According to UE=12C(V)2 (Eq. 27.3), a greater capacitance means more energy is stored by the capacitor, but according to UE = Q2/2C (Eq. 27.2), a greater capacitance means less energy is stored. How can both of these equations be correct?

Check Your Understanding When a cylindrical capacitor is given a charge of 0.500 nC, a potential difference of 20.0 V is measured between the cylinders, (a) What is the capacitance of this system? (b) If the cylinders are 1.0 m long, what is the ratio of their radii?

Check Your Understanding The radius of the outer sphere of a spherical capacitor is five times the radius of its inner shell. What are the dimensions of this capacitor if its capacitance is 5.00 pF?

Problem 26 27. (11) Consider three capacitors, of capacitance 3100 pF, 5800 pF, and 0.0100 F. What maximum and minimum capacitance can you form from these? How do you make the connection in each case? 28. (II) In Fig. 24-25, suppose C₁=C₂=C3=C4 = C. (a) Determine the equivalent capacitance between points a and b. (b) Determine the charge on each capacitor and the potential differ

(b) A student has three capacitors. Two of the capacitors have a capacitance of 4.0 µF and one has a capacitance of 8.0 µF. Draw labelled circuit diagrams, one in each case, to show how the three capacitors may be connected to give a total capacitance of: (i) 1.6uF (ii) 10µF.

(III) Two resistors and two uncharged capacitors are arranged as shown in Fig. 19–72. Then a potential difference of 24 V is applied across the combination as shown. (a) What is the potential at point a with switch S open? (Let V = 0 at the negative terminal of the source.) (b) What is the potential at point b with the switch open? (c) When the switch is closed, what is the final potential of point b? (d) How much + charge flows through 24 V 8.8 N 0.48 μF a S the switch S after it is closed? 4.4 2 0.36 μF FIGURE 19–72 Problem 58.

5. (II) What is the ratio of the voltage V, across capacitor C, in Fig. 19–65 to the voltage V2 across capacitor C,? C2 = 1.0 µF C1 = 1.0 μF 10 V . +C3 = 1.0 µF FIGURE 19-65 Problem 45.

(2)What happens to the capucitan ce of each of the two identical capacitors, each with an initial Capacitance Co, connected in Series when the Charge on each capacitor is doubled

*22 In Fig. 25-37, V = 10 V, C = 10 uF, and C = C, = 20 µF. Switch S is first thrown to the left side until capac- itor 1 reaches equilibrium. Then the switch is thrown to the right. When equilibrium is again reached, how much charge is on capacitor 1? Figure 25-37 Problem 22.