NEET Electrostatic Potential and Capacitance — Set 13

Question 1

Three capacitors $ 4 \, \text{pF} $, $ 8 \, \text{pF} $, and $ 16 \, \text{pF} $ are in parallel. What is the total capacitance?

Accepted Answer

$ C = 4 + 8 + 16 = 28 \, \text{pF} $.

Question 2

An isolated charged capacitor is connected across a resistor momentarily. Why does the energy stored in the capacitor decrease to zero after a long time?

Accepted Answer

When a charged capacitor is connected across a resistor, it discharges through the resistor, forming an RC circuit. The charge $ Q $ on the capacitor decreases exponentially ($ Q(t) = Q_0 e^{-t/RC} $). After a long time ($ t \to \infty $), $ Q \to 0 $, so the energy $ U = \frac{Q^2}{2C} \to 0 $. The energy is dissipated as heat in the resistor during discharge, leaving no energy stored in the capacitor.

Question 3

A dipole $ p = 8 \times 10^{-9} \, \text{C m} $ is rotated from $ \theta = 0^\circ $ to $ 180^\circ $ in a field $ E = 1 \times 10^5 \, \text{N/C} $. What is the work done?

Accepted Answer

Work done: $ W = p E (\cos \theta_0 - \cos \theta_1) = 8 \times 10^{-9} \times 1 \times 10^5 \times (\cos 0^\circ - \cos 180^\circ) $. $ W = 8 \times 10^{-9} \times 1 \times 10^5 \times (1 - (-1)) = 8 \times 10^{-9} \times 1 \times 10^5 \times 2 = 1.6 \times 10^{-3} \, \text{J} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 13

Q1. Three capacitors \( 4 \, \text{pF} \), \( 8 \, \text{pF} \), and \( 16 \, \text{pF} \) are in parallel. What is the total capacitance?

Q2. An isolated charged capacitor is connected across a resistor momentarily. Why does the energy stored in the capacitor decrease to zero after a long time?

Q3. A dipole \( p = 8 \times 10^{-9} \, \text{C m} \) is rotated from \( \theta = 0^\circ \) to \( 180^\circ \) in a field \( E = 1 \times 10^5 \, \text{N/C} \). What is the work done?

Q4. Two charges \( 18 \, \mu\text{C} \) and \( -9 \, \mu\text{C} \) are at \( (2, 0, 0) \) and \( (-2, 0, 0) \, \text{cm} \). What is the potential at midpoint? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q5. Three capacitors \( 10 \, \text{pF} \), \( 20 \, \text{pF} \), and \( 40 \, \text{pF} \) are in parallel. What is the total capacitance?

Q6. A \( 6 \, \mu\text{F} \) capacitor charged to \( 100 \, \text{V} \) is connected to an uncharged \( 18 \, \mu\text{F} \) capacitor. What is the energy lost?

Q7. Why does the potential difference between the plates of a parallel plate capacitor remain constant when a dielectric slab is inserted while the capacitor is connected to a battery?

Q8. A dipole with \( p = 5 \times 10^{-9} \, \text{C m} \) makes an angle of \( 30^\circ \) with a uniform field \( E = 3 \times 10^5 \, \text{N/C} \). What is its potential energy?

Q9. Two capacitors of \( 70 \, \text{pF} \) and \( 140 \, \text{pF} \) are connected in series. What is the equivalent capacitance?

Q10. Two charges \( 12 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \) are at \( (5, 0, 0) \) and \( (-5, 0, 0) \, \text{cm} \). What is the potential at midpoint? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).