For the system of four capacitors shown in the figure below, find the following.

Question

For the system of four capacitors shown in the figure below, find the following. (Use C_1 = 1.00 mu F, C_2 = 9.00 mu F, C_3 = 3.00 mu F, and C_4 = 5.00 mu F for the figure.) (a) the total energy stored in the system (b) the energy stored by each capacitor Your response differs from the correct answer by more than 100%. Your response differs from the correct answer by more than 100%. Your response differs from the correct answer by more than 10%. Double check your calculations. Your response differs from the correct answer by more than 10%. Double check your calculations. (c) Compare the sum of the answers in part (b) with your result to part (a) and explain your observation.

Explanation / Answer

Here , for the net capacitance

Cnet = 1 * 9/(1 + 9) + 3 * 5/(3 + 5)

Cnet = 2.78 uF

a) total energy stored in the system = 0.5 * C * V^2

total energy stored in the system = 0.50 * 2.78 *10^-6 * 90^2

total energy stored in the system = 0.0113 J = 11.3 mJ

b)

for the charge on C1 and C2

Q1 = Q2 = 1 * 9/(1 + 9) * 90 uC

Q1 = Q2 = 81 uC

energy stored in C1 = 0.50 * (81 *10^-6)^2/(1 *10^-6)

energy stored in C1 = 3.28 mJ

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energy stored in C2 = 0.50 * (81 *10^-6)^2/(9 *10^-6)

energy stored in C2 = 0.365 mJ

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for charge at C3 and C4

Q4 = Q3 = 3 * 5/(3 + 5) * 90 = 168.8 uC

energy stored in C3 = 0.50 * (168.8 *10^-6)^2/(3 *10^-6)

energy stored in C3 = 4.75 mJ

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energy stored in C4 = 0.50 * (168.8 *10^-6)^2/(5 *10^-6)

energy stored in C4 = 2.84 mJ

c)

sum of answers in b = 3.28 + 0.365 + 4.75 + 2.84

sum of answers in b = 11.23 mJ

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