Question

Two capacitors, C119.0 F and C2 32.0 uf are connected in series, and a 9.0-V battery is connected across them (a) Find the equivalent capacitance, and the energy contained in this equivalent capacitor. equivalent capacitance total energy stored (b) Find the energy stored in each individual capacitor. energy stored in C1 energy stored in C2 Show that the sum of these two energies is the same as the energy found in part (a). Will this equality always be true, or does it depend on the number of capacitors and their capacitances? This answer has not been graded yet. (c) If the same capacitors were connected in parallel, what potential difference would be required across them so that the combination stores the same energy as in part (a)? which capacitor stores more energy in this situation, C1 or C2? C1 C2 Both C1 and C2 store the same amount of energy.

Answer 1

(a) Equivalent capacitance: implies C_eq = c_1 c_2/c_1 + c_2 = (19 times 32/19 + 32) mu F = 608/51 mu F = 11.92156863 mu F therefore C_eq = 11.92 mu F total energy stored: u = 1/2 C_eq v^2 implies u = 1/2 times (608/51 times 10^-6) times (9)^2 J = 4.828235294 times 10^-4 J therefore u approximatelyequalto 4.83 times 10^-4 J (b) charge through the power source: implies Q = C_eq v = (608/51 times 10^-6 times 9) c = 1.072941176 times 10^-4 c in series charge remains the same. \r\n energy stored in c_1: u_1 = Q^2/2 c_1 implies u_1 = (1.072641176 times 10^-4)^2/2 times 19 times 10^-6 J = 3.029480969 times 10^-4 J therefore u_1 approximatelyequalto 3.03 times 10^-4 J energy stored in C_2: u_2 = Q^2/2 c_1 implies u_2 = (1.072941176 times 10^-4)^2/2 times 32 times 10^-6 J = 1.798754325 times 10^-4 J therefore u_2 approximatelyequalto 1.80 times 10^-4 J