Exam 24: Capacitance and Dielectrics

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?

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?

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?

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.)

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)

The electric field between square the plates of a parallel-plate capacitor has magnitude E.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 magnitude of the electric field between the plates is now equal to

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.

A charged capacitor stores energy U.Without connecting this capacitor to anything,dielectric having dielectric constant K is now inserted between the plates of the capacitor,completely filling the space between them.How much energy does the capacitor now store?

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

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.)

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?

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?

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

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?

The capacitance per unit length of a very long coaxial cable,made of two concentric cylinders,is 50 pF/m.What is the radius of the outer cylinder if the radius of the inner one is 1.0 mm? (k = 1/4πε₀ =

A parallel-plate capacitor,with air between the plates,is connected across a voltage source.This source establishes a potential difference between the plates by placing charge of magnitude on each plate.The space between the plates is then filled with a dielectric material,with a dielectric constant of 7.74.What must the magnitude of the charge on each capacitor plate now be,to produce the same potential difference between the plates as before?

Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m²,and the separation of the plates is 0.080 mm.An electric field of 5.3 × 10⁶ V/m is present between the plates.What is the energy density between the plates? (ε₀ = 8.85 × 10^-12 C²/N • m²)

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?

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

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?