Concept explainers
In Figure P27.7, capacitor 1 (C1 = 20.0 μF) initially has a potential difference of 50.0 V and capacitor 2 (C2 = 5.00 μF) has none. The switches are then closed simultaneously. a. Find the final charge on each capacitor after a long time has passed. b. Calculate the percentage of the initial stored energy that was lost when the switches were closed.
FIGURE P27.7
(a)
The final charge on each capacitor.
Answer to Problem 7PQ
The final charges on each capacitor are
Explanation of Solution
Write the equation for the final charge in capacitor 1.
Here,
Write the equation for the final charge in capacitor 2.
Here,
Write the expression for the equivalent capacitance.
Here,
Write the expression for the new potential difference.
Here,
Write the expression for the initial charge.
Here,
Rewrite the expression for the final charge on capacitor 1.
Rewrite the expression for the final charge on capacitor 2.
Conclusion:
Substitute
Substitute
Thus, the final charges on each capacitor are
(b)
The percentage of the initial stored energy that was lost when the switches were closed.
Answer to Problem 7PQ
The percentage of the initial stored energy that was lost when the switches were closed is
Explanation of Solution
Write the equation for the fraction of loss of energy.
Here,
Write the expression for the initial energy,
Write the expression for the final energy,
Rewrite the expression for the fraction of loss of energy.
Conclusion:
Substitute
Thus, the percentage of the initial stored energy that was lost when the switches were closed is
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Chapter 27 Solutions
Student Solutions Manual For Katz's Physics For Scientists And Engineers: Foundations And Connections, Volume 1
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