26. Capacitors & Dielectrics

A cardiac defibrillator can be modeled as a parallel plate capacitor. When it is charged to a voltage of 2 kV, it has a stored energy of 1 kJ. What is the capacitance of the defibrillator?

An air capacitor is made from two flat parallel plates 1.50 mm apart. The magnitude of charge on each plate is 0.0180 uC when the potential difference is 200 V. (a) What is the capacitance? (b) What is the area of each plate? (c) What maximum voltage can be applied without dielectric breakdown? (Dielectric breakdown for air occurs at an electric-field strength of 3.0x10^6 V/m.) (d) When the charge is 0.0180 uC, what total energy is stored?

(II) A 3500-pF air-gap capacitor is connected to an 18-V battery. If a piece of mica fills the space between the plates, how much charge will flow from the battery?

A huge 4.0-F capacitor has enough stored energy to heat 2.4 kg of water from 21°C to 95°C. What is the potential difference across the plates?

(II) The electric field near the Earth is about 150 N/C.

(a) What is the energy density near the Earth?

(b) Approximately how much electric energy is stored in the Earth’s electric field in the first 10 m above the Earth’s surface?

(c) Compare (by a ratio) the answer to part (b) with the daily output from a 2000-MW power station.

(II) How much energy is stored by the electric field between two square plates, 8.0 cm on a side, separated by a 1.5-mm air gap? The charges on the plates are equal and opposite and of magnitude 420 μC.

(II) How much energy must a 24-V battery expend to charge a 0.45-μF and a 0.20-μFcapacitor fully when they are placed

(a) in parallel,

(b) in series?

(c) How much charge flowed from the battery in each case?

(II) How much work would be required to remove a metal sheet from between the plates of a capacitor (as in Problem 18a), assuming:

(a) the battery remains connected so the voltage remains constant;

(II) A cylindrical capacitor (Example 24–2) has Rₐ = 3.5 mm and R₆.= 0.50 mm. The two conductors have a potential difference of 625 V, with the inner conductor at the higher potential.

(a) Calculate the energy stored in a 1.0-m length of the capacitor.

(II) Suppose the capacitor in Example 24–13 remains connected to the battery as the dielectric is removed. What will be the work required to remove the dielectric in this case?

(II) In Example 24–14 what percent of the stored energy is stored in the electric field in the dielectric?

A 2.1-μF capacitor is fully charged by a 9.0-V battery. The battery is then disconnected. The capacitor is not ideal and the charge slowly leaks out from the plates. The next day, the capacitor has lost half its stored energy. Calculate the amount of charge lost.

The power supply for a pulsed nitrogen laser has a 0.080-μF capacitor with a maximum voltage rating of 25 kV.

(a) Estimate how much energy could be stored in this capacitor.

(b) If 15% of this stored electrical energy is converted to light energy in a pulse that is 4.0 μs long, what is the power of the laser pulse?

The 300 μF capacitor in FIGURE P30.75 is initially charged to 100 V, the 1200 μF capacitor is uncharged, and the switches are both open.<IMAGE>

a. What is the maximum voltage to which you can charge the 1200 μF capacitor by the proper closing and opening of the two switches?

The potential energy stored in a capacitor can be written as either CV²/2 or Q²/2C. In the first case the energy is proportional to C; in the second case the energy is proportional to 1/C.

(a) Explain how both of these equations can be correct.

(b) When might you use the first equation and when might you use the second equation?

(II) Suppose in Fig. 24–27 that C₁ = C₃ = 8.0μF , C₂ = C₄ = 16μF, and Q₃ = 21μC. Determine

(b) the voltage across each capacitor, and

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(II) Suppose in Fig. 24–27 that C₁ = C₃ = 8.0μF , C₂ = C₄ = 16μF, and Q₃ = 21μC. Determine

(c) the voltage V₆ₐ across the combination.

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A parallel-plate capacitor has plate area A, plate separation 𝓍, and has a charge Q stored on its plates (Fig. 24–38).

(a) Determine the work required to double the plate separation to 2𝓍, assuming the charge remains constant at Q. (Hint: See Example 24–10.)

(b) Show that your answer is consistent with the change in energy stored by the capacitor.

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