Chapter 24, Problem 97GP

Paper has a dielectric constant K = 3.7 and a dielectric strength of 15 × 10⁶ V/m. Suppose that a typical sheet of paper has a thickness of 0.030 mm. You make a “homemade” capacitor by placing a sheet of 21 × 14 cm paper between two aluminum foil sheets (Fig. 24–41). The thickness of the aluminum foil is 0.040 mm. (a) What is the capacitance C₀ of your device? (b) About how much charge could you store on your capacitor before it would break down? (c) Show in a sketch how you could overlay sheets of paper and aluminum for a parallel combination. If you made 100 such capacitors, and connected the edges of the sheets in parallel so that you have a single large capacitor of capacitance 100 C₀, how thick would your new large capacitor be? (d) What is the maximum voltage you can apply to this 100 C₀ capacitor without breakdown?

FIGURE 24–41 Problem 97.