NEET Electrostatic Potential and Capacitance — Set 5

Question 1

A parallel plate capacitor with capacitance $ 200 \, \text{pF} $ has a dielectric ($ K = 5 $, thickness $ d/6 $) inserted. What is the new capacitance? (Original separation $ d $).

Accepted Answer

Potential difference: $ V = E_0 \left( \frac{5d}{6} \right) + \frac{E_0}{K} \left( \frac{d}{6} \right) = E_0 d \left( \frac{5}{6} + \frac{1}{6 \times 5} \right) $. $ V = E_0 d \left( \frac{5}{6} + \frac{1}{30} \right) = E_0 d \times \frac{26}{30} = E_0 d \times \frac{13}{15} $. $ C = \frac{Q}{V} = \frac{Q}{\frac{13}{15} V_0} = \frac{15}{13} \times 200 \approx 230.77 \, \text{pF} $.

Question 2

Three capacitors $ 6 \, \text{pF} $, $ 12 \, \text{pF} $, and $ 24 \, \text{pF} $ are in parallel. What is the total capacitance?

Accepted Answer

$ C = 6 + 12 + 24 = 42 \, \text{pF} $.

Question 3

A $ 4 \, \mu\text{F} $ capacitor charged to $ 150 \, \text{V} $ is connected to an uncharged $ 12 \, \mu\text{F} $ capacitor. What is the energy lost?

Accepted Answer

Initial energy: $ U_i = \frac{1}{2} \times 4 \times 10^{-6} \times (150)^2 = 0.045 \, \text{J} $. Charge: $ Q = 4 \times 10^{-6} \times 150 = 6 \times 10^{-4} \, \text{C} $. Total $ C = 4 + 12 = 16 \, \mu\text{F} $, $ V = \frac{6 \times 10^{-4}}{16 \times 10^{-6}} = 37.5 \, \text{V} $. Final energy: $ U_f = \frac{1}{2} \times 16 \times 10^{-6} \times (37.5)^2 = 0.01125 \, \text{J} $. Loss: $ U_i - U_f = 0.045 - 0.01125 = 0.03375 \, \text{J} $.

NEET Physics: Electrostatic Potential and Capacitance — Practice Set 5

Q1. A parallel plate capacitor with capacitance \( 200 \, \text{pF} \) has a dielectric (\( K = 5 \), thickness \( d/6 \)) inserted. What is the new capacitance? (Original separation \( d \)).

Q2. Three capacitors \( 6 \, \text{pF} \), \( 12 \, \text{pF} \), and \( 24 \, \text{pF} \) are in parallel. What is the total capacitance?

Q3. A \( 4 \, \mu\text{F} \) capacitor charged to \( 150 \, \text{V} \) is connected to an uncharged \( 12 \, \mu\text{F} \) capacitor. What is the energy lost?

Q4. A \( 8 \, \mu\text{F} \) capacitor charged to \( 80 \, \text{V} \) is connected to an uncharged \( 24 \, \mu\text{F} \) capacitor. What is the energy lost?

Q5. A parallel plate capacitor has plates of area \( 0.03 \, \text{m}^2 \) and separation 0.5 mm in air. What is its capacitance? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).

Q6. Two capacitors of \( 50 \, \text{pF} \) and \( 100 \, \text{pF} \) are connected in series. What is the equivalent capacitance?

Q7. In a system where a charged conductor is grounded while placed near a point charge, why does the potential of the conductor become zero?

Q8. Two charges \( 7 \, \mu\text{C} \) and \( -2 \, \mu\text{C} \) are at \( (8, 0, 0) \) and \( (-8, 0, 0) \, \text{cm} \). What is the potential at midpoint? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Q9. A parallel plate capacitor with \( C = 60 \, \text{pF} \) in air has a dielectric (\( K = 7 \)) inserted fully between plates. What is the new capacitance?

Q10. A \( 6 \, \mu\text{F} \) capacitor is charged to \( 300 \, \text{V} \). What is the energy stored in it?