Exam 24: Capacitance and Dielectrics

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

A 15-μF air-filled capacitor is connected to a 50-V voltage source and becomes fully charged.The voltage source is then removed and a slab of dielectric that completely fills the space between the plates is inserted.The dielectric has a dielectric constant of 5.0. (a)What is the capacitance of the capacitor after the slab has been inserted? (b)What is the potential difference across the plates of the capacitor after the slab has been inserted?

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.

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)

A cylindrical capacitor is made of two thin-walled concentric cylinders.The inner cylinder has radius ,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?

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?

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?

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

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?

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?

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?

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

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?

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?

The network shown in the figure is assembled with uncharged capacitors X,Y,and Z,with ,and and open switches,S₁ and S₂.A potential difference V_ab = +120 V is applied between points a and b.After the network is assembled,switch S₁ is closed for a long time,but switch S₂ is kept open.Then switch S₁ is opened and switch S₂ is closed.What is the final voltage across capacitor X?

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?

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?

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?

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 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