26. Capacitors & Dielectrics

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?

The current that charges a capacitor transfers energy that is stored in the capacitor's electric field. Consider a 2.0 μF capacitor, initially uncharged, that is storing energy at a constant 200 W rate. What is the capacitor voltage 2.0 μs after charging begins?

(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.

A parallel-plate air capacitor has a capacitance of 920 pF. The charge on each plate is 3.90 uC. (a) What is the potential difference between the plates? (b) If the charge is kept constant, what will be the potential difference if the plate separation is doubled? (c) How much work is required to double the separation?

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?

An air capacitor is made from two flat parallel plates $1.50$ mm apart. The magnitude of charge on each plate is $0.0180$ $\mu$C 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 $3.0\times {10}^6$ V/m.)

(d) When the charge is $0.0180$ $\mu$C, what total energy is stored?

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.

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?

How much work would be required to remove a metal sheet from between the plates of a capacitor (as in Problem 18a), assuming the battery remains connected so the voltage remains constant?

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?