26. Capacitors & Dielectrics

Suppose in Fig. 24–27 that C₁ = C₃ = 8.0μF, C₂ = C₄ = 16μF, and Q₃ = 21μC. Determine the voltage across each capacitor.

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. Explain how both of these equations can be correct.

Suppose in Fig. 24–27 that C₁ = C₃ = 8.0μF, C₂ = C₄ = 16μF, and Q₃ = 21μC. Determine the voltage V_ba across the combination.

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.

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?

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.

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 in series?

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.

An isolated 5.0 μF parallel-plate capacitor has 4.0 mC of charge. An external force changes the distance between the electrodes until the capacitance is 2.0 μF. How much work is done by the external force?

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

A $5.80$-$\mu$F, parallel-plate, air capacitor has a plate separation of $5.00$ mm and is charged to a potential difference of $400$ V. Calculate the energy density in the region between the plates, in units of J/m³.

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?

A 2.0-cm-diameter parallel-plate capacitor with a spacing of 0.50 mm is charged to 200 V. What are (a) the total energy stored in the electric field and (b) the energy density?

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

You've built a device that uses the energy from a rapidly discharged capacitor to launch the capacitor straight up. One capacitor, with a mass of 3.5 g, is launched to a height of 1.6 m after having been charged to 100 V. What is its capacitance in μF?