Electrostatic Potential & Capacitance

A capacitor stores a charge of 600 µC when connected across a battery of emf 12 V. Find its capacitance.

A capacitor of capacitance 4 µF is charged to a potential difference of 250 V. Calculate the energy stored in it.

An isolated spherical conductor of radius 9 cm is kept in air. Find its capacitance. (Take 1/4πε₀ = 9 × 10⁹ SI units)

A spherical capacitor has an inner sphere of radius 9 cm and a concentric outer sphere of radius 10 cm, which is earthed. Find its capacitance in air.

A parallel plate capacitor has plates of area 200 cm² separated by 1 mm of air. Find its capacitance. (ε₀ = 8.85 × 10⁻¹² F/m)

The capacitor of the previous type (A = 200 cm², d = 1 mm) is now completely filled with a dielectric of dielectric constant 5. Find the new capacitance.

A parallel plate capacitor has capacitance C₀. If the area of its plates is made 3 times larger and the separation between them is reduced to one-third, what is the new capacitance?

A parallel plate capacitor of capacitance 8 µF (no dielectric) is connected to a 25 V battery. Without disconnecting the battery, a dielectric of dielectric constant 3 is inserted to completely fill the gap. Find the charge on the capacitor after the dielectric is inserted.

The surface charge density on a charged conducting plate is 4.0 × 10⁻⁶ C/m². Find the electrostatic pressure on the surface. (ε₀ = 8.85 × 10⁻¹² F/m)

At a point in an electric field, E = 3 × 10⁴ V/m. Find the energy density of the field at that point. (ε₀ = 8.85 × 10⁻¹² F/m)

Three capacitors of 6 µF, 3 µF and 2 µF are connected in series. Find the equivalent capacitance.

Capacitors of 2 µF, 3 µF and 5 µF are connected in parallel across a 12 V battery. Find the total charge supplied by the battery.

Two capacitors of 4 µF each are connected in series, and this combination is connected in parallel with another 4 µF capacitor. Find the equivalent capacitance of the whole network.

A capacitor of 4 µF is charged to a potential of 12 V, and another capacitor of 2 µF is charged to a potential of 6 V (same polarity). They are then connected together by a wire. Find the common potential after connection.

For the two capacitors of the previous question (4 µF at 12 V, 2 µF at 6 V, same polarity) connected together by a wire, calculate the heat dissipated in the process.

An uncharged capacitor is connected to a 20 V battery through a resistor R, with time constant RC = 4 s. Find the potential difference across the capacitor after 4 s.

A capacitor charged to 100 µC discharges through a resistor with a time constant of 5 s. Find the charge remaining on it after 5 s.

A Van de Graaff generator is able to build up a potential of the order of 10⁷ V mainly because —