In the LC circuit in Figure 33.11, the inductance is L = 19.8 mH and the capacitance is C = 19.6 mF. At some moment, UB = UE= 17.5 mJ. a. What is the maximum charge stored by the capacitor? b. What is the maximum current in the circuit? c. At t = 0, the capacitor is fully charged. Write an expression for the charge stored by the capacitor as a function of lime. d. Write an expression for the current as a function of time.
(a)
The maximum charge stored by the capacitor.
Answer to Problem 23PQ
The maximum charge stored by the capacitor is
Explanation of Solution
Write the expression to calculate the total; energy.
Here,
Write the expression to calculate the maximum charge.
Here,
Conclusion:
Substitute
Substitute
Therefore, the maximum charge stored by the capacitor is
(b)
The maximum current in the circuit.
Answer to Problem 23PQ
The maximum current in the capacitor is
Explanation of Solution
Write the expression to calculate the maximum current.
Here,
Conclusion:
Substitute
Therefore, the maximum current in the capacitor is
(c)
The expression for the charge stored by the capacitor as function of time.
Answer to Problem 23PQ
The expression for the charge stored by the capacitor as function of time is
Explanation of Solution
Write the expression to calculate the angular frequency.
Here,
Write the expression for the charge stored by the capacitor as function of time
Here,
Conclusion:
Substitute
Substitute
Therefore, the expression for the charge stored by the capacitor as function of time is
(d)
The expression for the current as function of time.
Answer to Problem 23PQ
The expression for the current as function of time is
Explanation of Solution
Write the expression for current as function of time
Here,
Conclusion:
Substitute
Therefore, the expression for the current as function of time is
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Chapter 33 Solutions
Physics for Scientist and Engineers (Foundations And Connection; Volume I and II) LLF edition
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- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning