Exam 20: The Second Law of Thermodynamics

Energy in capacitors: In the circuit shown in the figure, all the capacitors are air-filled. With the switch S open, the 40.0-µF capacitor has an initial charge of 5.00 µC while the other three capacitors are uncharged. The switch is then closed and left closed for a long time. Calculate the initial and final values of the total electrical energy stored in these four capacitors.

Energy density: 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?

Dielectrics: A parallel-plate capacitor consists of two parallel, square plates that have dimensions 1.0 cm by 1.0 cm. If the plates are separated by and the space between them is filled with teflon, what is the capacitance of this capacitor? (The dielectric constant for teflon is 2.1, and ε₀ = 8.85 × 10^-12 C²/N ∙ m².)

Energy in capacitors: Equal but opposite charges Q are placed on the square plates of an air-filled parallel-plate capacitor. The plates are then pulled apart to twice their original separation, which is small compared to the dimensions of the plates. Which of the following statements about this capacitor are true? (There may be more than one correct choice.)

Energy in capacitors: 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 capacitance was C₀, what is the new capacitance?

Energy in capacitors: Two square air-filled parallel plates that are initially uncharged are separated by 1.2 mm, and each of them has an area of 190 mm². How much charge must be transferred from one plate to the other if 1.1 nJ of energy are to be stored in the plates? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Parallel-plate capacitors: A parallel-plate capacitor has plates of area 0.40 m² and plate separation of 0.20 mm. The capacitor is connected across a 9.0-V potential source. (ε₀ = 8.85 × 10^-12 C²/N ∙ m²) (a) What is the magnitude of the electric field between the plates? (b) What is the capacitance of the capacitor? (c) What is the magnitude of the charge on each plate of the capacitor?

Energy in capacitors: 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?

Capacitors in combination: The capacitors in the network shown in the figure all have a capacitance of 5.0 µF. What is the equivalent capacitance, C_ab, of this capacitor network?

Dielectrics: A parallel-plate capacitor has a capacitance of 10 mF and is charged with a 20-V power supply. The power supply is then removed and a dielectric material of dielectric constant 4.0 is used to fill the space between the plates. What is the voltage now across the capacitor?

Dielectrics: An air-filled parallel-plate capacitor is connected to a battery and allowed to charge up. Now a slab of dielectric material is placed between the plates of the capacitor while the capacitor is still connected to the battery. After this is done, we find that

Capacitors in combination: Three capacitors, of capacitance 5.00 μF, 10.0 μF, and 50.0 μF, are connected in series across a 12.0-V voltage source. (a) How much charge is stored in the 5.00-μF capacitor? (b) What is the potential difference across the 10.0-μF capacitor?

Parallel-plate capacitors: The charge on the square plates of a parallel-plate capacitor is Q. The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation, which is small compared to the dimensions of the plates. The amount of charge on the plates is now equal to

Capacitors in combination: The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, V_ab = +100V, is applied across the network. The switch S in the network is initially open but is then closed. Assume that all the capacitances shown are accurate to two significant figures. What is the equivalent capacitance between ab (a) with the switch S open? (b) with the switch S closed?

Cylindrical capacitors: 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)

Cylindrical capacitors: A cylindrical capacitor is made of two thin-walled concentric cylinders. The inner cylinder has radius = 4.0 mm, and the outer one a radius = 8.0 mm. The common length of the cylinders is L = 150 m. What is the potential energy stored in this capacitor when a potential difference 4.0 V is applied between the inner and outer cylinder? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Capacitors in combination: The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, V_ab = +100V, is applied across the network. The switch S in the network is kept open. Assume that all the capacitances shown are accurate to two significant figures. What is potential difference V_cd across the open switch S?

Energy in capacitors: 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?

Dielectrics: A parallel-plate capacitor with plate separation of 1.0 cm has square plates, each with an area of 6.0 × 10^-2 m². What is the capacitance of this capacitor if a dielectric material with a dielectric constant of 2.4 is placed between the plates, completely filling them? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Capacitors in combination: The four identical capacitors in the circuit shown in the figure are initially uncharged. Let the charges on the capacitors be Q₁, Q₂, Q₃, and Q₄ and the potential differences across them be V₁, V₂, V₃, and V₄. The switch is thrown first to position A and kept there for a long time. It is then thrown to position B. Which of the following conditions is true with the switch in position B?