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 = 5.00 mu F, C_2 = 5.00 mu F, C_3 = 3.00 mu F, and C_4 = 3.00 mu F for the figure.) (a) the total energy stored in the system mJ (b) the energy stored by each capacitor C_1 mJ C_2 mJ C_3 mJ C_4 mJ (c) Compare the sum of the answers in part (b) with your result to part (a) and explain your observation. An electric heater carries a current of 17.5 A when operating at a voltage of 1.50 times 10^2 V. What is the resistance of the heater? Ohm

Explanation / Answer

1) for the net capacitance

Cnet = C1 * C2/(C1 + C2) + C3 * C4/(C3 + C4)

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

Cnet = 4 uF

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

total energy stored = 0.5 * 4 *10^-6 * 90^2

total energy stored = 0.0162 J = 16.2 mJ

b) for the energy stored in each capacitor

energy stored in C1 = 0.50 * (2.5 *10^-6 * 90)^2/(5 *10^-6)

energy stored in C1 = 0.00506 J = 5.06 mJ

energy stored in C2 = energy stored in C1

energy stored in C2 = 5.06 mJ

energy stored in C3 = 0.50 * (1.5 *10^-6 * 90)^2/(3 *10^-6)

energy stored in C3 = 0.00304 J

energy stored in C3 = 3.04 mJ

energy stored in C4 = 3.04 mJ

c)

the sum is equal

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