Parallel plate capacitor with a dielectric; energy stored — NEET & JEE Questions

Question 1 · difficulty L1 · recall

For a parallel-plate capacitor in vacuum with plate area A and separation d, capacitance is

• A. $C=\epsilon_0A/d$
• B. $C=\epsilon_0d/A$
• C. $C=Ad/\epsilon_0$
• D. $C=\epsilon_0/(Ad)$

Question 2 · difficulty L2 · understanding

A $$600 ~\mathrm{pF}$$ capacitor is charged by $$200 \mathrm{~V}$$ supply. It is then disconnected from the supply and is connected to another uncharged $$600 ~\mathrm{pF}$$ capacitor. Electrostatic energy lost in the process is ____________ $$\mu \mathrm{J}$$

Question 3 · difficulty L2 · understanding

A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ___________ nJ.

Question 4 · difficulty L2 · understanding

A sphere of capacitance 100 pF is charged to a potential of 100 V . Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha \times 10^{-7} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$ . (combined capacitance of spheres is 200 pF )

• A. 5
• B. $\frac{5}{2}$
• C. $\frac{7}{2}$
• D. $\frac{9}{2}$

Question 5 · difficulty L2 · understanding

A parallel plate capacitor of capacitance 1 µF is charged to a potential difference of 20 V. The distance between plates is 1 µm. The energy density between plates of capacitor is :

• A. $1.8 \times 10^3$ J/m 3
• B. $2 \times 10^2$ J/m 3
• C. $2 \times 10^{-4}$ J/m 3
• D. $1.8 \times 10^5$ J/m 3

Question 6 · difficulty L2 · understanding

A parallel plate capacitor was made with two rectangular plates, each with a length of $l=3 \mathrm{~cm}$ and breath of $\mathrm{b}=1 \mathrm{~cm}$. The distance between the plates is $3 \mu \mathrm{~m}$. Out of the following, which are the ways to increase the capacitance by a factor of 10 ? A. $l=30 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}$ B. $l=3 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=30 \mu \mathrm{~m}$ C. $l=6 \mathrm{~cm}, \mathrm{~b}=5 \mathrm{~cm}, \mathrm{~d}=3 \mu \mathrm{~m}$ D. $l=1 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=10 \mu \mathrm{~m}$ E. $l=5 \mathrm{~cm}, \mathrm{~b}=2 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}$ Choose the correct answer from the options given below:

• A. C only
• B. A only
• C. B and D only
• D. C and E only

Question 7 · difficulty L2 · understanding

An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity $10^6 \mathrm{~m} / \mathrm{s}$. If the magnitude of the electric field between the plates is $9.1 \mathrm{~V} / \mathrm{cm}$, then the vertical component of velocity of electron is (mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$ and charge of electron $=1.6 \times 10^{-19} \mathrm{C}$ )

• A. $1 \times 10^6 \mathrm{~m} / \mathrm{s}$
• B. $16 \times 10^6 \mathrm{~m} / \mathrm{s}$
• C. $16 \times 10^4 \mathrm{~m} / \mathrm{s}$
• D. 0

Question 8 · difficulty L2 · understanding

A parallel plate capacitor of capacitance $$2 \mathrm{~F}$$ is charged to a potential $$\mathrm{V}$$, The energy stored in the capacitor is $$E_{1}$$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $$\mathrm{E}_{2}$$. The ratio $$\mathrm{E}_{2} / \mathrm{E}_{1}$$ is :

• A. 1 : 2
• B. 2 : 3
• C. 2 : 1
• D. 1 : 4

Question 9 · difficulty L2 · understanding

An electron with kinetic energy K 1 enters between parallel plates of a capacitor at an angle '$$\alpha$$' with the plates. It leaves the plates at angle '$$\beta$$' with kinetic energy K 2 . Then the ratio of kinetic energies K 1 : K 2 will be :

• A. $${{{{\cos }^2}\beta } \over {{{\cos }^2}\alpha }}$$
• B. $${{\cos \beta } \over {\cos \alpha }}$$
• C. $${{{{\sin }^2}\beta } \over {{{\cos }^2}\alpha }}$$
• D. $${{\cos \beta } \over {\sin \alpha }}$$

Question 10 · difficulty L2 · understanding

A parallel plate capacitor has charge $5 \times 10^{-6} \mathrm{C}$. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is $4 \times 10^{-6} \mathrm{C}$ then the dielectric constant of the slab is _______________.