Capacitors and Capacitance Quiz

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.