26. Capacitors & Dielectrics

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?

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. 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. 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 across each capacitor.

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

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.

(II) Suppose the roller-coaster car in Fig. 8–33 passes point 1 with a speed of 1.30 m/s. If the average force of friction is equal to 0.23 of its weight, with what speed will it reach point 2? The distance traveled is 45.0 m.