Concept explainers
For (he system of four capacitors shown in Figure P26.19. find (a) the total energy stored in the system and (b) the energy stored by each capacitor, (c) (Compare the sum of the answers in part (b) with your result to part (a) and explain your observation.
(a)
The energy stored in the system.
Answer to Problem 26.56AP
The energy stored in the system is
Explanation of Solution
Given info: The electric potential in the system is
The Figure of the circuit diagram is shown below.
Figure (1)
Since, the capacitors
Here,
Substitute
Thus, the equivalent capacitance of the first row is
Since, the capacitors
Here,
Substitute
Thus, the equivalent capacitance of the second row is
Since, the first and second rows are in parallel to each other. So, the equivalent capacitance of the system is,
Here,
Substitute
Thus, the equivalent capacitance of the system is
Formula to calculate the energy stored in the system is,
Here,
Substitute
Conclusion:
Therefore, the energy stored in the system is
(b)
The energy stored by each capacitor.
Answer to Problem 26.56AP
The energy stored in capacitors
Explanation of Solution
Given info: The electric potential in the system is
Since, the electric potential through each capacitor is same.
Formula to calculate the charge on the first row of capacitor is,
Here,
Substitute
Thus, the charge on the first row of capacitor is
Formula to calculate the energy stored is,
Here,
The energy stored in capacitor
Here,
Substitute
Thus, the energy stored in capacitor
The energy stored in capacitor
Here,
Substitute
Thus, the energy stored in capacitor
Formula to calculate the charge on the first row of capacitor is,
Here,
Substitute
Thus, the charge on the first row of capacitor is
The energy stored in capacitor
Here,
Substitute
Thus, the energy stored in capacitor
The energy stored in capacitor
Here,
Substitute
Thus, the energy stored in capacitor
Conclusion:
Therefore, the energy stored in capacitors
(c)
The comparison of the sum of the energy in part (b) with energy of part (a) and explain it.
Answer to Problem 26.56AP
The sum of the energy of par (b) is same as the energy in part (a).
Explanation of Solution
Given info: The electric potential in the system is
The sum of the energy of the part (b) is,
Substitute
The sum of the energy of par (b) is same as the energy in part (a).
Conclusion:
Therefore, the sum of the energy of par (b) is same as the energy in part (a).
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Chapter 26 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
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