3. Capacitance and dielectrics

3

8 The potential difference between the plates of a 3 μ F capacitor is 100 V. How much energy is stored in the capacitor? U = 15 mJ How many 1 μ F capacitors connected in parallel would it take to store a total charge of 1 mC if the potential difference of across each capacitor is 10 V? n = 100

C = 2.72 nF You are a laboratory assistant in a physics department that has budget problems. Your supervisor wants to construct cheap parallel-plate capacitors for use in introductory laboratory experiments. The design uses polyethylene, which has a dielectric constant of 2.3, between two sheets of aluminum foil. The area of each sheet of foil is 400 cm 2 and the thickness of the polyethylene is 0.3 mm. Find the capacitance of this arrangement ( ε 0 = 8.85 ✕ C 2 /N.m 2 ).

17 The positively charge plate of a parallel-plate capacitor has a charge equal to Q. When the space between the plates is evacuated of air, the electric field strength between the plates is 2.5 × 10 5 V/m. When the space is filled with a certain dielectric material, the field strength between the plates is reduced to 1.2 × 10 5 V/m. ( a ) What is the dielectric constant of the material? ( b ) If Q = 10 nC, what is the area of the plates? ( c ) What is the total induced bound charge on either face of the dielectric material? K = 2.1; A = 45 cm 2 ; Q ind = 5.2 nC;

18 A spherical capacitor contains a charge of 3.3 nC when connected to a potential difference of 230 V. If its plates are separated by vacuum and the inner radius of the outer shell is 4.6 cm. Calculate its capacitance and its inner radius. C = 14.3 pF, a = 3.4 cm A coaxial cable from a television has a diameter of the inner conductor and the diameter of the shield are 1 and 5 mm, respectively. The dielectric constant of the dielectric separating the two conductors is K = 3. Determine the capacitance per unit length of the cable. C/L = 0.1 nF/m