For the system of four capacitors shown in the figure below, find the following. (Use C, = 3.00 uF, C2 = 6.00 µF, C3 = 1.00 µF, and C = 5.00 µF for thefigure.)CzuFC,90.0 v(a) the total energy stored in the systemmJ(b) the energy stored by each capacitormJC2C3CAmJmJmJ

Given data: C1=3 μF=3×10-6 F C2=6 μF=6×10-6 F C3=1 μF=1×10-6 F C4=5 μF=5×10-6 F The potential is…

Answered: For the system of four capacitors shown…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter27: Capacitors And Batteries

Section: Chapter Questions

Problem 24PQ: An arrangement of capacitors is shown in Figure P27.23. a. If C = 9.70 105 F, what is the...

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Question

For the system of four capacitors shown in the figure below, find the following. (Use C, = 3.00 uF, C2 = 6.00 µF, C3 = 1.00 µF, and C = 5.00 µF for the
figure.)
CzuF
C,
90.0 v
(a) the total energy stored in the system
mJ
(b) the energy stored by each capacitor
mJ
C2
C3
CA
mJ
mJ
mJ

Expert Solution

Step 1

Given data:

$C_{1} = 3 μF = 3 \times 10^{- 6} F$
$C_{2} = 6 μF = 6 \times 10^{- 6} F$
$C_{3} = 1 μF = 1 \times 10^{- 6} F$
$C_{4} = 5 μF = 5 \times 10^{- 6} F$
The potential is $V = 90 V$

Calculating the equivalent capacitance across the circuit as follows:

$\begin{array}{rcl} C_{e q} & = & \frac{C_{1} C_{2}}{C_{1} + C_{2}} + \frac{C_{3} C_{4}}{C_{3} + C_{4}} \\ = & \frac{3 \times 6}{3 + 6} + \frac{1 \times 5}{1 + 5} \\ = & 2 + 0.83 \\ = & 2.83 μ F \\ = & 2.83 \times 10^{- 6} F \end{array}$

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