Details SerCP8 16 P046 Two capacitors, C1-26.0 F and C2-35.0 F, are connected in

Question

Details SerCP8 16 P046 Two capacitors, C1-26.0 F and C2-35.0 F, are connected in series, and a 3.0 V battery is connected across them. (a) Find the equivalent capacitance, and the energy contained in this equivalent capacitor total energy stored Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. (b) Find the energy stored in each individual capacitor energy stored in C1·3846 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. 3 28 67 energy stored in C2 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. 3 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 th this does not depend on the number of capactators. This equality will always be true If the same capacitors were connected in parallel, what potential difference would be required across them so that the combination store§ the same 1 484 energy as in part (a)? v V Which capacitor stores more energy in this situation?

Explanation / Answer

Given,

C1 = 26 uF ; c2 = 35 uF ; V = 3 V

a)Ceq = C1C2/(C1 + C2)

Ceq = 26 x 35/(26 + 35) = 14.9 uF

Hnece, Ceq = 14.9 uF

U = 1/2 C V^2

U = 0.5 x 14.9 x 10^-6 x 3^2 = 67.1 x 10^-6 J

Hence, U = 67.1 x 10^-6 J = 6.71 x 10^-5 J

b)the same charge flows through the capacitors connected in series

q1 = q2 = CV = 14.9 x 3 = 44.7 uC

U1 = 1/2 q^2/C1 = 0.5 x (44.7 x 10^-6)^2/(26 x 10^-6) = 38.42 x 10^-6 J

U2 = 1/2 (44.7 x 10^-6)^2/(35 x 10^-6) = 28.5 x 10^-6 J

Hence, U1 = 38.4 x 10^-6 J ; U2 = 28.5 x 10^-6 J

c)Ceq = C1 + C2 = 26 + 35 = 61 uF

1/2 C V^2 = 67.1 x 10^-6

V = sqrt (2 x 67.1 x 10^-6/61 x 10^-6) = 1.48 V

Hence, V = 1.48 V

d)C2 will have more energy.

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