Concept explainers
(a)
The expression for the time constant for this circuit.
(a)
Answer to Problem 74PQ
The expression for the time constant is
Explanation of Solution
Write the expression for the equivalent resistance for this circuit as.
Here,
Write the expression for the time constant for the circuit parameter.
Here,
Conclusion:
Substitute
Thus, the expression for the time constant is
(b)
The expression for the time when the capacitor has lost half of its charge.
(b)
Answer to Problem 74PQ
The expression for the time when the capacitor has lost half of its charge is
Explanation of Solution
Write the expression for the charge store in capacitor as.
Here,
Write the expression for the initial charge stored in capacitor as.
Here,
Write the expression for voltage across capacitor as a function of time as.
Here,
Conclusion:
Substitute
Substitute
Substitute
Thus, the expression for the time when the capacitor has lost half of its charge is
(c)
The expression for the current through the capacitor at that time.
(c)
Answer to Problem 74PQ
The expression for the current through the capacitor at that time is
Explanation of Solution
Write the expression current through the capacitor at time
Conclusion:
Substitute
Substitute
Thus, the expression for the current through the capacitor at that time is
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Chapter 29 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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