Exam 23: Capacitance and Dielectrics

Two capacitors of capacitance 6.00 μF and 8.00 μF are connected in parallel. The combination is then connected in series with a 12.0-V voltage source and a 14.0-μF capacitor, as shown in the figure. (a) What is the equivalent capacitance of this combination? (b) What is the charge on the 6.00-μF capacitor? (c) What is the potential difference across the 6.00-μF capacitor?

An ideal parallel-plate capacitor consists of a set of two parallel plates of area A separated by a very small distance d. When the capacitor plates carry charges +Q and -Q, the capacitor stores energy U0. If the separation between the plates is doubled, how much electrical energy is stored in the capacitor?

A 6.00-μF parallel-plate capacitor has charges of ±40.0 μC on its plates. How much potential energy is stored in this capacitor?

A metal cylinder of radius 2.0 mm is concentric with another metal cylinder of radius 5.0 mm. If the space between the cylinders is filled with air and the length of the cylinders is 50 cm, what is the capacitance of this arrangement? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Two thin-walled concentric conducting spheres of radii 5.0 cm and 10 cm have a potential difference of 100 V between them. (k = 1/4πε0 = 8.99 × 10⁹ N ∙ m²/C²) (a) What is the capacitance of this combination? (b) What is the charge carried by each sphere?

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates. All the geometric parameters of the capacitor (plate diameter and plate separation) are now DOUBLED. If the original energy density between the plates was u₀, what is the new energy density?

Two capacitors, C₁ and C₂, are connected in series across a source of potential difference. With the potential source still connected, a dielectric is now inserted between the plates of capacitor C₁. What happens to the charge on capacitor C₂?

Three capacitors are arranged as shown in the figure. C₁ has a capacitance of 5.0 pF, C₂ has a capacitance of 10.0 pF, and C₃ has a capacitance of 15.0 pF. Find the voltage drop across the entire arrangement if the voltage drop across C₂ is 311 V.

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates. All the geometric parameters of the capacitor (plate diameter and plate separation) are now DOUBLED. If the original energy stored in the capacitor was U₀, how much energy does it now store?

A 1.0 μF capacitor has a potential difference of 6.0 V applied across its plates. If the potential difference across its plates is increased to 8.0 V, how much ADDITIONAL energy does the capacitor store?

An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of 48 mm and 84 mm. The electric potential of the inner conductor with respect to the outer conductor is -400 V. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The energy stored in a 1.0-m length of this capacitor is closest to

An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial And have radii of 13 mm and 85 mm. The electric potential of the inner conductor with respect to the outer conductor is -600 V. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The maximum energy density of the capacitor is closest to