NEET Electrostatic Potential and Capacitance — Set 19

Question 1

A $ 14 \, \mu\text{F} $ capacitor charged to $ 20 \, \text{V} $ is connected to an uncharged $ 14 \, \mu\text{F} $ capacitor. What is the final potential difference?

Accepted Answer

Initial charge: $ Q = 14 \times 10^{-6} \times 20 = 2.8 \times 10^{-4} \, \text{C} $. Total capacitance: $ 14 + 14 = 28 \, \mu\text{F} $. Final voltage: $ V = \frac{Q}{C} = \frac{2.8 \times 10^{-4}}{28 \times 10^{-6}} = 10 \, \text{V} $.

Question 2

A $ 5 \, \mu\text{F} $ capacitor charged to $ 120 \, \text{V} $ is connected to an uncharged $ 15 \, \mu\text{F} $ capacitor. What is the energy lost?

Accepted Answer

Initial energy: $ U_i = \frac{1}{2} \times 5 \times 10^{-6} \times (120)^2 = 0.036 \, \text{J} $. Charge: $ Q = 5 \times 10^{-6} \times 120 = 6 \times 10^{-4} \, \text{C} $. Total $ C = 5 + 15 = 20 \, \mu\text{F} $, $ V = \frac{6 \times 10^{-4}}{20 \times 10^{-6}} = 30 \, \text{V} $. Final energy: $ U_f = \frac{1}{2} \times 20 \times 10^{-6} \times (30)^2 = 0.009 \, \text{J} $. Loss: $ U_i - U_f = 0.036 - 0.009 = 0.027 \, \text{J} $.

Question 3

A parallel plate capacitor has plates of area $ 0.07 \, \text{m}^2 $ and separation 0.35 mm in air. What is its capacitance? (Take $ \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} $).

Accepted Answer

$ C = \frac{\varepsilon_0 A}{d} = \frac{8.85 \times 10^{-12} \times 0.07}{0.35 \times 10^{-3}} = 1.77 \times 10^{-9} \, \text{F} = 1770 \, \text{pF} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 19

Q1. A \( 14 \, \mu\text{F} \) capacitor charged to \( 20 \, \text{V} \) is connected to an uncharged \( 14 \, \mu\text{F} \) capacitor. What is the final potential difference?

Q2. A \( 5 \, \mu\text{F} \) capacitor charged to \( 120 \, \text{V} \) is connected to an uncharged \( 15 \, \mu\text{F} \) capacitor. What is the energy lost?

Q3. A parallel plate capacitor has plates of area \( 0.07 \, \text{m}^2 \) and separation 0.35 mm in air. What is its capacitance? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q4. A parallel plate capacitor with \( C = 20 \, \text{pF} \) in air has a dielectric (\( K = 3 \)) inserted fully between plates. What is the new capacitance?

Q5. In a system where a charged particle moves along a curved path between two points with different potentials, what can be inferred about the work done by the electric field?

Q6. A dipole \( p = 10 \times 10^{-9} \, \text{C m} \) is rotated from \( \theta = 0^\circ \) to \( 90^\circ \) in a field \( E = 4 \times 10^5 \, \text{N/C} \). What is the work done?

Q7. Why does the electric field inside a uniformly charged spherical shell vary linearly with distance from the center if a point charge is placed at the center?

Q8. A dipole \( p = 5 \times 10^{-9} \, \text{C m} \) is rotated from \( \theta = 90^\circ \) to \( 180^\circ \) in a field \( E = 2 \times 10^5 \, \text{N/C} \). What is the work done?

Q9. Four capacitors of \( 20 \, \mu\text{F} \) each are in series. What is the equivalent capacitance?

Q10. A \( 4 \, \mu\text{F} \) capacitor is charged to \( 50 \, \text{V} \) and then connected to an uncharged \( 2 \, \mu\text{F} \) capacitor. What is the final energy?