Capacitance

1 Mark Questions q Ans.Line B corresponds to C-, because slope (q/v) of B is less than slope of A.

2.A capacitor has been charged by a DC source. What are the magnitude of conduction and displacement current when it is fully charged?[Delhi 2013]

Ans.

Electric flux through capacitor's plates,

<math>\phi_E = \frac{q}{\epsilon_0}</math>

Here, <math>q = \text{charge on capacitor}</math>

Displacement current,

<math display="block">I_D = \varepsilon_0 \frac{d\phi_E}{dt} = \varepsilon_0 \frac{d\left(\frac{q}{\varepsilon_0}\right)}{dt} = 0</math>

Conduction current, <math>I = C \frac{dV}{dt} = 0</math>, as voltage

becomes constant when the capacitor becomes fully charged. (1)

3.Distinguish between a dielectric and a conductor. [Delhi 2012]

Ans. Dielectrics are non-conductors and do not have free electrons at all. While conductor has free electrons in its any volume which makes it able to pass the electricity through it.

4.Define the dielectric constant of a medium. What is its unit? [Delhi 2011c]

Ans. Dielectric When a dielectric slab is introduced between the plates of charged capacitor or in the region of electric field, an electric field EP induces inside the dielectric due to induced charge on dielectric in a direction opposite to the direction of applied external electric field. Hence, net electric field inside the dielectric gets reduced to <math>\pounds_0 - \pounds_P</math>, where <math>\pounds_0</math> is external electric field. The ratio of applied external electric field and reduced electric field is known as dielectric constant K of dielectric medium, i.e.

<math display="block">K = \frac{E_0}{E_0 - E_0}</math>

5.A metal plate is introduced between the plates of a charged parallel plate capacitor. What is its effect on the capacitance of the capacitor?[Foreign 2009]

Ans. If a metal plate is introduced between the plates of a charged parallel plate capacitor. The capacitance of parallel plate capacitor will becomes infinite.

6.In the figure given below X, Y represent parallel plate capacitors having the same area of plates and the same distance of separation between them. What is the relation between the energies stored in the capacitors?

<math>\mathbf{H}_{X}</math> lγ

<math>\varepsilon_r = 6</math> Air

[Foreign 2008]

Ans.

<math>\langle \rangle</math> Charge on each capacitor connected in series combination is same. Also, two capacitors having same plate area and in equal separation have equal capacitance in air or vacuum. : <math>C_X = 6C_Y</math>

Charge, q is same on both capacitors as connected in series combination.

Energy stored in a capacitor is given by

<math>U = \frac{q^2}{2C} \implies U \propto \frac{1}{C}</math> ٠. <math display="block">\frac{U_X}{U_Y} = \frac{C_Y}{C_X} = \frac{1}{6}</math>

<math>U_X = \frac{1}{6}U_Y</math> (1)

1. The following graph shows the variation of charge Q with voltage V for two capacitors K

and L In which capacitor is more electrostatic energy stored? Q V

[HOTS, Foreign 2008]

Ans.

The slope of Q -V graph of capacitor gives capacitance. Therefore, capacitor L have greater capacitance. Since, two capacitors are given same voltage V, therefore energy stored in a capacitor will be given by formula.

<math>U = \frac{1}{2}CV^2</math> and for same V

<math>U \propto C</math>

<math>\cdot</math>

<math>C_L > C_K</math>

<math>\Rightarrow</math>

<math>U_{l} > U_{K}</math>

⇒ Capacitor L will store more electrostatic energy. (1)

8.Define dielectric strength of a dielectric. [Delhi 2008 C]

Ans. The dielectric strength of a dielectric is the maximum value of applied electric field required to just breakdown of the dielectric material.

2 Marks Questions