NEET Electrostatic Potential and Capacitance — Set 17

Question 1

A $ 8 \, \mu\text{F} $ capacitor charged to $ 50 \, \text{V} $ is connected to an uncharged $ 8 \, \mu\text{F} $ capacitor. What is the final potential difference?

Accepted Answer

Initial charge: $ Q = 8 \times 10^{-6} \times 50 = 4 \times 10^{-4} \, \text{C} $. Total capacitance: $ 8 + 8 = 16 \, \mu\text{F} $. Final voltage: $ V = \frac{Q}{C} = \frac{4 \times 10^{-4}}{16 \times 10^{-6}} = 25 \, \text{V} $.

Question 2

Two capacitors of $ 40 \, \text{pF} $ and $ 80 \, \text{pF} $ are connected in series. What is the equivalent capacitance?

Accepted Answer

$ \frac{1}{C} = \frac{1}{40} + \frac{1}{80} = \frac{2 + 1}{80} = \frac{3}{80} $. $ C = \frac{80}{3} \approx 26.67 \, \text{pF} $.

Question 3

A parallel plate capacitor has plates of area $ 0.06 \, \text{m}^2 $ and separation 0.3 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 0.06}{0.3 \times 10^{-3}} = 1.77 \times 10^{-9} \, \text{F} = 1770 \, \text{pF} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 17

Q1. A \( 8 \, \mu\text{F} \) capacitor charged to \( 50 \, \text{V} \) is connected to an uncharged \( 8 \, \mu\text{F} \) capacitor. What is the final potential difference?

Q2. Two capacitors of \( 40 \, \text{pF} \) and \( 80 \, \text{pF} \) are connected in series. What is the equivalent capacitance?

Q3. A parallel plate capacitor has plates of area \( 0.06 \, \text{m}^2 \) and separation 0.3 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 has plates of area \( 0.09 \, \text{m}^2 \) and separation 0.5 mm in air. What is its capacitance? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q5. Why does the potential at the surface of a charged conductor vary if the conductor has an irregular shape?

Q6. Why does the electric field inside a conductor remain zero when a non-symmetric external field is applied?

Q7. An electric dipole with moment \( p = 2 \times 10^{-9} \, \text{C m} \) lies along the z-axis. What is the potential at \( (0, 0, 4) \, \text{m} \)? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q8. A spherical conductor of radius 8 cm has a charge of \( 4 \times 10^{-8} \, \text{C} \). What is the electric field at 12 cm from the center? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q9. A parallel plate capacitor with \( C = 30 \, \text{pF} \) in air has a dielectric (\( K = 6 \)) inserted fully between plates. What is the new capacitance?

Q10. Two charges \( 6 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \) are 12 cm apart. What is the potential energy of the system? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).