Exam 20: The Second Law of Thermodynamics

Dielectrics: 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?

Capacitors in combination: Five capacitors are connected across a potential difference V_ab as shown in the figure. Because of the dielectrics used, each capacitor will break down if the potential across it exceeds 30.0 V. The largest that V_ab can be without damaging any of the capacitors is closest to

Parallel-plate capacitors: Each plate of a parallel-plate air-filled capacitor has an area of 0.0020 , and the separation of the plates is An electric field of is present between the plates. What is the surface charge density on the plates? (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

Capacitors in combination: Four capacitors are connected across a 90-V voltage source as shown in the figure. (a) What is the charge on the 4.0-μF capacitor? (b) What is the charge on a 2.0-μF capacitor? (c) What is the charge on the 3.0-μF capacitor? (d) What is the potential difference across the 6.0-μF capacitor

Spherical capacitors: 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?

Capacitors in combination: 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?

Energy in capacitors: A 1.0 μF capacitor has a potential difference of applied across its plates. If the potential difference across its plates is increased to how much ADDITIONAL energy does the capacitor store?

Energy in capacitors: A charge of 2.00 μC flows onto the plates of a capacitor when it is connected to a 12.0-V potential source. What is the minimum amount of work that must be done in charging this capacitor?

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 this capacitor is connected to a battery that maintains a constant potential difference between the plates, the energy stored in the capacitor is U₀. If the separation between the plates is doubled, how much energy is stored in the capacitor?

Capacitors in combination: When two or more capacitors are connected in series across a potential difference,

Capacitors in combination: Three capacitors are connected as shown in the figure. What is the equivalent capacitance between points a and b?

Cylindrical capacitors: A 1.0 m long piece of coaxial cable has a wire with a radius of and a concentric conductor with inner radius The area between the cable and the conductor is filled with a dielectric. If the voltage drop across the capacitor is when the line charge density is find the value of the dielectric constant. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

Capacitors in combination: 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.

Capacitors in combination: When two or more capacitors are connected in parallel across a potential difference,

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 energy stored in the capacitor was U₀, how much energy does it now store?

Dielectrics: An air-filled capacitor stores a potential energy of due to its charge. It is accidentally filled with water in such a way as not to discharge its plates. How much energy does it continue to store after it is filled? (The dielectric constant for water is 78 and for air it is 1.0006.)

Energy in capacitors: An isolated air-filled parallel-plate capacitor that is no longer connected to anything has been charged up to Q = 2.9 nC. The separation between the plates initially is 1.20 mm, and for this separation the capacitance is 31 pF. Calculate the work that must be done to pull the plates apart until their separation becomes 5.30 mm, if the charge on the plates remains constant. (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

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

Capacitors in combination: A 1.0-μF and a 2.0-μF capacitor are connected in series across a 3.0-V voltage source. (a) What is the charge on the 1.0-μF capacitor? (b) What is the voltage across the 2.0-μF capacitor

Dielectrics: A parallel-plate capacitor has a capacitance of 10 mF and 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. How much energy is now stored by the capacitor?