Capacitors and Capacitance Quiz
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Questions and Answers

What is the formula for the capacitance of an isolated sphere?

  • $C = rac{4 ext{π}ε₀r^2}{3}$ (correct)
  • $C = 4 ext{π}ε₀r$
  • $C = rac{4 ext{π}ε₀r}{3}$
  • $C = 4 ext{π}ε₀r^2$

    • What is the formula for the energy stored in a capacitor?

  • $U = rac{1}{2}QV$
  • $U = rac{1}{2}CV$
  • $U = rac{1}{2}CV^2$ (correct)
  • $U = rac{1}{2}Q^2/C$

    • In which type of capacitor is the potential gradient constant?

  • Spherical capacitor
  • Parallel-plate capacitor (correct)
  • Cylindrical capacitor
  • Variable capacitor

    • What is the formula for the force of attraction between oppositely-charged plates of a capacitor?

    <p>$F = rac{Q^2}{2ε₀A}$</p> Signup and view all the answers

    What is the formula for the time constant in an RC circuit?

    <p>$τ = rac{R}{C}$</p> Signup and view all the answers

    Study Notes

    Capacitance of an Isolated Sphere

    • Capacitance (C) of an isolated sphere is given by the formula:
      • ( C = 4 \pi \epsilon_0 r ), where ( \epsilon_0 ) is the vacuum permittivity and ( r ) is the radius of the sphere.

    Energy Stored in a Capacitor

    • The energy (U) stored in a capacitor can be calculated using the formula:
      • ( U = \frac{1}{2} C V^2 ), where ( C ) is the capacitance and ( V ) is the voltage across the capacitor.

    Potential Gradient in Capacitors

    • A capacitor with a parallel plate design exhibits a constant potential gradient, due to uniform electric field distribution between the plates.

    Force of Attraction Between Oppositely-Charged Plates

    • The formula for the force (F) of attraction between oppositely charged plates of a capacitor is:
      • ( F = \frac{1}{2} \frac{Q^2}{C} ), where ( Q ) is the charge on one plate and ( C ) is the capacitance.

    Time Constant in an RC Circuit

    • The time constant (( \tau )) in an RC circuit is defined as:
      • ( \tau = R C ), where ( R ) is the resistance and ( C ) is the capacitance. This indicates the time taken for the charge or voltage to reach about 63.2% of its maximum value.

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    Description

    Test your knowledge of capacitors and capacitance with this quiz. Explore topics such as capacitance of isolated spheres, spherical and cylindrical capacitors, potential gradient, capacitors in series and parallel, and more. Sharpen your understanding of these important concepts in electronics and physics.

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