Capacitor · Physics · Class 12

Dielectrics play an important role in design of capacitors. The molecules of a dielectric may be polar or non-polar. When a dielectric slab is placed in an external electric field, opposite charges appear on the two surfaces of the slab perpendicular to electric field. Due to this an electric field is established inside the dielectric.

The capacitance of a capacitor is determined by the dielectric constant of the material that fills the space between the plates. Consequently, the energy storage capacity of a capacitor is also affected. Like resistors, capacitors can also be arranged in series and/or parallel.

(i) Which of the following is a polar molecule?

(A) $\mathrm{O}_2$

(B) $\mathrm{H}_2$

(C) $\mathrm{N}_2$

(D) HCl

(ii) Which of the following statements about dielectrics is correct?

(A) A polar dielectric has a net dipole moment in absence of an external electric field which gets modified due to the induced dipoles.

(B) The net dipole moments of induced dipoles is along the direction of the applied electric field.

(C) Dielectrics contain free charges.

(D) The electric field produced due to induced surface charges inside a dielectric is along the external electric field.

(iii) When a dielectric slab is inserted between the plates of an isolated charged capacitor, the energy stored in it

(A) increases and the electric field inside it also increases.

(B) decreases and the electric field also decreases.

(C) decreases and the electric field increases.

(D) increases and the electric field decreases.

(iv) (a) An air-filled capacitor with plate area A and plate separation $d$ has capacitance $\mathrm{C}_0$. A slab of dielectric constant K, area A and thickness $\left(\frac{d}{5}\right)$ is inserted between the plates. The capacitance of the capacitor will become

(A) $\left[\frac{4 \mathrm{~K}}{5 \mathrm{~K}+1}\right] \mathrm{C}_0$

(B) $\left[\frac{K+5}{4}\right] C_0$

(C) $\left[\frac{5 \mathrm{~K}}{4 \mathrm{~K}+1}\right] \mathrm{C}_0$

(D) $\left[\frac{K+4}{5 K}\right] C_0$

OR

(b) Two capacitors of capacitances $2 \mathrm{C}_0$ and $6 \mathrm{C}_0$ are first connected in series and then in parallel across the same battery. The ratio of energies stored in series combination to that in parallel is

(A) $\frac{1}{4}$

(B) $\frac{1}{6}$

(C) $\frac{2}{15}$

(D) $\frac{3}{16}$

A capacitor is a system of two conductors separated by an insulator. The two conductors have equal and opposite charges with a potential difference between them. The capacitance of a capacitor depends on the geometrical configuration (shape, size and separation) of the system and also on the nature of the insulator separating the two conductors. They are used to store charges. Like resistors, capacitors can be arranged in series or parallel or a combination of both to obtain desired value of capacitance.

(i) Find the equivalent capacitance between points A and B in the given diagram.

(ii) A dielectric slab is inserted between the plates of a parallel plate capacitor. The electric field between the plates decreases. Explain.

(iii) A capacitor A of capacitance C, having charge Q is connected across another uncharged capacitor B of capacitance $$2 C$$. Find an expression for (a) the potential difference across the combination and (b) the charge lost by capacitor A.

OR

(iii) Two slabs of dielectric constants $$2 \mathrm{~K}$$ and $$\mathrm{K}$$ fill the space between the plates of a parallel plate capacitor of plate area A and plate separation $$d$$ as shown in figure. Find an expression for capacitance of the system.

(a) Two charged conducting spheres of radii $$a$$ and $$b$$ are connected to each other by a wire. Find the ratio of the electric fields at their surfaces.

OR

(b) A parallel plate capacitor (A) of capacitance C is charged by a battery to voltage $$V$$. The battery is disconnected and an uncharged capacitor (B) of capacitance $$2 \mathrm{C}$$ is connected across $$\mathrm{A}$$. Find the ratio of

(i) final charges on A and B.

(ii) total electrostatic energy stored in A and B finally and that stored in A initially.

The capacitors, each of $$4 \mu \mathrm{F}$$ are to be connected in such a way that the effective capacitance of the combination is $$6 \mu \mathrm{F}$$. This can be achieved by connecting