Concept explainers
(a)
The expression for energy stored in the capacitor
(a)
Answer to Problem 83PQ
The expression for energy stored in the capacitor
Explanation of Solution
Write the expression to find the equivalent capacitance of the capacitors connected in parallel.
Here,
Write the expression charge on
Here,
Write the expression to find the voltage across the parallel combination.
Here,
Substitute equation (I), (II) in (III) to find the voltage across the parallel combination.
Write the equation for initial energy in the capacitor
Here,
Write the equation for final energy in the capacitor
Here,
Substitute
Conclusion:
Re-write the expression using equation (IV).
Therefore, the expression for energy stored in the capacitor
(b)
Show that
(b)
Answer to Problem 83PQ
Explanation of Solution
Write the expression for
Re-arrange the above expression to find the maximum point for
Substitute
The denominator has to be minimum to maximize the
Differentiate
Differentiate the above expression to find the points of maxima and minima
The second derivative gives a positive value when
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Chapter 27 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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