In the figure, $C=20\mu \mathrm{F}$. The switch has been in position a for a long time. At$t=0\mathrm{s}$ the switch is moved to position b. At what time will the voltmeter read$7.2\mathrm{V}?$

A capacitor is made from two hollow, coaxial, iron cylinders, one inside the other. The inner cylinder is negatively charged and the outer is positively charged; the magnitude of the charge on each is $10.0$ pC. The inner cylinder has radius $0.50$ mm, the outer one has radius $5.00$ mm, and the length of each cylinder is $18.0$ cm.

(a) What is the capacitance?

(b) What applied potential difference is necessary to produce these charges on the cylinders?

A spherical capacitor with a 1.0 mm gap between the shells has a capacitance of 100 pF. What are the diameters of the two spheres?

A coaxial cable, Fig. 24–35, consists of an inner cylindrical conducting wire of radius R_b surrounded by a dielectric insulator. Surrounding the dielectric insulator is an outer conductor of radius R_a, which is usually “grounded.” Determine an expression for the capacitance per unit length of a cable whose insulator has dielectric constant K.

A coaxial cable, Fig. 24–35, consists of an inner cylindrical conducting wire of radius R_b surrounded by a dielectric insulator. Surrounding the dielectric insulator is an outer conductor of radius Rₐ, which is usually “grounded.” For a given cable, R_b = 2.5 mm and R_a = 9.0 mm. The dielectric constant of the dielectric insulator is K = 3.2. Suppose that there is a potential of 1.0 kV between the inner conducting wire and the outer conducting sheath. Find the charge, and capacitance, per meter of the cable.

Find an expression for the capacitance of a spherical capacitor, consisting of concentric spherical shells of radii R₁ (inner shell) and R₂ (outer shell).

High-frequency signals are often transmitted along a coaxial cable, such as the one shown in FIGURE P26.68. For example, the cable TV hookup coming into your home is a coaxial cable. The signal is carried on a wire of radius R₁ while the outer conductor of radius R₂ is grounded (i.e., at V=0 V). An insulating material fills the space between them, and an insulating plastic coating goes around the outside. Evaluate the capacitance per meter of a cable having R₁=0.50 mm and R₂=3.0 mm.

A spherical capacitor contains a charge of $3.30$ nC when connected to a potential difference of $220$ V. If its plates are separated by vacuum and the inner radius of the outer shell is $4.00$ cm, calculate: (a) the capacitance; (b) the radius of the inner sphere; (c) the electric field just outside the surface of the inner sphere.

A capacitor is made from two hollow, coaxial, iron cylinders, one inside the other. The inner cylinder is negatively charged and the outer is positively charged; the magnitude of the charge on each is $10.0$ pC. The inner cylinder has radius $0.50$ mm, the outer one has radius $5.00$ mm, and the length of each cylinder is $18.0$ cm.

(a) What is the capacitance?

(b) What applied potential difference is necessary to produce these charges on the cylinders?