Exam 26: Capacitance and Dielectrics

A parallel plate capacitor of capacitance C₀ has plates of area A with separation d between them. When it is connected to a battery of voltage V₀, it has charge of magnitude Q₀ on its plates. It is then disconnected from the battery and the space between the plates is filled with a material of dielectric constant 3. After the dielectric is added, the magnitudes of the capacitance and the potential difference between the plates are

Two spheres are made of conducting material. Sphere #2 has twice the radius of Sphere #1. What is the ratio of the capacitance of Sphere #2 to the capacitance of sphere #1?

Determine the equivalent capacitance of the combination shown when C = 45 μF.

If C = 10 μF, what is the equivalent capacitance for the combination shown?

A 15-μF capacitor and a 25-μF capacitor are connected in parallel, and charged to a potential difference of 60 V. How much energy is then stored in this capacitor combination?

If V_A − V_B = 50 V, how much energy is stored in the 36-μF capacitor?

What is the total energy stored in the group of capacitors shown if the charge on the 30-μF capacitor is 0.90 mC?

An electric dipole having dipole moment of magnitude p is placed in a uniform electric field having magnitude E. What is the magnitude of the greatest change in potential energy that can happen for this dipole in this field?

A 15-μF capacitor and a 30-μF capacitor are connected in series, and charged to a potential difference of 50 V. What is the resulting charge on the 30-μF capacitor?

A 200-volt battery is connected to a 0.50-microfarad parallel-plate, air-filled capacitor. Now the battery is disconnected, with care taken not to discharge the plates. Some Pyrex glass is then inserted between the plates, completely filling up the space. What is the final potential difference between the plates? (The dielectric constant for Pyrex is κ = 5.6.)

A parallel plate capacitor of capacitance C₀ has plates of area A with separation d between them. When it is connected to a battery of voltage V₀, it has charge of magnitude Q₀ on its plates. It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them. After the plates are 2d apart, the new capacitance and the potential difference between the plates are

Determine the equivalent capacitance of the combination shown when C = 45 μF.

Which of the following statements is incorrect?

A 30-μF capacitor is charged to 40 V and then connected across an initially uncharged 20-μF capacitor. What is the final potential difference across the 30-μF capacitor?

Determine the charge stored by C₁ when C₁ = 20 μF, C₂ = 10 μF, C₃ = 30 μF, and V₀ = 18 V.

A 0.120 pF parallel-plate capacitor is charged to a potential difference of 10.0 V and then disconnected from the battery. A cosmic ray burst creates 1.00 × 10⁶ electrons and 1.00 × 10⁶ positive charges between the plates. If the charges do not recombine, but reach the oppositely charged plates, by how much is the potential difference between the capacitor plates reduced?

The equivalent capacitance of the circuit shown below is

The plates of a parallel plate capacitor of capacitance are horizontal. Into the gap a slab of dielectric material with is placed, filling the bottom half of the gap between the plates. What is the resulting new capacitance?

Determine the energy stored in C₁ when C₁ = 10 μF, C₂ = 12 μF, C₃ = 15 μF, and V₀ = 70 V.

A 4.0-mF capacitor initially charged to 50 V and a 6.0-mF capacitor charged to 30 V are connected to each other with the positive plate of each connected to the negative plate of the other. What is the final charge on the 6.0-mF capacitor?