Figure P29.60 shows a simple RC circuit with a 2.50-μF capacitor, a 3.50-MΩ resistor, a 9.00-V emf, and a switch.
What are
- a. the charge on the capacitor,
- b. the current in the resistor,
- c. the rate at which the capacitor is storing energy, and
- d. the rate at which the battery is delivering energy exactly 7.50 s alter the switch is closed?
(a)
Find the charge on the capacitor.
Answer to Problem 60PQ
The charge on the capacitor at
Explanation of Solution
Write the expression for the initial charge on a capacitor as.
Here,
Write the expression for the charge in a series RC circuit as.
Substitute
Here,
Conclusion:
Substitute
Thus, the charge on the capacitor at
(b)
Find the current in the circuit.
Answer to Problem 60PQ
The current in the circuit at
Explanation of Solution
Write the expression for the initial current in the circuit as.
Here,
Write the expression for the current flowing in series RC circuit as.
Substitute
Here,
Conclusion:
Substitute
Thus, the current in the circuit at
(c)
Determine the rate at which the capacitor is storing energy.
Answer to Problem 60PQ
The rate of energy stored in the capacitor at
Explanation of Solution
Write the expression for the energy stored in a capacitor as.
Here,
Write the expression for the rate of storing energy in the capacitor as.
Substitute
Conclusion:
Substitute
Thus, the rate of energy stored in the capacitor at
(d)
The rate at which battery is delivering energy exactly
Answer to Problem 60PQ
The rate of energy delivered by battery at
Explanation of Solution
The rate of energy delivered by the battery is the power generated at the battery.
Write the expression for the rate of energy delivered by battery as.
Here,
Conclusion:
Substitute
Thus, the rate of energy delivered by battery at
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Chapter 29 Solutions
Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
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