Concept explainers
A parallel-plate capacitor is charged and then is disconnected from the battery. By what factor does the stored energy change when the plate separation is then doubled? (a) It becomes four times larger. (b) It becomes two times larger. (c) It stays the same. (d) It becomes one-half as large. (e) It becomes one-fourth as large.
Find the factor in which the energy stored in the capacitor changes when the distance between the plates is doubled.
Answer to Problem 1OQ
Option (B) It becomes two times larger.
Explanation of Solution
Write the equation for capacitance
Here,
If the distance between the plates is doubled then the above equation becomes,
As the charge remains constant the capacitance decreases by factor of 2.
Write the equation for potential energy stored.
Here,
Substitute equation II in III.
Therefore, the potential energy becomes doubles when the distance between the plates are doubled.
Conclusion:
From the above calculation the potential energy is two times the original. Thus, option (B) is correct.
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Chapter 20 Solutions
Principles of Physics: A Calculus-Based Text
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