$ flows through the $1 \Omega$ resistor. The key is closed at time $t=t_0$. Which of the follo...

A medium having dielectric constant $K>1$ fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is $d$. The capacitor is connected to a battery of voltage $V$, as shown i...

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 \(\mu\)C. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 \(\mu\)C.The...

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 \(\mu\)C. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 \(\mu\)C.The...

Two capacitors with capacitance values C1 = 2000 \(\pm\) 10 pF and C2 = 3000 \(\pm\) 15 pF are connected in series. The voltage applied across this combination is V = 5.00 \(\pm\) 0.02 V. The percentage error in the calculation of the...

A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness, \(\delta = {d \over N}\). The dielec...

Three identical capacitors \({C_1},{C_2}\) and \({C_3}\) have a capacitance of \(1.0\,\mu F\) each and they are unchanged initially. They are connected in a circuit as shown in the figure and \({C_1}\) is then filled completely with a diele...

In Process 2, total energy dissipated across the resistance ED is

In Process 1, the energy stored in the capacitor EC and heat dissipated across resistance ED are related by

A parallel plate capacitor having plates of area S and plate separation d, has capacitance C1 in air. When two dielectrics of different relative permittivities (\(\varepsilon\)1 = 2 and \(\varepsilon\)2 = 4) are introduced between the two...

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 portio...

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 ...

In the given circuit, a charge of \(+80\) \(\mu C\) is given to the upper plate of the \(4\) \(\mu F\) capacitor. Then in the steady state, the charge on the upper plate of the \(3\) \(\mu F\) capacitor is

A \(2\) \(\mu F\) capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch \(S\) is turned to position \(2\) 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 becomes 4 V? (Take ln5 = 1.6, ln3 = 1.1)

Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening ...

A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is

In the following circuits, it is given that $\mathrm{R}_1=1 \Omega, \mathrm{R}_2=2 \Omega, \mathrm{C}_1=2 \mu \mathrm{~F}$ and $\mathrm{C}_2=4 \mu \mathrm{~F}$.The time constants (in $\mu \mathrm{s}$ ) for the circuits I, II, III are, rcspe...

In the given circuit, the switch S is closed at time \(t=0\). The charge Q on the capacitor at any instant t is given by \(Q(t)=Q_0(1-e^{-\alpha t})\). Find the value of Q\(_0\) and \(\alpha\) in terms of given parameters shown in the circu...