Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainPhysicsCapacitance

One plate of a parallel plate capacitor is connected to a spring as shown in the figure. The area of each plate of the capacitor is A and the distance between the plates is d , when the battery is not connected and the spring is unstretched. After connecting the battery, in the steady state the distance between the plates is 0.75 d , then the force constant of the spring is

Options

  1. A3 8 ₀ V^2 A d^3
  2. B8 3 ₀ V^2 A d^3
  3. C9 32 ₀ V^2 A d^3
  4. D32 9 ₀ V^2 A d^3

Correct answer

D. 32 9 ₀ V^2 A d^3

Step-by-step solution

In equilibrium, force between plates of capacitor = spring force q^2 2 ₀ A =k x where, x= extension in spring. Now before charging, when spring is unstretched (x=0) distance of plates is d and after charging it is 3 4 d . So, x=d- 3 4 d= 1 4 d Hence, aligned k & = q^2 2 ₀ A x = C^2 V^2 2 ₀ A x & = ₀^2 A^2 ( 3 4 d ) V^2 2 ₀ A 1 4 d = 32 9 ( ₀ V^2 A d^3 ) aligned

Practice Capacitance on Quantrex Academy →

More from Capacitance

Passage: A container of height 2 m, length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates ( M₁ and M₂ ) which extend far beyond 2026A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1 , F when the space between the plates is filled with an insulating material of re 2026A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the to 2026From the circuit given below, the capacitance between terminals A and B shown in the circuit is ______ F. (take C₁=C₂=C₃=1 F and C₄=2 F.) 2026A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed v . If x is the separation between the plates at any instant, then the time r 2026Consider a circuit consisting of a capacitor ( 20 F), resistor ( 100 ) and two identical diodes as shown in figure. The resistance of diode under forward biasing condition is 10 . 2026The dimensional formula of 1 2 ₀ E^2 ( ₀ = permittivity of vacuum and E = electric field) is M^a L^b T^c . The value of 2a - b + c = _______. 2026A parallel plate air capacitor has a capacitance C . When it is half filled as show in figure with a dielectric constant K = 5 , the percentage increase in the capacitance is _____ 2026 Full Capacitance list All 99 Percentile Qs Bank for JEE Main PYQs