NEET Electrostatic Potential and Capacitance — Set 1

Question 1

Five capacitors of $ 10 \, \mu\text{F} $ each are in series. What is the equivalent capacitance?

Accepted Answer

$ \frac{1}{C} = \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} = \frac{5}{10} $. $ C = \frac{10}{5} = 2 \, \mu\text{F} $.

Question 2

A parallel plate capacitor has plates of area $ 0.08 \, \text{m}^2 $ and separation 0.4 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 0.08}{0.4 \times 10^{-3}} = 1.77 \times 10^{-9} \, \text{F} = 1770 \, \text{pF} $.

Question 3

A $ 4 \, \mu\text{F} $ capacitor is charged to $ 250 \, \text{V} $. What is the energy stored in it?

Accepted Answer

$ U = \frac{1}{2} C V^2 = \frac{1}{2} \times 4 \times 10^{-6} \times (250)^2 $. $ U = \frac{1}{2} \times 4 \times 10^{-6} \times 62500 = 0.125 \, \text{J} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 1

Q1. Five capacitors of \( 10 \, \mu\text{F} \) each are in series. What is the equivalent capacitance?

Q2. A parallel plate capacitor has plates of area \( 0.08 \, \text{m}^2 \) and separation 0.4 mm in air. What is its capacitance? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q3. A \( 4 \, \mu\text{F} \) capacitor is charged to \( 250 \, \text{V} \). What is the energy stored in it?

Q4. A spherical conductor of radius 12 cm has a charge of \( 3 \times 10^{-8} \, \text{C} \). What is the electric field at 30 cm from the center? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q5. Why is the electric field inside a hollow conducting shell zero when no charges are present inside, regardless of the external field?

Q6. A dielectric slab is inserted into a parallel plate capacitor while maintaining a constant charge. Why does the potential difference between the plates increase if the slab is removed partially?

Q7. Two charges \( 28 \, \mu\text{C} \) and \( -14 \, \mu\text{C} \) are placed 28 cm apart. What is the potential energy of the system? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

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

Q9. In a series combination of capacitors, why does each capacitor have the same charge but different potential differences?

Q10. Two charges \( 20 \, \mu\text{C} \) and \( -8 \, \mu\text{C} \) are placed 20 cm apart. What is the potential energy of the system? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).